Ad combination recommendation method based on structured bayesian learning and endogeneity correction

Abstract

The application relates to the technical field of advertisement delivery, in particular to an advertisement combination recommendation method based on structured Bayesian learning and endogeneity correction, which comprises the following steps: constructing an observation data set, obtaining an observable feature vector and a instrumental variable vector of an advertisement commodity; identifying an endogenous variable and performing regression analysis based on the instrumental variable vector to obtain a residual term; constructing a structured combination utility function; constructing a local competition subset by using a signal function satisfying an equal probability constraint, and combining the function to calculate a conditional selection probability of an observation sample on the local competition subset; constructing a global log-likelihood objective function, and obtaining optimal model parameters of the structured combination utility function by using a stochastic gradient optimization method; and calling the structured utility function by using the obtained optimal model parameters, calculating a selection probability of a candidate advertisement combination, and performing advertisement combination recommendation. The application can effectively overcome the calculation efficiency bottleneck and accurately correct attribution bias caused by feature endogeneity.

Description

Technical Field

[0001] This application relates to the field of advertising delivery technology, and in particular to an advertising mix recommendation method based on structured Bayesian learning and endogenous correction. Background Technology

[0002] In the field of modern computational advertising and recommendation systems, accurately predicting user preferences for advertised products is crucial for improving platform revenue and optimizing user experience. With the evolution of advertising formats, recommendation scenarios have shifted from predicting click-through rates for single products to recommending more complex bundled products. Advertisers and platforms urgently need to understand user selection behavior when faced with massive amounts of potential product bundles in order to develop better pricing strategies and ad mixes. In this context, building efficient and interpretable models to capture users' non-linear preferences for bundles has become a vital technical means of connecting massive ad inventories with user needs.

[0003] Existing technologies for predicting user choice behavior mainly fall into two categories. One category comprises classic recommendation models based on machine learning and statistics, such as collaborative filtering. Collaborative filtering primarily relies on historical interaction matrices to calculate similarity. While computationally simple, it utilizes only ID information, making it difficult to handle the cold-start problem. Furthermore, it typically recommends single items, failing to effectively capture complex complementary or substitutive relationships within product combinations. The other category includes logistic regression and its extensions, such as the multinomial Logit model. While the multinomial Logit model generalizes logistic regression to some extent for handling multi-class classification problems, it relies on the assumption of independence of irrelevant options—that is, that a user's choice of a particular option is unaffected by the existence of other options. This assumption often fails in scenarios involving strongly correlated combinations. More critically, these models require normalization of all alternatives (calculating the partition function) when calculating probabilities. When faced with an exponential combination space of hundreds or thousands of products in advertising scenarios, the computational load explodes, exceeding the real-time processing capabilities of existing hardware, rendering the model often infeasible in practical applications. In addition, the field of econometrics also has Bayesian structured choice models, which use utility functions and instrumental variables (IVs) to handle endogeneity, and then use Markov chain Monte Carlo (MCMC) methods to achieve posterior estimation of parameters. This method can theoretically model choice preferences in a structured way and obtain statistical confidence intervals for parameter distributions, and has been widely used in early economics and marketing research.

[0004] However, existing technologies still have significant limitations when facing complex scenarios involving ad mix recommendations. First, the combinatorial explosion problem renders computation infeasibility. In real-world ad campaigns, the number of candidate products often reaches hundreds or thousands, and the number of potential ad mixes grows exponentially. Besides the inapplicability of traditional multinomial logit models, Bayesian structured selection models require traversing the entire dataset in each iteration, converging only after multiple iterations, with training times typically measured in days or weeks. This also fails to meet the rapid model update requirements of advertising systems. Second, feature endogeneity leads to systematic errors in preference estimation. In ad bidding and recommendation environments, high prices or prime placements are often associated with unobserved ad quality or brand power. However, existing models generally assume these features are exogenous, directly predicting based on historical click or conversion data. As a result, the model easily correlates price or placement directly with user preferences, incorrectly learning false patterns. This attribution bias can lead to misleading decisions during budget allocation or strategy optimization, failing to accurately reflect users' true causal preferences. Therefore, how to construct a user preference model that can effectively overcome the computational efficiency bottleneck caused by the combination explosion and accurately correct the attribution bias caused by feature endogeneity when facing massive ad combination recommendation scenarios, so as to achieve efficient user preference modeling with real causal explanatory power, is an urgent problem to be solved. Summary of the Invention

[0005] This application provides an ad combination recommendation method based on structured Bayesian learning and endogeneity correction, which can effectively overcome the computational efficiency bottleneck caused by combinatorial explosion and accurately correct the attribution bias caused by feature endogeneity. This application provides the following technical solution:

[0006] Firstly, this application provides a method for recommending advertising combinations based on structured Bayesian learning and endogeneity correction, the method comprising:

[0007] An observation dataset is constructed based on the acquired advertising transaction data, the full set of advertising products is defined, and the observable feature vector and instrumental variable vector of each advertising product are obtained.

[0008] Endogenous variables are identified from the observable feature vectors, and regression analysis is performed based on the instrumental variable vectors to calculate residual terms for endogeneity correction.

