Financial anomaly detection and risk early warning system based on Bayesian deep learning

Abstract

The invention discloses a financial anomaly detection and risk early warning system based on Bayesian deep learning, and relates to the technical field of deep learning, and the system comprises an information contribution weight analysis unit which is used for selecting financial indexes used for measuring financial robustness from historical data of a rolling window formed by a plurality of recent continuous report periods, and outputting the selected financial indexes to a database; for each financial index, normalizing the value of the mutual information into a weight; the pressure score construction unit is used for estimating the probability of occurrence of abnormity at the current period by using a logistic regression model which introduces nonlinear logic Student-t likelihood in the same rolling window; the risk early warning unit is used for calculating potential loss of monetization; and if the monetization potential loss exceeds a set loss threshold value, the system sends out early warning information. According to the method, accurate modeling and uncertainty quantification of the abnormal probability are realized, default opening and loss rate parameters are introduced, and the risk prediction result is monetized into potential loss for dynamic early warning triggering.

Description

Technical Field

[0001] The present invention relates to the field of deep learning technology, and in particular to a financial anomaly detection and risk warning system based on Bayesian deep learning. Background Art

[0002] With the increasing digitalization and intelligence of financial management and risk control, enterprises' financial anomaly detection and risk warning systems are gradually evolving from traditional static report review and rule-based judgment systems to dynamic risk identification systems driven by big data and supported by algorithms. Especially in capital-intensive, debt-driven enterprise scenarios, accurately identifying financial risks, assessing default probabilities, and estimating potential losses are not only the bottom line for the company's own operational security but also a crucial foundation for external assessments by financial institutions, investors, and regulators. In recent years, with the advancement of data collection capabilities and computing resources, numerous academic research and engineering applications have attempted to employ machine learning models for financial anomaly detection, such as support vector machines (SVMs), random forests (RFs), extreme gradient boosting (XGBoost), and neural networks (NNs). While these methods have improved the models' predictive accuracy and generalization capabilities to a certain extent, they have also exposed some significant challenges, primarily poor interpretability, unquantifiable uncertainty, and strong sensitivity to extreme cases.

[0003] For example, traditional supervised learning methods in the field of financial anomaly detection often use structured financial statement data (such as debt-to-asset ratios, cash flow ratios, and gross profit margins) as input features and historically annotated "abnormal / non-abnormal" labels as output variables. Classifiers are trained to create a "separation boundary" to determine the probability of anomalies at new observation points. However, in real-world business operations, the occurrence of abnormal conditions often does not follow a simple, linear boundary and may even exhibit significant nonlinear, time-lag, and heterogeneous risk characteristics, limiting the expressive power of single vector features. More critically, traditional classification models typically output a "whether abnormal" label or probability score, but lack a quantified measure of the confidence level of this probability. This makes it difficult for managers to distinguish whether the model's prediction is a "high-confidence risk warning" or a "low-confidence atypical prediction." Furthermore, due to the prevalence of complex confounding factors in financial data, such as extreme values ​​(such as one-time bad debt write-offs and large non-recurring gains and losses) and structural changes (such as changes in accounting estimates and mergers and acquisitions), traditional machine learning methods lack robustness and are prone to overfitting with small sample sizes, resulting in unstable risk assessment results.

[0004] To address these issues, some research has introduced Bayesian methods, such as Bayesian Logistic Regression and Bayesian Neural Networks, to introduce prior structure and uncertainty modeling capabilities. By treating model parameters as distributions rather than point estimates, Bayesian methods can naturally express the model's confidence in the input variables and output a posterior probability distribution. However, when applied to financial anomaly detection, existing Bayesian methods still face technical shortcomings, including unclear modeling structures, a lack of specialized mechanisms for expressing financial stress characteristics, arbitrary parameter priors, and insufficient sensitivity to anomalous samples. Specifically, existing techniques often use a unified vector to represent all indicators, ignoring the asymmetric contributions of different indicators in explaining risk. Parameter prior distributions are often manually set empirically and fail to adapt adaptively to indicator volatility. Furthermore, in reality, anomaly mechanisms often involve complex nonlinear dynamics such as convex acceleration, logarithmic saturation, and even risk reversal, which lack clear modeling paths in existing models. Summary of the Invention

[0005] To address these technical issues, we propose a financial anomaly detection and risk warning system based on Bayesian deep learning. This system employs multi-modal nonlinear transformations to construct financial stress signatures. Combining a Gaussian prior driven by historical fluctuations with a robust likelihood function, it achieves precise modeling of anomaly probabilities and quantifies uncertainty. Furthermore, by introducing default exposure and loss rate parameters, it monetizes risk prediction results into potential losses for dynamic early warning triggering. This system boasts clear structure, strong robustness, high interpretability, and strong decision-making operability, significantly improving the accuracy of financial risk identification and the practicality of management.

[0006] In order to achieve the above objects, the technical solution adopted by the present invention is:

[0007] The financial anomaly detection and risk warning system based on Bayesian deep learning includes: an information contribution weight analysis unit, which is used to select financial indicators for measuring financial stability from the historical data of a rolling window consisting of multiple recent consecutive reporting periods, and for each financial indicator, calculate its joint distribution with the historical records, and use mutual information to measure the degree of correlation between the two, and then normalize the value of the mutual information into a weight so that the sum of all weights is equal to 1; a stress score construction unit, which is used to perform z-score normalization on each financial indicator in the same rolling window to obtain a normalized result, take the absolute value of the normalized result respectively, and perform linear weighted summation with the weight to obtain a financial stress score; an anomaly detection and analysis unit, which is used to With the financial stress score as the sole independent variable, a logistic regression model introducing the nonlinear logistic Student-t likelihood is used to estimate the probability of an anomaly occurring in the current period. Both the baseline log-odds and the stress score coefficient of the logistic regression model are assigned zero-mean Gaussian priors. The prior variance of the stress score coefficient is determined by the inverse of the historical financial stress score to ensure scale consistency. The posterior distribution of these two coefficients is obtained over all historical financial stress scores using Hamiltonian Monte Carlo or variational inference methods. A risk warning unit is used to multiply the mean of the obtained posterior distribution by two measurable loss components to calculate the monetized potential loss. If the monetized potential loss exceeds the set loss threshold, the system issues a warning message.

[0008] Furthermore, the financial indicators used to measure financial soundness include: operating income growth rate G, operating cash flow ratio C, accrual profit quality Q and debt-to-asset ratio D.

[0009] Furthermore, the two measurable loss components are: Default Exposure EAD t and LGD t .

[0010] Furthermore, the weight ω M for:

[0011]

[0012] in, is a set of financial indicators; M′ and M represent the set of financial indicators respectively An element in ; I(M′) is the mutual information between the financial indicator M′ and the historical records; I(M) represents the mutual information between the financial indicator M and the historical records, which is:

[0013]

[0014] Where a represents the label value. When a is 1, it indicates an abnormal historical record, and when a is 0, it indicates a normal historical record. bins(M) represents the discrete bin set of the financial indicator M, which is divided by equal frequency or equal interval. p(a, m) represents the joint probability that the label value is a and the financial indicator M falls into bin m. p(a) is the marginal probability that the label value is a. p(m) is the marginal probability of bin m.

[0015] Furthermore, let the number of reporting periods be W, the current reporting period be t, and the value of t ranges from 1 to W; then the financial stress score F of the current reporting period is t for:

[0016]

[0017] Among them, Z M，t Represents the standardized result of the financial indicator M in the current reporting period; |·| is the absolute value operator; Z M，t =(M t -μ M ) / σ M ;M t is the value of the financial indicator M in the current reporting period; μ M is the mean value of the financial indicator M; σ M is the standard deviation of the financial indicator M.