[0009] By calling the observable feature vector and residual terms, a structured combined utility function is constructed, which includes nonlinear feature utility, interaction utility and endogenous correction utility. The function is used to describe the user's choice behavior for the advertising combination.

[0010] A local competitive subset is constructed using a signal function that satisfies the equal probability constraint, and the conditional selection probability of the observed sample on the local competitive subset is calculated by combining the structured combination utility function.

[0011] A global log-likelihood objective function is constructed based on the conditional selection probability, and the optimal model parameters of the structured combined utility function are obtained by using the stochastic gradient optimization method.

[0012] The optimal model parameters obtained from training are used to call the structured utility function to calculate the selection probability of candidate ad combinations and perform ad combination recommendations.

[0013] In one specific implementation scheme, the construction of the observation dataset based on the acquired advertising transaction data, defining the full set of advertising products, and obtaining the observable feature vector and instrumental variable vector for each advertising product includes:

[0014] Historical advertising transaction data were extracted from the advertising log database to construct an observation dataset. ,in, The total number of samples, Indicates the first The combination of advertised products selected by the user in this second display;

[0015] Define the full set of advertising products as Extract the observable feature vector of each advertised product. and instrumental variable vector The observable feature vector The instrumental variable vector is used to describe the known characteristics of the advertised product in terms of content, price, and attributes. Exogenous auxiliary variables refer to those that can significantly influence the pricing strategy of advertised goods, but are not directly related to the unobserved potential quality attributes of the goods.

[0016] In one specific implementation, the step of identifying endogenous variables from the observable feature vector and performing regression analysis based on the instrumental variable vector to calculate residual terms for endogeneity correction includes:

[0017] Identify endogenous variables from the observable feature vectors. And by calling the instrumental variable vector, the linear regression equation is constructed as follows:

[0018] ;

[0019] in, This represents the identified endogenous variables. Represents an instrumental variable vector. The regression coefficients to be estimated are: For the residual term, This represents the transpose operation of a vector;

[0020] The linear regression equation is fitted using the least squares method to obtain estimated values ​​of the regression coefficients. And based on the estimated value The residual term for each advertised product is calculated as follows:

[0021] ;

[0022] in, This refers to the residual term used for endogeneity correction.

[0023] In a specific implementation scheme, the step of calling the observable feature vector and residual term to construct a structured combined utility function that includes nonlinear feature utility, interaction utility, and endogeneity correction utility includes:

[0024] Set the combination of advertising products for users Composed of several advertised products, advertising mix The selection instructions for each product are as follows: When advertising products Included in the combination China Times, Otherwise, it is 0; based on the observable feature vectors of each item in the combination. The aggregate feature vector of the combination is calculated as follows: ;

[0025] The structured composition utility function is constructed as follows:

[0026] ;

[0027] in, For nonlinear characteristic utility, For interactive utility, For endogenous modification effect;

[0028] The complete expression for the structured composition utility function is shown below:

[0029] ;

[0030] in, For the set of parameters to be estimated, For the first The aggregated value of each feature, This represents the number of dimensions in each product feature vector. The coefficient of the linear term, The coefficient of the quadratic term, Let be a binary vector representing the co-occurrence relationship of each pair of items in the combination. For the interaction parameter vector, For the corresponding weight parameters, This is the residual term used for endogeneity correction.

[0031] In a specific implementation, the step of constructing a local competitive subset using a signal function that satisfies equal probability constraints, and calculating the conditional selection probability of the observed sample on the local competitive subset in conjunction with the structured combination utility function, includes:

[0032] For each observed true choice We introduce a random mapping as the signal function, denoted as . ;

[0033] Based on observed real choices As the initial seed node, it is used to generate [various nodes] by performing a random perturbation operation. There are several different competing combinations, among which A local competitive subset is generated based on a preset number of negative samples. ;

[0034] For the generated subset Any two combinations and The signal function generates this specific set. The probabilities are equal, meaning they satisfy the following symmetric equation:

[0035] ;

[0036] Construct the following formula for calculating the probability of conditional choice:

[0037] ;

[0038] in, This means that the known competition range is limited to a local subset. Under the premise that users hit the true choice The conditional choice probability, and Combinations With competing combinations The aggregated feature vector.

[0039] In a specific feasible implementation, the step of constructing a global log-likelihood objective function based on the conditional choice probability and obtaining the optimal model parameters of the structured combined utility function using a stochastic gradient optimization method includes:

[0040] Based on the conditional selection probability, a global log-likelihood objective is constructed, and a variational inference framework is introduced, setting the approximate posterior distribution of the parameter to be estimated as an independent Gaussian distribution that satisfies the mean field assumption.

[0041] A lower bound of evidence is constructed as the objective function for optimization. The lower bound of evidence is used to characterize the difference between the joint probability density of the observed data and parameters and the approximate posterior distribution.

[0042] In the gradient calculation process, a reparameterization technique is introduced, which introduces a standard normal distribution noise variable and rewrites the parameter to be estimated as a differentiable function of the mean, variance and noise variable to support the backpropagation of the gradient.

[0043] The stochastic gradient optimization process is performed, which draws samples from the observation dataset in batches and generates corresponding local competitive subsets in real time. The lower bound gradient of evidence for the current batch is calculated based on the reparameterized parameters, and the variational parameters of the approximate posterior distribution are iteratively optimized using the gradient update algorithm until the model converges and the optimal model parameters are output.

[0044] In a specific implementation scheme, the step of using the optimal model parameters obtained from training to call the structured utility function, calculating the selection probability of candidate ad combinations, and performing ad combination recommendations includes:

[0045] Extract a set of candidate ad combinations that are currently available for display from the ad delivery database. Each candidate combination consists of several ad products.

[0046] For each candidate combination, the constructed structured combination utility function is invoked, and the optimal parameter set is substituted. Calculate the utility value of this combination;

[0047] After obtaining the utility values ​​of all candidate ad combinations, the conditional selection probability model is invoked to perform normalization calculation on the utility results, and the selection probability of each candidate ad combination is obtained. The candidate ad combinations are sorted from high to low according to the selection probability, and the ad combination with the highest probability is selected as the preferred placement plan.

[0048] Secondly, this application provides an advertising combination recommendation system based on structured Bayesian learning and endogeneity correction, employing the following technical solution:

[0049] An advertising combination recommendation system based on structured Bayesian learning and endogeneity correction includes:

[0050] The vector extraction module is used to construct an observation dataset based on the acquired advertising transaction data, define the full set of advertising products, and obtain the observable feature vector and instrumental variable vector for each advertising product.

[0051] The residual calculation module is used to identify endogenous variables from the observable feature vector and perform regression analysis based on the instrumental variable vector to calculate residual terms for endogeneity correction.

[0052] The function construction module is used to call the observable feature vector and residual terms to construct a structured combined utility function that includes nonlinear feature utility, interaction utility and endogeneity correction utility. The function is used to describe the user's choice behavior for the advertising combination.

[0053] The probability calculation module is used to construct a local competitive subset using a signal function that satisfies the equal probability constraint, and to calculate the conditional selection probability of the observed sample on the local competitive subset in combination with the structured combination utility function.

[0054] The parameter optimization module is used to construct a global log-likelihood objective function based on the conditional selection probability, and to obtain the optimal model parameters of the structured combined utility function using a stochastic gradient optimization method.

[0055] The ad recommendation module is used to call the structured utility function using the optimal model parameters obtained from training, calculate the selection probability of candidate ad combinations, and perform ad combination recommendations.

[0056] Thirdly, this application provides an electronic device, the device including a processor and a memory; the memory stores a program, the program being loaded and executed by the processor to implement an advertising combination recommendation method based on structured Bayesian learning and endogeneity correction as described in the first aspect.

[0057] Fourthly, this application provides a computer-readable storage medium storing a program that, when executed by a processor, is used to implement an advertising combination recommendation method based on structured Bayesian learning and endogeneity correction as described in the first aspect.

[0058] In summary, the beneficial effects of this application include at least the following:

[0059] (1) This application effectively solves the computational infeasibility problem caused by the exponential explosion of the combination space in large-scale advertising combination recommendation scenarios by constructing a structured Bayesian learning framework based on dynamic subset inference. When faced with massive product combinations, existing technologies often cannot apply high-precision probability models due to the excessive computational cost of full probability normalization. This application creatively utilizes a signal function that satisfies statistical consistency to dynamically construct a local subset containing finite competing options for each observation, transforming the originally unsolvable global full-space probability calculation into a conditional probability calculation based on local subsets, thereby significantly reducing the computational complexity from exponential to linear. At the same time, under the variational inference framework, this application uses reparameterization techniques and stochastic gradient optimization algorithms to replace the traditional inefficient Markov chain Monte Carlo (MCMC) sampling, realizing a fast approximation and update of the posterior distribution of parameters. This collaborative modeling paradigm enables complex structured probability models to be efficiently trained and inferred online on large-scale streaming advertising data, ensuring the real-time response capability of the recommendation system while retaining the statistical advantages of Bayesian methods in parameter uncertainty estimation.

[0060] (2) This application significantly enhances the causal explanatory power and business guidance value of the user preference model by introducing a structured utility analysis mechanism that includes endogeneity correction, nonlinear saturation effect, and complementary interaction. Addressing the endogeneity attribution bias caused by the high correlation between price features and unobserved quality (such as brand premium) in the advertising bidding environment, this application uses instrumental variables to perform two-stage regression analysis, precisely decomposing the observed features into an exogenous driving part and an endogenous residual term. This residual is then explicitly embedded as an independent correction factor into the utility function, mathematically severing the implicit association between price and error terms, ensuring that the model can remove noise and learn the user's true causal preferences for product attributes. Furthermore, by constructing a quadratic saturation term and interaction topology in the utility function, this application can precisely capture the diminishing marginal utility threshold of users for specific attributes and the complementary or substitutive strength between different products. This enables the model to not only output highly accurate click predictions but also to transform them into specific willingness-to-pay (WTP) indicators and optimal bundling strategies, providing advertisers with economically meaningful interpretable evidence for optimizing pricing systems and developing refined placement plans.