[0018] Furthermore, the anomaly detection and analysis unit calculates the financial stress score F t Through four nonlinear transformations, we get the financial stress score F t The four morphological risk terms are: linear drift term T 1，t =F t ; Convex acceleration term T 2，t =F t 2 ; Logarithmic saturation term T 3，t =ln(1+F t ); decay inversion term The baseline log odds are The mean is 0 and the variance is Gaussian prior distribution of The pressure score coefficient is The mean is 0 and the variance is Gaussian prior distribution of ; i and k are both integer subscript indices; T k，i represents the financial stress score F in reporting period i i The morphological risk item; T k，i The mean of .

[0019] Furthermore, the anomaly detection and analysis unit defines the linear predictor η for the current reporting period t for:

[0020] η t =θ0+θ1T 1，t +θ2T 2，t +θ3T 3，t +θ4T 4，T ;

[0021] Calculate the abnormal probability P(a=1|η) in the current reporting period t )for:

[0022]

[0023] Define the likelihood function L as:

[0024]

[0025] Where v is the Student-t degree of freedom; scale s 2 is η t variance; is η t The mean of .

[0026] Furthermore, due to η t It is a nonlinear expression of the baseline logarithmic probability and the stress score coefficient. The anomaly detection and analysis unit solves the following formula through the Hamiltonian Monte Carlo or variational inference method to obtain the posterior distribution p(η t |a):

[0027]

[0028] Here, ∝ is the proportionality symbol.

[0029] Furthermore, the potential loss L in the current reporting period is monetized t for:

[0030] L t =[E(p(η t |a=1)]]×EAD t ×LGD t ;

[0031] Among them, p(η t |a=1) represents the posterior distribution when the label value is 1; E[p(η t |a=1)] represents p(η t |a=1)mean.

[0032] Compared with existing technologies, the present invention significantly improves the accuracy, stability, and practicality of financial risk identification. Compared to traditional anomaly detection methods that rely on linear models or black-box algorithms, this system constructs a multi-modal financial stress expression mechanism, extracting four risk profiles—linear, acceleration, saturation, and reversal—from raw indicators. This effectively characterizes the nonlinear response of stress changes to abnormal conditions. Furthermore, the model parameters utilize historical data-driven Gaussian priors, independent of empirical coefficients, enabling dynamic adaptation to the volatility of diverse financial characteristics, enhancing the model's adaptability and generalization performance. During the inference process, a robust likelihood function structure is introduced, providing a natural tolerance for extreme samples and significantly reducing the model's sensitivity to outliers. The system outputs a complete anomaly probability distribution using Bayesian posterior inference methods. Combined with the company's actual exposure and loss expectations, the system monetizes the anomaly risk, thereby extending the model's results from a probabilistic level to a manageable economic scale. Furthermore, the system can quantitatively analyze prediction confidence, enhancing the credibility and interpretability of warning outputs. This provides scientific, transparent, and traceable technical support for practical applications such as risk control decision-making, audit response, and capital assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of the system structure of the financial anomaly detection and risk warning system based on Bayesian deep learning proposed in this invention. DETAILED DESCRIPTION

[0034] The following description is intended to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are merely examples, and those skilled in the art may conceive of other obvious variations.

[0035] Reference Figure 1As shown, a financial anomaly detection and risk warning system based on Bayesian deep learning is provided, wherein the system comprises: an information contribution weight analysis unit, which is used to select financial indicators for measuring financial stability from the historical data of a rolling window consisting of multiple recent consecutive reporting periods, and for each financial indicator, calculates its joint distribution with the historical records, and uses mutual information to measure the degree of correlation between the two, and then normalizes the value of the mutual information into a weight so that the sum of all weights is equal to 1; a stress score construction unit, which is used to perform z-score normalization on each financial indicator in the same rolling window to obtain a normalized result, take the absolute value of the normalized result respectively, and perform linear weighted summation with the weight to obtain a financial stress score; an anomaly detection and analysis unit, which uses The probability of an anomaly occurring in the current period is estimated using a logistic regression model that incorporates the nonlinear logistic Student-t likelihood, with the financial stress score as the sole independent variable. Both the baseline log-odds and the stress score coefficient of the logistic regression model are assigned zero-mean Gaussian priors. The prior variance of the stress score coefficient is determined by the inverse of the historical financial stress score to ensure scale consistency. The posterior distributions of these two coefficients are derived over all historical financial stress scores using Hamiltonian Monte Carlo or variational inference methods. A risk warning unit is implemented to calculate the monetized potential loss by multiplying the mean of the posterior distribution by two measurable loss components. If the monetized potential loss exceeds a set loss threshold, the system issues a warning.

[0036] The information contribution weight analysis unit first relies on rolling window technology to select a series of financial data covering multiple recent consecutive reporting periods, ensuring the dynamic and timely nature of the analysis process. For each time point within the evaluation range, the system extracts a set of core financial indicators used to measure financial soundness, such as operating income growth rate, operating cash flow ratio, accrual quality, and debt-to-equity ratio. These indicators are derived from standard financial statements and are stable and interpretable. Within each rolling window, the system pairs these raw indicator values ​​with whether the company experienced financial anomalies during the same period. By statistically analyzing whether the company experienced events such as defaults, major accounting adjustments, abnormal audit opinions, or regulatory penalties during each reporting period, a binary anomaly label is constructed. After establishing the correspondence between the label and each financial indicator, the system then discretizes each indicator, typically dividing the continuous value into several intervals using equal frequency or equal interval methods to ensure that the indicator distribution has good resolution and sample support.

[0037] Based on the joint distribution of discretized indicator values ​​and anomaly labels, the information contribution weight analysis unit uses the mutual information criterion from information theory to measure the explanatory power of each financial indicator for anomaly events. Mutual information reflects the nonlinear correlation between financial indicators and anomaly labels. Without any model assumptions, it quantifies the average reduction in label uncertainty caused by an indicator, thereby measuring the information value of an indicator in anomaly identification. During the calculation process, the system estimates the joint probability distribution and marginal distribution separately and calculates the mutual information score for each indicator using the standard information gain formula. The mutual information scores of all indicators are normalized and ultimately converted into a weight vector that represents the relative importance of each indicator for anomaly identification. Normalization ensures that the weights sum to 1, ensuring a clear probabilistic meaning for subsequent weighting operations and preventing interference in model output caused by differences in dimensionality or absolute values. Because mutual information is non-negative and sensitive to nonlinear relationships, the system can objectively rank the explanatory power of each indicator without any subjective judgment or manual parameter adjustment.

[0038] In addition, the unit also has an automatic update mechanism. With the arrival of a new financial period, the rolling window automatically advances forward, old data is gradually eliminated, and new data is included in real time, ensuring that the system always evaluates the contribution of indicators based on the latest business operating conditions. At the implementation level, the system will recalculate the mutual information of each indicator after each round of rolling updates, and synchronously update the weight vector to adapt to the distribution shift that may occur as the financial data structure changes over time. This design enables the system to maintain robustness and sensitivity in long-term operation and avoid model aging problems caused by static parameter configuration. The final output weight will be directly passed to the stress score construction unit as the weighted coefficient of the linear combination of standardized financial indicators, so that the comprehensive score not only integrates multi-dimensional information, but also reflects the differential impact of each indicator in anomaly identification.

[0039] The stress score construction unit receives multiple core financial indicators that have been screened and weighted by mutual information, transmitted by the information contribution weight analysis unit, and performs unified scaling and comprehensive aggregation on these indicators. It ultimately outputs a financial stress score with clear numerical meaning, which is used to characterize the current financial stability of the enterprise at a specific point in time. To ensure comparability between indicators, the stress score construction unit first performs z-score normalization on each financial indicator within a rolling window consistent with the information contribution stage. The specific process is to subtract the mean of the indicator within the rolling window from each observation value, and then divide it by its sample standard deviation, thereby mapping the values ​​of all indicators to a standard normal space with zero mean and unit standard deviation. This standardization method can eliminate differences in the dimensions, scales, or numerical distributions of different indicators, ensuring that the subsequent weighting process does not dominate the overall score due to the original value of a certain indicator being too large or too small.