[0061] This application provides an advertising combination recommendation method based on structured Bayesian learning and endogeneity correction. First, by introducing instrumental variables, regression analysis is performed on the endogeneous variables in the advertising transaction data to calculate residual terms for endogeneity correction. These residual terms are then integrated with nonlinear feature utility and interaction utility to construct a structured combination utility function that describes complex user choice behavior. Next, a local competitive subset is constructed using a signal function satisfying equal probability constraints. The conditional choice probability of the observed sample on the local subset is calculated, and the optimal model parameters are obtained using a stochastic gradient optimization method based on the global log-likelihood objective function. Finally, the candidate combination probability is calculated using these parameters to perform recommendations. This scheme solves the following technical problems through the above steps: On the one hand, by using instrumental variables to calculate residuals and explicitly incorporating them into the utility function, the bias caused by endogeneous variables in the observable features is corrected, thereby more accurately quantifying the user's true choice utility; on the other hand, by constructing a local competitive subset and calculating the conditional choice probability, the complex probability calculation on the full set of advertising products is transformed into calculation on a local subset. Combined with the stochastic gradient optimization method, efficient acquisition of optimal model parameters and accurate advertising combination recommendations are achieved.

[0062] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating the advertising combination recommendation method based on structured Bayesian learning and endogeneity correction in the embodiments of this application.

[0064] Figure 2 This is a schematic diagram of the overall process of the advertising combination recommendation method based on structured Bayesian learning and endogenous correction in the embodiments of this application.

[0065] Figure 3 This is a structural block diagram of the advertising combination recommendation system based on structured Bayesian learning and endogenous correction in the embodiments of this application.

[0066] Figure 4 This is a block diagram of an electronic device that recommends advertising combinations based on structured Bayesian learning and endogenous correction, as described in an embodiment of this application. Detailed Implementation

[0067] The specific embodiments of this application will be described in further detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate this application, but are not intended to limit the scope of this application.

[0068] Optionally, this application uses the advertising combination recommendation method based on structured Bayesian learning and endogeneity correction provided in various embodiments as an example for application in an electronic device. The electronic device is a terminal or a server. The terminal can be a computer, tablet computer, etc. This embodiment does not limit the type of electronic device.

[0069] Reference Figure 1 This is a flowchart illustrating an embodiment of an advertising combination recommendation method based on structured Bayesian learning and endogeneity correction provided in this application. The method includes at least the following steps:

[0070] Step S101: Construct an observation dataset based on the acquired advertising transaction data, define the full set of advertising products, and obtain the observable feature vector and instrumental variable vector for each advertising product.

[0071] In step S101, historical advertising transaction data of the advertising system is obtained, and a complete set of advertising products is defined based on this data. Simultaneously, the observable feature vector and its corresponding instrumental variable vector for each advertising product are obtained. The purpose of this step is to transform the raw log data into structured modeling input, enabling advertising products, transaction behaviors, and feature information to be expressed within a unified data framework.

[0072] Specifically, historical ad transaction data is first extracted from the existing ad log database. This data includes, but is not limited to, ad display identifiers, user identifiers, display time, bid amount, display location, clicks, or conversion feedback. An observation dataset is then constructed using a single ad display or a single user selection as a sample. ,in, The total number of samples, Indicates the first The combination of advertised products selected by the user in this second display.

[0073] Furthermore, the entire set of advertised products is defined as... Each of the advertised products These are all independent ad units that can be run within the advertising system. Observation dataset Each sample in Each of these elements corresponds to several elements in the set of advertised products, forming an interaction sample between the user and the advertised products.

[0074] Next, for each advertised product in the full set of advertised products, two types of feature data are extracted. The first type is the observable feature vector. This refers to a data set that can be directly read from the business database or product attribute table, used to characterize the external form and inherent attributes of advertised products. It describes the known characteristics of advertised products at the content, price, and attribute levels, including but not limited to product price, category tags, text descriptions, image features, or historical exposure information. This type of feature directly reflects the explicit attributes of advertised products that can be recorded and analyzed by the system. The second type is instrumental variable vectors. Instrumental variables refer to exogenous auxiliary variables that can significantly influence the pricing strategy of advertised goods but are not directly related to the unobserved potential quality attributes of the goods. In this application, instrumental variable vectors include, but are not limited to, raw material cost indices, regional average purchase prices, or advertising inventory supply. The reason for selecting these variables is that fluctuations in these variables directly lead to changes in product prices (satisfying correlation), but increases in raw material costs or inventory do not directly change users' perceptions of the fashionability or design of the goods (satisfying exogeneity). Therefore, by introducing this variable, the model can help identify which price changes are driven by cost rather than quality. After data extraction, standardization and numerical processing are performed on various feature vectors. Continuous features are adjusted to a uniform scale through linear normalization or standardization, while discrete features are represented using one-hot encoding or embedded vectors to ensure scale consistency and clear structure among features.

[0075] Step S102: Identify endogenous variables from the observable eigenvectors and perform regression analysis based on the instrumental variable vectors to calculate the residual terms used for endogeneity correction.

[0076] In step S102, the observable feature vectors obtained in step S101 are first analyzed to identify endogenous variables that may be statistically correlated with unobserved factors. This is because, in an advertising bidding and recommendation environment, while price or bid-related features are directly observable, they are often not entirely independent of the potential quality factors of the advertised goods. For example, high prices or high bids are usually associated with strong brand awareness, superior content design, or high market recognition. These potential factors are not explicitly recorded but can simultaneously influence user click and selection behavior. Therefore, there is an implicit correlation between price-related features and model error terms, forming an endogeneity problem. If such features are directly included in the modeling, the model may incorrectly interpret "high price" as "user preference," resulting in systematic errors in preference estimation. Therefore, to eliminate this endogeneity bias, this step uses the corresponding instrumental variable vectors to perform regression modeling and calculate residual terms that can be used for endogeneity correction. Through this step, exogenous information in the features of advertised goods can be separated from endogenous components affected by potential quality.

[0077] Specifically, this step constructs a linear regression model based on the control function method, performing feature projection and decoupling on the endogenous variables of the price class. From the observable feature vectors... Identifying endogenous variables For example, advertising bids or product prices, and call the instrumental variable vector extracted in step S101. The linear regression equation is constructed as follows:

[0078] ;

[0079] in, This represents the identified endogenous variables. Represents an instrumental variable vector. The regression coefficients to be estimated are: For the residual term, This represents the transpose of a vector. The equation reflects the statistical dependence between prices and exogenous instrumental variables; that is, the explanatory portion of price formation caused by external factors such as costs, inventories, or regional supply is determined by... express.

[0080] The linear regression equation was then fitted using Ordinary Least Squares (OLS) to obtain estimates of the regression coefficients. And based on the estimated value The residual term for each advertised product is calculated as follows:

[0081] ;

[0082] in, This refers to the residual term used for endogeneity correction, also defined as a control variable. Statistically, it reflects the portion of advertised product prices that cannot be explained by exogenous costs or inventory changes; this fluctuation is highly correlated with unobserved quality factors. Retaining and inputting this information into subsequent utility function modeling allows for the explicit removal of the correlation between price and error terms, thus ensuring that the user preference parameters estimated by the model are no longer affected by endogenous bias. It should be noted that... This represents the theoretically true residual term in the regression equation, which objectively exists but cannot be directly observed. These are the residual estimates obtained through regression calculations.

[0083] Step S103: Call the observable feature vector and residual term to construct a structured combined utility function that includes nonlinear feature utility, interaction utility and endogenous correction utility. The function is used to describe the user's choice behavior for the advertising combination.

[0084] In step S103, based on the observable feature vector extracted in step S101 and the residual term calculated in step S102 for endogeneity correction, a structured combinatorial utility function is constructed to characterize the user's decision-making logic in the process of choosing an advertising combination. This function, by jointly modeling feature effects, inter-item interaction effects, and endogeneity bias, depicts the user's selection tendency and decision-making basis when faced with different advertising combinations.

[0085] In implementation, the combination of advertised products faced by users is defined. Composed of several advertised products, advertising mix The selection instructions for each product are as follows: When advertising products Included in the combination China Times, Otherwise, it is 0. Based on the observable feature vectors of each item in the combination. The aggregate feature vector of the combination is calculated as follows: Based on this, the structured combined utility function is constructed as follows:

[0086] ;

[0087] in, For nonlinear characteristic utility, For interactive utility, It is an endogenous corrective effect.

[0088] Specifically, firstly, nonlinear feature utility is used to capture the law of diminishing marginal utility for users of product attributes, and its specific expression is as follows:

[0089] ;

[0090] in, For the first The aggregated value of the feature, for example, if the feature is... Each feature represents the video duration. This is the sum of the durations of all ad videos in the combination; if the feature is a category label, then... This refers to the number of times this category of ads appears. This represents the number of dimensions in each product feature vector. The coefficient of the linear term, The coefficient of the quadratic term is introduced to simulate the saturation effect. That is, as a certain characteristic (such as the number of ad impressions or total duration) increases, the user's satisfaction (utility) initially rises, but after exceeding a certain threshold, the increase slows down or even turns negative (causing annoyance). This inverted U-shaped relationship must be expressed in quadratic function form to ensure that the model conforms to the real psychological laws of users.

[0091] Secondly, the interaction utility is used to quantify the correlation between products within a combination, and its specific expression is shown below:

[0092] ;

[0093] in, It is a binary vector representing the co-occurrence relationship of each pair of products in the combination. For example, if both product A and product B exist in the combination, the corresponding dimension in the vector is marked as 1, otherwise it is 0. This represents the transpose operation of a vector. For the interaction parameter vector, if A positive value indicates a complementary effect (e.g., buying running shoes leads to a tendency to buy socks), increasing total utility; if... A negative value indicates a substitution effect (e.g., buying brand A phones means not buying brand B), reducing total utility. This item reflects the influence of synergistic or conflicting effects within the combination's internal structure when a user chooses a combination.