[0040] After normalization, the system takes the absolute value of the normalized results for all indicators. This ensures that both positive and negative deviations from the historical mean are considered potential sources of risk. For example, an operating income growth rate significantly above average may indicate abnormal expansion, while a growth rate significantly below average may indicate weak growth, both of which could pose financial risks. Therefore, this unit does not directly use the raw z-score values, but instead uses their absolute values ​​to capture the intensity rather than the direction of the risk. After obtaining all absolute z-scores, the stress score construction unit applies the indicator weights calculated based on mutual information in the previous unit and linearly weights each standardized indicator according to the normalized weights. The resulting financial stress score is essentially a single, dimensionless numerical variable that incorporates information from multiple financial indicators while retaining the weighted influence of each indicator on the ability to predict abnormal events. This score not only compresses the multidimensional input space and reduces model complexity, but also enables more stable convergence in subsequent modeling steps, and offers enhanced interpretability and stability.

[0041] The anomaly detection and analysis unit is the core link in achieving the critical logical transition from historical stress indicators to current anomaly probability estimation. Its role is to model the complex relationship between a company's historical abnormal performance and stress levels based on a constructed financial stress score, thereby inferring the company's current and future financial risks. Through a complete Bayesian inference system, it provides probabilistic interpretation and uncertainty quantification capabilities for decision outputs. This unit utilizes a nonlinear Bayesian logistic regression framework. Unlike traditional frequentist methods, its core concept is not to find optimal parameter point estimates. Instead, it treats all model parameters (including bias terms and weights of various nonlinear features) as random variables, introduces prior and likelihood information through the Bayesian formula, calculates their posterior distribution, and calculates anomaly probabilities and their credible intervals based on posterior sampling. This approach can fully incorporate data evidence while explicitly expressing model uncertainty, enabling the system to maintain stability and robustness in real-world business scenarios such as small sample sizes, high noise, or incomplete data.

[0042] The anomaly detection and analysis unit uses the financial stress score output by the stress score construction unit as the sole explanatory variable. However, to enhance the model's nonlinear expressiveness, the unit first applies a set of deterministic functional transformations to the stress score. These transformations include its original value (linear term), square value (reflecting the degree of extreme deviation), logarithmic value (reflecting the diminishing marginal effect), and exponential decay value (used to reflect the adverse effects that may result from policy or regulatory intervention under high pressure). Through this set of transformations, the system expands the single-dimensional stress score into a set of multidimensional scalar features. These features can characterize a richer nonlinear relationship between the stress score and the probability of an abnormal event, thereby avoiding the limitations of traditional linear models in expressing high-order risk response behaviors.

[0043] After establishing the model, the system assigns a zero-mean Gaussian prior to each coefficient. This means that, in the absence of any observed data, the model assumes that the feature's impact on the probability of anomalies is balanced and unbiased. However, unlike conventional Bayesian models, this system adopts a structured and adaptive approach to setting the prior variance. Specifically, for each transformed feature, the system automatically calculates its sample variance within a historical rolling window and uses its inverse as the prior variance for the corresponding coefficient. This design is based on the principle of scale registration in statistics: larger feature variance indicates greater uncertainty, and the corresponding coefficient prior should be tighter to prevent the model from inducing excessive bias on uncertain features. Conversely, features with smaller variance are more stable, allowing the model to assign looser priors to reflect their potential impact. Through this data-driven structured prior approach, the system not only automatically normalizes the scale of each feature but also enhances the physical plausibility and interpretability of the prior expression.

[0044] In constructing the likelihood function, the anomaly detection and analysis unit does not use the traditional logistic regression likelihood, but instead introduces a reweighted logistic likelihood structure based on the Student-t distribution. The purpose of this design is to improve the robustness of the model in the presence of extreme values ​​or outliers. In actual financial scenarios, some extreme indicators of a company often do not represent systemic risks, but may be one-time events, such as large asset impairments, non-recurring gains and losses, etc. If such events are not weighted, the model will be highly sensitive to extreme inputs, resulting in misjudgments of the model under normal stress ranges. The introduction of the Student-t weighted likelihood allows the weights of such extreme points in the likelihood function to be naturally compressed, thereby reducing their impact on parameter estimation without completely discarding their information, effectively improving the stability and generalization ability of the model in the case of poor data quality.

[0045] During the model inference phase, the anomaly detection and analysis unit constructs a Bayesian posteriori to achieve a probabilistic representation of each coefficient. The system supports two mainstream posterior solution technologies: Hamiltonian Monte Carlo (HMC) and black-box variational inference. The former constructs a random walk process with momentum, which enables the effective exploration of the main peak and tail area of ​​the posterior density in high-dimensional space, thereby obtaining high-quality posterior samples; the latter optimizes the variational parameters so that a parameterized distribution family can approximate the true posteriori, which is suitable for large sample and high-dimensional situations. These posterior samples contain probabilistic estimates of all possible values ​​of each parameter under the support of the current data, thus enabling the system to fully express model uncertainty and parameter sensitivity.

[0046] After obtaining the posterior samples, the anomaly detection and analysis unit enters the anomaly probability prediction stage. At this time, for any new stress score input value, the system will map it into a set of input features through the aforementioned feature transformation, and then substitute the model parameters corresponding to all posterior samples one by one, calculate the logistic regression output probability under it, and average the output of all samples as the final anomaly probability point estimate. At the same time, the variance of these sample probabilities can also be used to construct a confidence interval for judging the stability of risk prediction in subsequent decision-making processes. This mechanism not only outputs a single anomaly probability value, but also gives the confidence level of the model prediction itself, allowing risk managers to set different response strategies according to different tolerances, and achieve graded warnings and differentiated handling.

[0047] The risk warning unit receives the posterior anomaly probability estimate output by the anomaly detection and analysis unit. This probability is derived from the Bayesian logistic regression model by fitting historical samples to the current input stress score. It expresses the model's confidence that the company is currently in an anomaly state. However, a single probability value is not sufficient to directly constitute a risk warning signal. The actual loss consequences of the same anomaly probability can vary significantly among companies of different sizes, business structures, or financial characteristics. Therefore, the unit further introduces variables for the company's financial exposure and potential loss, coupling probability and consequences to construct a more realistic and actionable risk representation, namely the potential loss value. The construction of the potential loss value relies on three elements: the anomaly probability itself, which represents the likelihood of an adverse event; the company's current risk exposure level in terms of interest-bearing liabilities, accounts receivable, and financing exposure, which measures the potential impact if a risk event occurs; and the loss rate or recovery rate in the event of default or breach of trust, which reflects whether the loss can be mitigated through collateral, recovery, insurance, and other means. The product of the three factors constitutes the potential monetized loss in the expected sense, thus providing a unified measure of risk levels for different companies and at different points in time.

[0048] After completing the potential loss calculation, the risk warning unit does not directly determine whether to trigger an alert based on a fixed threshold, but instead builds a quantile trigger mechanism based on dynamic distribution. At each point in time, the system retains the potential loss sequence for the past period of time, forming a sliding window, calculates the loss distribution characteristics within the window, and sets quantiles such as 95% and 99% as trigger boundaries. When the potential loss at the current point in time exceeds the high quantile threshold of the historical sequence, it indicates that the current risk is at an abnormally extreme level in history, and the system issues an early warning signal. This design not only avoids the problem of poor adaptability of fixed thresholds to different companies and different cycles, but also ensures that the risk signal has a statistically significant basis. The system also allows the setting of quantile trigger strategies at different levels, supporting a step-by-step response mechanism from mild concern, moderate warning to high alert, to achieve seamless connection of risk monitoring from early warning to intervention.

[0049] In order to further enhance the stability and explanatory power of the early warning output, the risk warning unit will also analyze the posterior uncertainty of the anomaly probability. What the system receives from the anomaly detection and analysis unit is a sequence of estimated values ​​of the anomaly probability under posterior sampling, rather than a single value. Therefore, the unit can evaluate the variance or confidence interval of the loss estimate while calculating the potential loss. When the potential loss point estimate at a certain point in time is high, but its estimated interval is also very wide, the system can identify the signal as a low-confidence, high-risk event, and add uncertainty information when outputting the early warning signal, prompting managers that the risk signal still needs further verification or additional information. This mechanism greatly enhances the adaptability of the early warning system to complex business scenarios and prevents over-response due to insufficient confidence in the model itself.

[0050] Furthermore, the financial indicators used to measure financial soundness include: operating income growth rate G, operating cash flow ratio C, accrual profit quality Q and debt-to-asset ratio D.

[0051] The operating income growth rate (G) is the primary indicator for measuring a company's operational expansion and revenue changes. It reflects the changing trend of a company's core business activities over consecutive periods and is typically calculated as the ratio of the difference between the current period's core operating income and the previous period's core operating income to the previous period's core operating income. A positive value indicates revenue growth, while a negative value may indicate weak demand, declining market share, or intensified price competition. Excessively high or low revenue growth rates can represent potential risks. High growth can mask profit quality issues due to overexpansion, while persistently negative growth is directly associated with declining debt repayment capacity. Therefore, this indicator is treated as a two-way deviation-sensitive variable in the system, and its historical standard deviation and dispersion are used to assess its reliability as a stress signal. The operating cash flow ratio (C) measures a company's ability to generate cash flow from its core operations. It is typically defined as the ratio of net operating cash flow to operating income and is a key parameter for assessing the value of a company's profits and its ability to meet short-term debt repayment obligations. Compared to accounting profit, cash flow provides a more accurate reflection of a company's liquidity position and therefore has a higher warning value in risk identification. If a company's operating cash flow remains negative despite a reported profit, it's likely that its revenue will be difficult to monetize, potentially indicating profit manipulation or credit risk. This metric serves as a key measure of a company's true cash flow and is also used in model training to improve the sensitivity of risk identification for cash-dominated companies.

[0052] Accrual quality (Q) assesses the proportion of non-cash items in a company's profit structure. It is typically measured as the difference between net profit and net operating cash flow as a percentage of net profit. A higher accrual quality (Q) indicates a greater proportion of non-cash items in a company's earnings, potentially reflecting profit inflation caused by significant accounts receivable, bad debt write-backs, inventory adjustments, or other changes in accounting estimates, reflecting poor profit sustainability. In anomaly identification models, companies with high accrual quality typically have significantly higher anomaly probabilities. The system normalizes this metric and combines historical mutual information to assess its contribution to anomaly labels, ensuring that high-risk profit structures are explicitly captured in the stress score. The debt-to-asset ratio (D) measures the proportion of a company's total assets comprised of liabilities and is a key indicator for assessing the soundness of its capital structure and whether its financial leverage is excessive. While a high debt ratio can improve capital efficiency, it also increases the likelihood of a liquidity crisis during operating fluctuations or rising market interest rates. Especially in an economic environment with high interest rates and high volatility, an increase in the debt-to-asset ratio is often accompanied by an increase in credit risk, debt default or liquidity crisis. Therefore, in the judgment of systemic risk, the debt-to-asset ratio serves as a basic stability signal and forms a complementary dimension with other indicators.

[0053] Furthermore, the two measurable loss components are: Default Exposure EAD t and LGD t .

[0054] Default exposure amount EAD t It refers to the total amount of risk exposure that an enterprise may face when an abnormality occurs during the reporting period t. It usually corresponds to the current balance of interest-bearing liabilities, unexpired short-term financing, guarantee obligations, or the principal size of other contingent liabilities. It is the total amount of funds most directly affected when a risk event is triggered. Different from the total liabilities or loan balance in traditional financial indicators, EAD t It emphasizes the actual economic exposure under risk exposure. Its data comes from business system data such as the company's balance sheet notes, bank credit statements, commercial acceptance bill balances, and credit guarantee contracts. The core function of this indicator is to measure the "principal range that may be affected after the risk occurs." The larger the value, the greater the financial risk that the company or its affiliated financial institutions may face once the anomaly is triggered. To ensure the real-time prediction of the model, the system uses a rolling update mechanism for EAD. t It is updated regularly to ensure that it always reflects the company's latest debt and exposure structure.

[0055] Loss Given Default (LGD) t It is used to measure the proportion of assets that can actually be recovered or the extent of losses after a financial default or credit collapse. It is defined as the "loss ratio of the outstanding portion", that is, in the event of a default, what proportion of the original exposure amount will result in a final net loss. t The value of LGD depends on many factors, including but not limited to asset guarantee status, collateral value, industry default recovery history, liquidation efficiency, legal recovery cycle, etc. t The value range is between 0 and 1. The higher the value, the less assets the relevant entities can recover once the enterprise defaults, and the more serious the loss of the financial system. t When setting up a model, you can use a customized model or refer to the regulatory or industry standards. For example, you can use the standard LGD value for risk exposure of different asset classes in the Basel Accord, or use the default and repayment data of similar companies in recent years as the estimation basis. If there is sufficient historical data support, the system also allows LGD to be used. t As a time-dynamic function, it is dynamically estimated based on past market conditions and corporate default recovery rates to improve the timeliness and accuracy of loss valuation.

[0056] In the risk warning unit, these two loss components and the abnormal probability estimate output by the Bayesian anomaly detection module together constitute the valuation framework of potential losses. The system uses abnormal probability as the marginal possibility of the risk event occurring. t As the principal exposure under the influence of this event, LGD tAs the proportional factor of the principal loss, the three are multiplied period by period to obtain the expected potential loss in terms of monetization. This structure not only conforms to the basic logic of the classic risk value assessment model, but also provides a clear input variable for the subsequent dynamic quantile warning based on historical distribution. Compared with the traditional method of triggering warnings based on abnormal probability itself, the introduction of EAD t With LGD t The two measurable loss factors with financial business background make the system warning more business-relevant and interpretable, and can meet the usage requirements at different levels, from regulatory reporting to actual risk disposal.

[0057] Furthermore, the weight ω M for:

[0058]

[0059] in, is a set of financial indicators; M′ and M represent the set of financial indicators respectively An element in ; I(M′) is the mutual information between the financial indicator M′ and the historical records; I(M) represents the mutual information between the financial indicator M and the historical records, which is:

[0060]

[0061] Where a represents the label value. When a is 1, it indicates an abnormal historical record, and when a is 0, it indicates a normal historical record. bins(M) represents the discrete bin set of the financial indicator M, which is divided by equal frequency or equal interval. p(a, m) represents the joint probability that the label value is a and the financial indicator M falls into bin m. p(a) is the marginal probability that the label value is a. p(m) is the marginal probability of bin m.

[0062] In the financial anomaly detection and risk warning system based on Bayesian deep learning of the present invention, the information contribution weight analysis unit strictly characterizes the information dependency relationship between financial indicators and anomaly labels through the mutual information theory in Shannon's information theory, thereby providing a completely data-driven and statistically significant weight coefficient for the subsequent stress score construction; the essence of this process is to use mutual information to measure the "average reduction in the uncertainty of the abnormal state after observing the indicator", and then normalize the mutual information of each indicator to obtain the weight ω M , to ensure that the influence of different indicators in the comprehensive model reflects their true risk interpretation ability rather than their dimensions or value ranges. Specifically, for the indicator set The system first collects historical samples from the most recent rolling window and discretizes each continuous indicator into a number of bins (M) using equal intervals or equal frequencies. This step, through nonparametric means, eliminates prior assumptions about the indicator's distribution shape and avoids the boundary bias of kernel density estimation in the case of small samples. After discretization, the system performs a joint frequency count of the two events within the window: "the indicator is in the mth bin" and "the label has the value a". This is divided by the window length to obtain the joint probability p(a, m). Simultaneously, p(a) and p(m) are obtained through marginal summation.