[0094] In actual engineering implementation, considering the entire commodity collection It may be quite large, leading to Due to the high dimensionality, this application employs sparse vector storage or feature hash mapping to construct... Alternatively, the co-occurrence relationship of each product pair can be statistically analyzed only for pre-defined high-frequency product pairs or interactions between product categories. The dimensions are limited to the computable range. In the formula... Only parameters corresponding to these effective interaction dimensions are used to capture key complementary or substitution effects while ensuring computational efficiency.

[0095] Finally, the endogeneity correction utility is used to explicitly address the biases that may arise from endogenous variables such as price in user choices. Its specific expression is shown below:

[0096] ;

[0097] in, The corresponding weight parameters are used to quantify the user's sensitivity to this potential factor. By introducing the residual term into the utility function, the model can statistically separate endogeneity bias from real user preferences, making the estimated utility closer to the user's true causal preference for the product combination.

[0098] In summary, the complete expression for the structured combination utility function is as follows:

[0099] ;

[0100] in, This is the set of parameters to be estimated, which encompasses all unknown parameters in the model that need to be learned through training. It is the set of coefficients for the first and second terms of all features. It is an interaction parameter vector. It is the set of weight parameters with endogenous adjustments. The goal of model training is to find an optimal set of weights. This ensures that the value calculated based on the utility function best matches the user's historical selection behavior.

[0101] Step S104: Construct a local competitive subset using a signal function that satisfies the equal probability constraint, and calculate the conditional selection probability of the observed sample on the local competitive subset by combining it with the structured combination utility function.

[0102] In step S104, based on the structured combined utility function constructed in step S103, for each sample in the observation dataset... The algorithm constructs a local subset containing finite competitive combinations using a signal function, and calculates the conditional probability of an observed sample being selected by the user on this subset. This step aims to solve the problem of the inability to calculate global probabilities due to the exponential explosion of the full ad combination space. By constructing a statistically unbiased local subset, the originally unsolvable global optimization problem is transformed into an operable local conditional probability calculation problem.

[0103] Specifically, first define the signal function. And use it to generate local competitive subsets Due to the full advertising portfolio space The set of all possible combinations of all goods in the system is approximately infinite, making it impractical to directly calculate the probability denominator based on this entire space. Therefore, for each observed true choice... (i.e., the positive samples actually selected by the user), introduce a random mapping as the signal function, denoted as . ,in, This indicates that the input field can be any combination of advertisements. In mathematics, it represents the total space. The power set of is the set of all possible subsets. Therefore, the specific physical meaning of this function is: based on the observed true combinations Starting from this point, a small subset of combinations containing the actual choice is mapped and generated according to a preset random rule. .

[0104] Secondly, subset generation and constraint control are performed based on add, delete, and replace operations. Subset The specific generation rule is: based on the observed true choices As the initial seed node, it is used to generate other nodes by performing random perturbation operations such as "add product", "delete product", or "replace product". There are 10 (e.g., 10) different competing combinations (i.e., negative samples), among which The subset generated is the preset number of negative samples. The total includes A combination.

[0105] In this process, to ensure the simplification of subsequent probability calculations, a key statistical constraint must be satisfied: for the generated subset Any two combinations and (Whether it's a positive sample or a generated negative sample), the signal function generates this specific set. The probabilities must be equal, that is, they must satisfy the following symmetric equation:

[0106] ;

[0107] The physical meaning of this equation is the symmetry of the sampling path: assuming the generated negative samples... Starting from this point, the signal function is run according to the same rules, which generates the current subset. The probability must be related to the probability from the real sample. This subset is generated from the start. The probabilities are completely consistent. This key constraint ensures that each sample within the subset is equally weighted in the generation mechanism, thereby mathematically eliminating sampling bias and eliminating the need to introduce complex sampling weight correction terms when calculating conditional probabilities in subsequent calculations.

[0108] It should be noted that, to ensure the symmetry equality constraints in subsequent steps are met, the random perturbation operation is not a simple uniform sampling, but rather employs an accept-rejection sampling or Metropolis-Hastings sampling mechanism. Specifically, it will be based on the current combination... With the generated candidate combinations Adjust the acceptance rate by the transition probability ratio between them, or in the construction The time-forced inclusion of the reverse generation path ensures that from generate The probability and from any The probabilities of generating this set are statistically equal. This process eliminates sampling bias, so that the conditional probability calculations in subsequent formulas do not require the introduction of additional weight correction terms.

[0109] Finally, based on the equiprobability generation property satisfied by the above signal function, the original uncomputable global likelihood function is transformed into a function based on local competing subsets. The conditional likelihood function. Since the symmetry of the sampling process eliminates bias, the structured combinatorial utility function output in step S103 can be directly called. The following formula is used to calculate the conditional choice probability:

[0110] ;

[0111] in, This means that the known competition range is limited to a local subset. Under the premise that users hit the true choice The probability of conditional selection. and Combinations With competing combinations The aggregated feature vector is obtained. Using this formula, the conditional choice probability of each observation combination can be calculated on a finite subset of combinations, while preserving the information of the structured combination utility function in describing user choice behavior. This step transforms the previously uncomputable global likelihood function into a conditional likelihood form on a finite local subset. This not only preserves the ability of the structured combination utility function to describe user decision-making behavior but also reduces computational complexity from exponential to linear, enabling the model to execute efficiently on large-scale advertising data.

[0112] Step S105: Construct a global log-likelihood objective function based on the conditional choice probability, and use the stochastic gradient optimization method to obtain the optimal model parameters of the structured combined utility function.

[0113] In step S105, the conditional choice probability of each observed sample on the local competitive subset calculated in step S104 is called, and a global log-likelihood objective function to measure the model's fit is constructed based on this probability. This objective function is used to train and optimize the parameter set of the structured combined utility function defined in step S103. The core objective of this step is to maximize the conditional probability of all observed samples so that the model can most accurately fit the user's behavioral pattern in the process of choosing ad combinations, thereby obtaining the optimal parameter estimate of the utility function. Furthermore, in order to efficiently solve for the optimal solution in the high-dimensional parameter space, this step abandons the traditional Markov chain Monte Carlo (MCMC) sampling method and instead adopts a variational inference framework, combining reparameterization techniques and stochastic gradient optimization algorithms to iteratively update the parameters to obtain the optimal model parameters of the structured combined utility function.

[0114] Specifically, based on the conditional selection probability in step S104, the global log-likelihood objective function is defined as follows:

[0115] ;

[0116] in, The objective function reflects the number of observed samples given parameters. The optimization objective is to make the model fit the overall sample size of all observed samples under the given conditions. Take the maximum value to obtain the parameter set that best reflects the user's true choice pattern. Essentially, it's a conditional log-likelihood function based on locally competing subsets. In large-scale sparse data scenarios, optimizing this conditional likelihood function has been mathematically proven to be an efficient approximation of optimizing the global likelihood function. By maximizing this objective function, the model can optimize the observed samples... In its local competitive environment The relative ranking is optimal, thus approximating the global optimal preference parameter estimate.

[0117] However, due to the parameter set It contains multiple sets of high-dimensional variables and their posterior distributions The likelihood gradient is difficult to analyze analytically, and directly calculating it through numerical integration is impractical in engineering. Therefore, this step employs variational inference to estimate the parameters, replacing the difficult-to-solve true posterior distribution with an approximate distribution. Let the approximate posterior distribution be... ,in This is the set of variational parameters. To reduce the dependence between parameters, the mean-field assumption is adopted, and the approximate posterior distribution of the parameters to be estimated is set as an independent Gaussian distribution that satisfies the mean-field assumption, i.e. Each component in Independent modeling is a Gaussian distribution: ;

[0118] in, Indicates parameters Expected value The variance is used to characterize the range of uncertainty. This assumption significantly simplifies the solution complexity of the joint distribution, transforming high-dimensional posterior inference into the estimation problem of several low-dimensional independent parameters. Based on this assumption, an Evidence Lower Bound (ELBO) is constructed as the optimization objective function. The Evidence Lower Bound characterizes the difference between the joint probability density of the observed data and parameters and the approximate posterior distribution. The optimization objective function is shown below:

[0119] ;

[0120] in, Representing observation data With parameters The joint probability density function is given by the following terms: the first term represents the model's explanatory power over the data, and the second term measures the difference between the variational distribution and the true posterior distribution. The optimal approximate posterior distribution can be obtained by maximizing the ELBO, i.e., minimizing the KL divergence between the two. This allows us to approximate the true parameter distribution.

[0121] To make the optimization process differentiable and support gradient backpropagation, this step introduces a reparameterization technique, introducing a standard normally distributed noise variable. The parameters to be estimated are rewritten as differentiable functions of the mean, variance, and noise variable to support gradient backpropagation. The sampling formula is rewritten as:

[0122] ;

[0123] in, The noise variable is a standard normally distributed variable. Through this reparameterization operation, the randomness is changed from... To take responsibility, and , All parameters are learnable. This reparameterization operation ensures that the gradient propagation path is no longer affected by randomness, thus enabling the modification of variational parameters within an automatic differentiation framework. Perform stable updates.

[0124] Then, a stochastic gradient optimization process is performed, randomly selecting a small batch of samples from the observed dataset. As the current training batch, according to the method in step S104, a corresponding local competition subset is generated for the samples in this batch in real time. Resampling noise Calculated according to the reparameterization formula And calculate the ELBO gradient for the current batch. Update variational parameters using the Adam optimization algorithm: ;

[0125] in, The learning rate controls the step size for each parameter update. By repeating the above process over multiple batches, the variational parameters... Continuously adjust until ELBO converges. Once convergence is achieved, the posterior mean of the output parameters is denoted as... ;in: This is the set of coefficients for the first and second terms of advertising features, used to describe the user's sensitivity to each feature attribute and the change in marginal utility. This is a vector of interaction parameters between products, used to characterize the strength of complementary or substitutive relationships within the combination; This is a set of weight parameters with endogenous adjustments, used to measure the magnitude of the adjustment of utility by potential quality factors. This parameter set is obtained through variational inference and stochastic gradient optimization. This represents the optimal model parameters for the structured combination utility function. This result can be used in subsequent steps to calculate the utility value and selection probability of any combination of advertised products, achieving accurate modeling of user combination selection behavior.