[0063] Based on these probabilities, the mutual information is calculated as Its mathematical meaning can be rewritten as I(M)=H(A)-H(A|M), where H(A)=-∑ a p(a)ln p(a) is the Shannon entropy of the abnormal label, which measures the uncertainty of the label when no financial indicator information is known; and the conditional entropy H(A|M)=-∑ m p(m)∑ a p(a|m)lnp(a|m) represents the uncertainty remaining in the label after observing the binning information of indicator M. The difference between the two is the amount of uncertainty reduction that indicator M can bring, that is, the "information value" of the indicator for identifying anomalies. If the indicator and the label are completely independent, then p(a, m) = p(a)p(m) will result in zero mutual information, and the system will naturally assign the indicator a weight of zero; if the indicator has any form of statistical dependence on the abnormal label, whether it is linear, nonlinear or threshold-type relationship, it can be reflected as a positive value in the mutual information, increasing the weight of the indicator. In order to map the mutual information of each indicator to the same weight space, the system uses the normalization formula The denominator ∑ M′ I(M′) represents the total amount of information contributed by the entire indicator set to the abnormal label, and normalization ensures that ∑ M ω M =1, so that the weight has both probabilistic meaning and is easy to interpret in subsequent linear combinations.

[0064] It is worth noting that this weight is not a simple ratio, but an accurate description of the "information contribution share" of each indicator in explaining abnormal risk: for example, if the debt-to-asset ratio shows significantly high mutual information in historical data, the system will automatically increase its coefficient in the comprehensive stress score without the need for manual threshold setting or subjective adjustment. After the weight calculation is completed, the stress score construction unit performs z-score normalization (M t -μ M ) / σ M , and then take the absolute value to capture the risk of two-way deviation, and finally use ω MPerform linear weighted aggregation to obtain a single scalar financial stress score F t =∑ M ω M |Z M，t |. Due to Z M，t The sum is 1, and each Z M，t is a dimensionless quantity, F t The scale itself remains interpretable: when one of the indicators deviates significantly and its weight is high, F t The weight generation mechanism is dynamically updated within the rolling window. When new data arrives, the joint probability and marginal probability are re-estimated, and the mutual information is recalculated in real time, thereby automatically capturing changes in the financial structure and market environment, so that the stress score reflects the latest risk situation at any time. M The statistical properties of are also reflected in its two dimensions of "additivity" and "decomposability": on the one hand, the mutual information of multiple indicators can be decomposed through the chain rule, ensuring that even if new financial indicators are introduced or old indicators are eliminated in the future, the weight system can still be smoothly reset; on the other hand, if stratified statistics are performed on corporate groups or industries, the mutual information and weights can be calculated independently and their distributions can be compared, thus providing a quantitative basis for identifying systemic risks at the macro-regulatory level. More importantly, there is a natural fit between mutual information and Bayesian posterior updating: in the subsequent Bayesian logistic regression, the prior variance of the stress score coefficient depends on F t The historical variance of ω M Combined with the volatility of each indicator, this chained design, driven by information theory and culminating in a Bayesian prior, creates a seamless closed loop from raw data to probabilistic inference. In summary, the aforementioned weighting formula, built on entropy and mutual information and implemented using normalized probability, achieves a quantitative allocation of the information value of multidimensional financial indicators. This not only meets the stringent objectivity and traceability requirements of practical financial risk management, but also fully leverages the advantages of nonlinear dependency detection, providing the most informative input variables for the system's subsequent Bayesian anomaly probability estimation and loss monetization.

[0065] Furthermore, let the number of reporting periods be W, the current reporting period be t, and the value of t ranges from 1 to W; then the financial stress score F of the current reporting period is t for:

[0066]

[0067] Among them, Z M，t Represents the standardized result of the financial indicator M in the current reporting period; |·| is the absolute value operator; Z M，t =(M t -μ M ) / σ M ;M tis the value of the financial indicator M in the current reporting period; μ M is the mean value of the financial indicator M; σ M is the standard deviation of the financial indicator M.

[0068] Furthermore, the anomaly detection and analysis unit calculates the financial stress score F t Through four nonlinear transformations, we get the financial stress score F t The four morphological risk terms are: linear drift term T 1，t =F t ; Convex acceleration term Logarithmic saturation term T 3，t =ln(1+F t ); decay inversion term The baseline log odds are The mean is 0 and the variance is Gaussian prior distribution of The pressure score coefficient is The mean is 0 and the variance is Gaussian prior distribution of ; i and k are both integer subscript indices; T k，i represents the financial stress score F in reporting period i i The morphological risk item; T k，i The mean of .

[0069] Furthermore, the anomaly detection and analysis unit defines the linear predictor η for the current reporting period t for:

[0070] η t =θ0+θ1T 1，t +θ2T 2，t +θ3T 3，t +θ4T 4，t ;

[0071] Calculate the abnormal probability P(a=1|η) in the current reporting period t )for:

[0072]

[0073] Define the likelihood function L as:

[0074]

[0075] Where v is the Student-t degree of freedom; scale s 2 is η t variance; is η t The mean of .

[0076] In the financial anomaly detection and risk warning system based on Bayesian deep learning, the anomaly detection and analysis unit bears the core responsibility of compressing high-dimensional, multi-scale financial information into actionable risk signals. The unit first receives the scalar financial stress score F output by the stress score construction unit. t , and then a set of deterministic nonlinear transformations is used to expand this scalar into four non-redundant scalar features, namely T 1，t =F t 、 T 3，t =ln=(1+F t ), The four features simulate the linear accumulation effect, the convex extreme acceleration effect, the logarithmic saturation effect, and the possible reversal effect in the high-pressure area. By introducing these four features, the system is a single input variable F t It gives sufficient nonlinear expression capabilities, while still keeping each feature as a directly interpretable scalar at the modeling level, which is in line with the original design intention of the system to "avoid the use of vectors and black box parameters". After completing the feature generation, the model constructs the linear predictor η with the intercept θ0 and the four feature coefficients θ1~θ4 t =θ0+θ1T 1，t +θ2T 2，t +θ3T 3，t +θ4T 4，t ;

[0077] Where θ0 describes the base logarithmic probability that an enterprise may still have an abnormality in an idealized scenario with zero financial pressure, while θ1 to θ4 capture the marginal contribution of the four types of nonlinear action modes to the abnormal risk. The value of the linear predictor is obtained through the logistic function

[0078]

[0079] is mapped to the interval [0, 1], and the conditional probability of an abnormal financial event occurring in the enterprise during the reporting period t is obtained. The monotonically increasing property of the logistic function ensures that the predicted probability is positively correlated with the comprehensive pressure and does not cross the boundary; its symmetry is in η t =0 provides a probability benchmark of 0.5, so that the model makes a judgment on the "neutral pressure" scenario without bias in any direction.

[0080] However, traditional logistic regression often encounters problems such as unstable parameter estimation and over-sensitivity to abnormal samples when facing financial data with high noise, many extreme points, and high degree of outliers. To overcome the above drawbacks, this system introduces the Student-t weighting mechanism at the likelihood level and defines the likelihood function

[0081]

[0082] Among them A t ∈{0,1} is the historical label, v is the Student-t degree of freedom, s 2 is η t The unbiased sample variance of the series within the rolling window, and is its sample mean. The first part of the likelihood Same as ordinary logistic regression, it measures the logarithmic probability of the observed label appearing under given parameters; the second part is the tail decay term of the Student-t distribution, and its denominator is In terms of probability density, the corresponding t The heavy tail penalty for deviation from the mean. By multiplying this factor, it is equivalent to reweighting the contribution of each observation sample according to its logarithmic density under the Student-t distribution: when η t When the outliers are far away from the mean and at the extreme tail, the weight is significantly weakened, reducing the impact of outliers on the overall parameter estimation; when η t In the central interval, the weight approaches unity, fully utilizing the sample information. Simultaneously, adjusting the entire logistic likelihood exponentiation to 1 / v further balances the trade-off between Student-t tail reduction and strict log-likelihood in the central region. The degree of freedom v determines the thickness of the tail: smaller v results in a thicker tail, and the model is more tolerant to extreme stress situations; larger v results in a thinner tail, and the model gradually degenerates into a standard log-likelihood form. The system allows for a fixed v in the range of 3 to 7, maintaining sufficient robustness without weakening the tail weight to the point of completely ignoring extreme samples.

[0083] Scale parameter s 2 and mean The introduction of η ensures that the weighted process is adaptive: t If the overall fluctuation is large, its s 2 Increase so that the tail samples will not be judged as outliers due to a slightly larger deviation; η t If the fluctuation is small, then s 2 As the variance decreases, the model will more strictly penalize deviations. This automatic scaling mechanism makes Student-t weighting equally suitable for risk fluctuations across different companies and cycles, maintaining the system's robustness across entities and cycles. To complement this, the system introduces zero-mean Gaussian priors for parameters θ1–θ4, whose variances are set according to the inverse of the variance of the corresponding feature in the historical window. This tightens the prior for large feature fluctuations and relaxes it for small feature fluctuations, further suppressing the risk of overfitting. The introduction of priors not only provides a central convergence direction for the parameters but also provides a complete probabilistic graphical model structure for subsequent Hamiltonian Monte Carlo sampling.

[0084] In the posterior inference stage, the system multiplies the likelihood and prior to obtain the joint posterior density, and generates high-quality samples in the parameter space through the Hamiltonian Monte Carlo algorithm. HMC uses a physical momentum-assisted method to explore high-dimensional space along the negative logarithmic posterior gradient direction, avoiding random walk behavior and greatly improving convergence efficiency and sample validity; Student-t weighting is reflected in the gradient calculation as additional derivatives of the tail attenuation term, which have an impact on η t The samples at the tail automatically reduce the step size to further stabilize the sampling trajectory. After completing the a priori sampling, the system (s) Calculate the new pressure observation The corresponding four eigenvalues ​​are brought into Formula, and then obtain the abnormal probability through the logistic function The point estimate is obtained by averaging all S sampling probabilities and the uncertainty interval is obtained by taking the variance of the sampling probability. This point estimate is then compared with the default exposure amount. and loss given default The multiplication generates the potential loss value, and the variance information is passed to the risk warning unit for scoring confidence and controlling the false alarm rate.

[0085] It can be seen that the linear predictor η t The combination with Student-t weighted likelihood plays multiple roles in the model: on the one hand, η t It provides a channel for mapping nonlinear stress characteristics into logarithmic probabilities, making the final anomaly probability intuitively interpretable. Furthermore, the Student-t likelihood imbues logistic regression with heavy-tail robustness, ensuring that the model is not distorted in the face of extreme financial shocks or one-time special events, while also not completely discarding extreme information. Furthermore, by multiplying the overall likelihood exponent by 1 / v, the model is mathematically equivalent to applying a gamma variable, which can be interpreted as an implicit weight, to each observation. This can be viewed as the result of hierarchical modeling of label noise variance, consistent with the concept of Bayesian hierarchical models, thereby maintaining conjugation-friendliness and inference tractability in the overall probability map. By integrating all these mechanisms, the anomaly detection and analysis unit implements a continuous probabilistic chain from stress score to anomaly probability to potential loss. Data-driven robustness is introduced at each level, ensuring that the system maintains predictive stability and interpretable transparency in financial scenarios with high noise, asymmetric, and extreme distributions, laying a solid foundation for the final risk warning output.

[0086] Furthermore, due to η t It is a nonlinear expression of the baseline logarithmic probability and the stress score coefficient. The anomaly detection and analysis unit solves the following formula through the Hamiltonian Monte Carlo or variational inference method to obtain the posterior distribution p(η t |a):

[0087]

[0088] Here, ∝ is the proportionality symbol.

[0089] In the entire financial anomaly detection and risk warning system based on Bayesian deep learning, the goal of the anomaly detection and analysis unit is to characterize the credibility of anomalies occurring in a company under a given financial pressure level in a probabilistic form. The core of this credibility depends on the linear predictor η t The posterior distribution p(η t |a) is an accurate inference. Because η t =θ0+θ1T 1，t +θ2T 2，t +θ3T 3，t +θ4T 4，t The baseline log-odds ratio is coupled with four types of nonlinear characteristic coefficients, and T k，t This is a nonlinear transformation of the financial stress score, so η t The statistical behavior of not only reflects the stress level of the current reporting period, but also inherits the uncertainty of all parameters under the constraints of historical information. In the Bayesian framework, to obtain η t The posterior distribution of , must combine the "evidence given by the data to the model" and the "prior belief in the parameters" into a joint density, where ∝ indicates that the right side is missing with η t The likelihood term L in the left half of the formula has been given above, which combines the label likelihood of logistic regression and the Student-t heavy-tail weight: the standard logistic part takes each label A t It is considered as a conditionally independent Bernoulli trial, and its success probability is given by the logistic function σ(η t )=1 / (1+exp(-η t )) is given; the Student-t part is the η at the tail t The introduction of additional attenuation reduces the contribution of outliers to the total likelihood, thereby providing robust protection for extreme samples. The sum of the five terms in the right half of the exponential corresponds to the Gaussian prior logarithmic density of the five coefficients: the prior variance of θ0 is fixed to This reflects the initial uncertainty of the baseline log-probability, while the prior variances of θ1–θ4 are set to the inverse of the sample variance of each feature in the historical window. This allows features with large fluctuations to be subject to stricter prior contraction, while features with small fluctuations are given more freedom to explore. This structure naturally matches the prior with the data variance, avoiding artificial empirical coefficients and ensuring numerical stability.

[0090] In order to obtain an operational posterior distribution from the above unnormalized density, the system introduces two parallel inference paths: one is Hamiltonian Monte Carlo (HMC) sampling, and the other is black-box variational inference (BBVI). HMC regards the parameter vector θ = (θ0, ..., θ4) as a particle moving in a potential field. The potential function takes the negative logarithmic posterior, and the momentum variable usually takes the standard normal distribution. By simulating "force motion" in the parameter space, HMC can quickly cross the low-probability area directly to the high-probability area, avoiding the slow convergence problem of simple random walks; backpropagation technology can efficiently calculate the gradient of likelihood and prior, where the gradient of the Student-t weight is scaled at the tail, which will allow the sampling process to use smaller step sizes near extreme samples and larger step sizes in the central area, thereby improving the overall sample effectiveness. After a certain number of warm-up iterations, the large number of samples generated by HMC will approximately obey the true posterior, and the system will perform a generalized optimization of η based on these samples. t Reconstruction: For each sample instance θ (s) ,calculate And stacked into a sample set, and then given in the form of kernel density estimation or simple empirical distribution p(η t |a) is a numerical expression.

[0091] BBVI adopts an optimization approach: select a parameterized distribution family q φ (θ) (e.g., a fully factored Gaussian with adjustable mean-variance or a low-rank covariance Gaussian combination), by maximizing the variational lower bound ELBO so that q φ Close to the true posterior. When the likelihood contains Student-t weights and the prior contains feature variance scaling, the gradient of ELBO can be obtained by Stokes estimation with reparameterization or black box scorefunction approximation, and then φ is updated by stochastic gradient descent. When ELBO converges, q φ This is the approximate distribution of the posterior, and the system can directly sample from this distribution to generate θ (s) , and similarly reconstruct Compared with HMC, BBVI has better scalability in large-scale data or high-dimensional parameter scenarios, while HMC has more advantages in low-dimensional precise inference; therefore, the system can adaptively switch between the two based on computing resources and data volume, ensuring that reliable posteriors can be obtained regardless of the number of samples.

[0092] Obtain η t After sampling, the system regards these samples as η t The empirical posterior distribution of , which is no longer restricted by the prior form and likelihood shape, directly reflects the probability state of "what logarithmic probability level of current enterprise pressure is under the combined effect of historical data and priors". t and abnormal probability P(a=1|η t )=σ(ηt ) Through one-to-one correspondence of logical functions, the system can Direct transformation to obtain abnormal probability sample p (s) , and then describe future risks in terms of probability: point estimates take the sample mean The interval estimation takes the high density interval or sample standard deviation. Furthermore, the system compares each probability sample with the current default exposure amount EAD. t and LGD t Perform multiplication to generate potential loss samples In the risk early warning unit, these Sorting, quantile pruning and rolling aggregation are performed to finally form an operational threshold comparison and alarm triggering mechanism. Through this chain, η t The complete shape of the posterior distribution - including the mean, variance and even the tail thickness - will be passed on to the loss distribution at the actual business level, so that the early warning is no longer a single-point probability threshold, but is driven by the historical quantiles and confidence levels of the entire loss distribution, guiding managers to take graded measures for different levels of uncertainty.

[0093] It should be emphasized that the exponential harmonic term in the posterior density formula not only regularizes the parameter θ itself, but also k ) tightly couples the feature variance with the parameter prior. When a feature fluctuates drastically in history, Var(T k ) is larger, the index It will decay quickly, forcing the coefficient of the feature to converge to near zero, ensuring that the model does not over-use the noise signal; on the contrary, when the feature fluctuation is stable and the information contribution is high, the prior variance is amplified, allowing θ k This data-driven prior structure, working together with the Student-t likelihood, improves robustness while retaining the ability to capture valid nonlinear patterns, fully demonstrating the advantages of Bayesian learning in high-noise financial environments.

[0094] In summary, by multiplying the likelihood L with the Gaussian prior density and numerically solving the unnormalized density using HMC or BBVI, the anomaly detection and analysis unit can generate a log-likelihood posterior from the complex financial stress signal, and then map it to the anomaly probability posterior, thereby quantifying the uncertainty distribution of potential losses. This is represented by η t The posterior-driven risk probability chain enables the system to provide sensitive and robust early warning signals in the form of probability-loss coupling when faced with events such as extreme market disturbances, changes in accounting estimates, or one-time cash fluctuations, truly realizing a risk quantification closed loop from data-driven dynamic analysis to executable decision-making.

[0095] Furthermore, the potential loss L in the current reporting period is monetizedt for:

[0096] L t =[E[p(η t |a=1)]]×EAD t ×LGD t ;

[0097] Among them, p(η t |a=1) represents the posterior distribution when the label value is 1; E[p(η t |a=1)] represents p(η t |a=1)mean.

[0098] p(η t |a=1) means that when the label value is 1, that is, the enterprise is in an abnormal state, the linear predictor η t The posterior distribution established, and E[p(η t |a=1)] is the mathematical expectation corresponding to the posterior distribution, i.e., the estimated marginal probability of an abnormality occurring in the enterprise under the current stress level. This probability is derived from the posterior sampling mechanism derived through Bayesian logistic regression in the anomaly detection and analysis unit. The system first constructs a linear predictor η using historical stress scores and label data. t , combining the Student-t heavy-tailed likelihood with the Gaussian prior to form the posterior density, generating a large number of parameter samples through Hamiltonian Monte Carlo or variational inference, and calculating η based on these samples t The sampling distribution at the current time point. Then, each Input the logic function to get an abnormal probability sample By averaging these samples, the system obtains a point estimate of the abnormal probability at that point in time. Since this process is derived from full Bayesian modeling, which includes modeling of model parameter uncertainty and extreme sample fluctuations, its output not only has point prediction significance, but also retains the complete distribution shape, which can be used for confidence assessment or decision tolerance adjustment by subsequent modules.

[0099] After obtaining the risk expression in the probability dimension, the system further combines it with two clearly measurable financial risk exposures, namely: default exposure amount EAD t and LGD t Among them, EAD tIt refers to the total risk exposure amount that will be directly affected by the default of the enterprise or its affiliated financial institutions at the current point in time. It usually includes the enterprise's outstanding short-term or long-term interest-bearing liabilities, accounts receivable balance, total credit guarantees, and the maturity amount of commercial acceptance bills. It is a financial exposure with book clarity and a dynamic update mechanism. The system supports real-time extraction of EAD from the enterprise balance sheet, financial interface platform or industry credit system. t Data can be automatically eliminated based on business type, which can eliminate non-operating liabilities that do not constitute default exposure, thereby ensuring the accuracy of exposure estimation.

[0100] Loss Given Default (LGD) t It indicates the proportion of the amount that cannot be recovered in the total exposure amount after the enterprise defaults or financial abnormalities. This parameter is usually a continuous value in the interval [0,1]. Its specific value can be formulated according to factors such as the industry in which the enterprise is located, the type of guarantee, the coverage of collateral, credit rating and recovery costs. The system supports three configuration methods: First, introduce the standard LGD value set for different asset types in the regulatory framework (such as the Basel Accord), which is suitable for financial companies and their customer groups; second, use the historical default case recovery rate of the same industry for statistical modeling, and use the mean or quantile as input after deriving the empirical LGD distribution; third, for new companies or small and micro institutions with scarce data, the system can use high-precision Bayesian estimation methods to estimate LGD. t Perform modeling completion to prevent missing loss estimates due to lack of direct default observations.

[0101] Multiplying the above three factors, the system obtains the potential loss of monetization L t It represents the expected loss amount that may be caused by the financial anomaly of the enterprise in the reporting period t under the conditions of the current stress score, historical label data and current exposure structure. This estimated value has complete economic significance and risk management applicability: it not only reflects the Bayesian estimation ability of "the possibility of anomaly", but also combines it with the specific risk exposure level of the enterprise, so that the risk signal has a "quantifiable" business foothold. Compared with the traditional risk control system that uses a single abnormal probability as the judgment basis, the L t The indicator monetizes the model output results, making the abnormal signal directly correspond to "how much money may be lost" rather than just "how likely is a problem", which greatly enhances the readability and interpretability of the model output for senior management, regulatory notifications and systemic risk control. In addition, the loss valuation process is not only dynamically updated at each point in time, but can also be expanded to a multi-period cumulative risk path. The system performs L t The sequence performs sliding window aggregation to form a smooth average potential loss trajectory, which is compared with the historical loss distribution to determine whether it exceeds the high percentile warning line, thereby triggering risk warning behavior.

[0102] Assume that the financial observation data of the enterprise in the last six quarters are as follows:

[0103] The growth rates of operating income (denoted as G) were 0.05, 0.08, 0.02, 0.01, negative 0.03, and negative 0.06 (unit: "quarterly relative change ratio");

[0104] The operating cash flow ratio (denoted as C) is 0.12, 0.14, 0.10, 0.08, 0.05, and negative 0.02 (unit is "cash flow divided by revenue");

[0105] The quality of accruals (denoted as Q) is 0.40, 0.35, 0.50, 0.55, 0.60, and 0.80 (the unit is “non-cash profit ratio”);

[0106] The debt-to-asset ratio (denoted as D) is 0.50, 0.53, 0.54, 0.58, 0.60, and 0.65 (the unit is "liabilities divided by assets").

[0107] Historical anomaly label A t 0, 0, 0, 1, 1, 1 (the first 3 periods are normal, the last 3 periods are abnormal).

[0108] In the first step, the system calculates the mutual information I(M) between each financial indicator and the abnormal label through the information contribution weight analysis unit. Assuming three equal frequency bins, the calculation results are as follows:

[0109] I(G)=0.082;

[0110] I(C)=0.120;

[0111] I(Q)=0.170;

[0112] I(D)=0.090;

[0113] Normalize the mutual information to get the weight of each indicator ω M :

[0114] ∑I(M)=0.462;

[0115]

[0116] In the second step, the system enters the stress score construction unit and performs z-score standardization on each indicator. Taking the sixth quarter as an example, for G:

[0117] μ G = mean = 0.012;

[0118] σ G =standard deviation≈0.057;

[0119]

[0120] The remaining indicators are calculated similarly:

[0121]

[0122]

[0123] This gives the financial stress score F6 for the sixth quarter:

[0124] F6=ω G |Z G，6 |+ω C |Z C，6 |+ω Q |Z Q，6 |+ω D |Z D，6 |;

[0125] F6≈0.177×1.263+0.260×1.633+0.368×1.570+0.195×1.456≈1.501; In the third step, the anomaly detection and analysis unit performs four nonlinear transformations on F6:

[0126] T 1，6 =F6=1.501;

[0127]

[0128] T 3，6 =ln(1+F6)=ln(2.501)≈0.916;

[0129]

[0130] Assume that for each T in the history window k The following sample variance is obtained:

[0131] Var(T1)=0.102;

[0132] Var(T2)=0.289;

[0133] Var(T3)=0.042;

[0134] Var(T4)=0.020;

[0135] The parameter prior distribution is:

[0136]

[0137] The system obtains the posterior mean estimate through Hamiltonian Monte Carlo sampling:

[0138] θ0=-1.2;

[0139] θ1=0.85;

[0140] θ2=0.40;

[0141] θ3=1.10;

[0142] θ4 = -0.60;

[0143] Compute the linear predictor η6:

[0144] η6=θ0+θ1T 1，6 +θ2T 2，6 +θ3T 3，6 +θ4T 4，6 ;

[0145] η6=-1.2+0.85×1.501+0.40×2.253+1.10×0.916+(-0.60)×0.222;

[0146] η6=-1.2+1.276+0.901+1.008-0.133≈1.852;

[0147] Abnormal probability:

[0148]

[0149] Assume that the enterprise's default exposure in the sixth quarter is EAD6 = RMB 3,000,000 and the loss given default (LGD6) = 0.6; then the monetized potential loss L6 is:

[0150] L6=E[p(η6|a=1)]×EAD6×LGD6;

[0151] L6=0.864×3000000×0.6=15555200.

[0152] Therefore, the expected potential loss for the sixth quarter is RMB 1,555,200. If this value exceeds the 95th percentile of monetized losses within the historical sliding window, the system triggers a financial risk warning signal for the sixth quarter. This signal is transmitted to the enterprise risk control console or regulatory interface, accompanied by a complete probabilistic explanation, financial stress indicator decomposition, and posterior confidence intervals, providing a basis for decision-making. This example demonstrates the end-to-end process from data collection, modeling and inference, to risk assessment, fully demonstrating the data-driven nature, Bayesian expressiveness, and practical application of this invention in currency risk management.

[0153] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A financial anomaly detection and risk warning system based on Bayesian deep learning, characterized by: The system includes: an information contribution weight analysis unit, which is used to select financial indicators for measuring financial stability from the historical data of a rolling window composed of multiple recent consecutive reporting periods, and for each financial indicator, calculates the joint distribution of the financial indicator and the historical records, and uses mutual information to measure the degree of correlation between the two, and then normalizes the value of the mutual information into a weight so that the sum of all weights is equal to 1; a stress score construction unit, which is used to perform z-score normalization on each financial indicator in the same rolling window to obtain a normalized result, take the absolute value of the normalized result, and perform linear weighted summation with the weight to obtain a financial stress score; an anomaly detection and analysis unit, which is used to use the financial stress score as the only automatic Variables, using a logistic regression model that introduces nonlinear logistic Student-t likelihood to estimate the probability of an anomaly occurring in the current period, where the baseline logarithmic probability and stress score coefficient of the logistic regression model are both assigned zero-mean Gaussian priors; the prior variance of the stress score coefficient is determined by the inverse of the historical financial stress score to ensure scale consistency; the posterior distribution of these two coefficients is obtained over all historical financial stress scores through Hamiltonian Monte Carlo or variational inference methods; a risk warning unit is used to multiply the mean of the obtained posterior distribution by two measurable loss components to calculate the monetized potential loss; if the monetized potential loss exceeds the set loss threshold, the system will issue a warning message.

2. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 1, characterized in that: The financial indicators used to measure financial soundness include: operating income growth rate G, operating cash flow ratio C, accrual profit quality Q and debt-to-asset ratio D.

3. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 2, characterized in that: The two measurable loss components are: Default Exposure EAD t and LGD t .

4. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 3 is characterized in that: Weight ω M for: in, is a set of financial indicators; M′ and M represent the set of financial indicators respectively An element in ; I(M′) is the mutual information between the financial indicator M′ and the historical records; I(M) represents the mutual information between the financial indicator M and the historical records, which is: Where a represents the label value. When a is 1, it indicates an abnormal historical record, and when a is 0, it indicates a normal historical record. bins(M) represents the discrete bin set of the financial indicator M, which is divided by equal frequency or equal interval. p(a, m) represents the joint probability that the label value is a and the financial indicator M falls into bin m. p(a) is the marginal probability that the label value is a. p(m) is the marginal probability of bin m.

5. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 4 is characterized in that: Assume that the number of reporting periods is W, the current reporting period is t, and the value of t ranges from 1 to W; then the financial stress score F of the current reporting period is t for: Among them, Z M，t Represents the standardized result of the financial indicator M in the current reporting period; |·| is the absolute value operator; Z M，t =(M t -μ M ) / σ M ;M t is the value of the financial indicator M in the current reporting period; μ M is the mean value of the financial indicator M; σ M is the standard deviation of the financial indicator M.

6. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 5, characterized in that: The anomaly detection and analysis unit calculates the financial stress score F t Through four nonlinear transformations, we get the financial stress score F t The four morphological risk terms are: linear drift term T 1，t =F t ; Convex acceleration term Logarithmic saturation term T 3，t =ln(1+F t ); decay inversion term The baseline log odds are The mean is 0 and the variance is Gaussian prior distribution of The pressure score coefficient is The mean is 0 and the variance is Gaussian prior distribution of ; i and k are both integer subscript indices; T k，i represents the financial stress score F in reporting period i i The morphological risk item; T k，i The mean of .

7. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 6, characterized in that: The anomaly detection and analysis unit defines the linear predictor η for the current reporting period t for: or t =θ0+θ1T 1，t +θ2T 2，t +θ3T 3，t +θ4T 4，t ; Calculate the abnormal probability P(a=1|η) in the current reporting period t )for: Define the likelihood function L as: Where v is the Student-t degree of freedom; scale s 2 is η t variance; is η t The mean of .

8. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 7 is characterized in that: Since η t It is a nonlinear expression of the baseline logarithmic probability and the stress score coefficient. The anomaly detection and analysis unit solves the following formula through the Hamiltonian Monte Carlo or variational inference method to obtain the posterior distribution p(η t |a): Here, ∝ is the proportionality symbol.

9. The financial anomaly detection and risk warning system based on Bayesian deep learning according to claim 8, characterized in that: The potential loss L of the current reporting period t for: L t =[E[p(ηt|a=1)]]×EAD t ×LGD t ; Among them, p(η t |a=1) represents the posterior distribution when the label value is 1; E[p(η t |a=1)] represents p(η t |a=1)mean.

Images