[0126] Step S106: Use the optimal model parameters obtained from training to call the structured utility function, calculate the selection probability of candidate ad combinations, and perform ad combination recommendation.

[0127] In step S106, the obtained optimal parameter set is used. The trained structured utility function is invoked to transition the model from the training phase to the actual ad recommendation phase. The utility value and selection probability of candidate ad combinations are calculated, and ad combination recommendations are executed based on the calculation results. The core objective of this step is to apply the model's learning results to ad delivery decisions, inferring user selection tendencies through parameterized utility functions, thereby generating optimal ad recommendation results in a dynamic advertising environment.

[0128] Specifically, the system extracts a set of currently displayable candidate ad combinations from the ad delivery database, where each candidate combination consists of several ad products. For each candidate combination, the system calls the structured combination utility function constructed in step S103 and substitutes the optimal parameter set. The system calculates the utility value of the combination. After obtaining the utility values ​​of all candidate ad combinations, the system calls the conditional selection probability model in step S104 to perform normalization calculation on the utility results, obtaining the selection probability distribution of each candidate ad combination. The selection probability reflects the user's relative preference among different combinations, and its magnitude directly determines the ranking priority of the combination in the recommendation list. Based on this, the system generates a preliminary recommendation sequence, that is, sorts the candidate ad combinations from high to low according to their selection probability, and the ad combination with the highest probability is selected as the preferred delivery option.

[0129] It should be noted that before calling the structured combination utility function to calculate the utility value of the candidate combination, the endogeneity correction residuals of each advertised item in the combination are first obtained. Since actual transaction prices have not yet been generated during the recommendation and prediction phase, the system cannot perform regression calculations in real time. Therefore, the following strategy is adopted to obtain... For advertised products that have been traded in the past, the system directly uses the mean residual calculated within the most recent time window (e.g., the past 7 days) as the inherent unobserved quality estimate for that product. For cold-start products with no historical data, the residual term is set to zero or the average residual of its category. This preprocessing step ensures that even without real-time price input, the model can still utilize historically accumulated quality factors. This allows for the revision of utility assessments, ensuring the feasibility of the forecasting process.

[0130] Furthermore, based on this, the system further performs structured correction and strategy optimization on the recommendation results according to the meaning of different parameters. Firstly, the system adjusts the recommendation results according to the parameters... Calculate the user's True Willingness to Pay (WTP) for ad attributes, a metric that reflects the value a user is willing to pay for a specific attribute. The calculation formula is shown below:

[0131] ;

[0132] in, Indicates when the ad attribute The acceptable price adjustment range for a user when the price changes by one unit. When the value is positive, it indicates that the attribute has a positive appeal to users. The system will prioritize displaying ad combinations with this attribute in ad ranking and bidding, thereby achieving ad optimization based on preference value.

[0133] Secondly, the system is based on interaction parameter vectors. The system analyzes the interactions between products. If the interaction parameter vector of a product pair is positive, it indicates complementarity between the two products. When a user browses either product, the system will automatically generate a bundled advertisement containing both products. If the interaction parameter vector is negative, it indicates substitution. The system will proactively avoid such co-occurrence during the combination generation process to prevent advertising resource conflicts or display redundancy. In this way, the recommendation results can balance the synergistic effect between advertisements and market competition.

[0134] Third, for entirely new ad combinations that have never appeared in historical observation samples, the system extracts their observable feature vectors and sets the endogeneity correction residual term to zero (i.e., assuming its unobserved quality is at an average level) or fills it with the mean residual of similar products. Then, it substitutes these residuals into a structured utility function to calculate the predicted utility value and selection probability. When the predicted selection probability of this new combination is higher than a preset threshold, the system identifies it as a potentially high-value combination and transmits the result to the real-time bidding (RTB) module for validation, thereby enabling the model to extrapolate and adaptively expand unknown ad combinations.

[0135] Through the above steps, the system achieves a complete closed loop from utility value calculation and selection probability inference to advertising recommendation decision-making, driven by optimal parameters. The resulting recommendation results are not only computable and interpretable, but also capable of capturing users' true preferences and providing precise guidance for advertising delivery strategies in dynamic advertising environments.

[0136] In summary, combining Figure 2This application proposes an advertising combination recommendation method based on structured Bayesian learning and endogenous correction. Its core lies in constructing a structured utility model that integrates causal inference and Bayesian inference. The scheme first introduces instrumental variables (such as raw material costs and inventory supply) to perform regression analysis on endogenous variables such as prices, calculating residual terms representing unobserved quality factors. These residual terms, along with nonlinear feature utility and inter-item interaction utility, are then used to construct a structured combination utility function, explicitly expressing users' preferences for attributes, their need for combination complementarity, and the impact of potential quality. At the model training level, the scheme employs a structured Bayesian learning framework, but abandons the traditional inefficient Markov chain Monte Carlo (MCMC) sampling, instead introducing variational inference techniques. Through reparameterization techniques and stochastic gradient optimization algorithms, it directly and efficiently approximates and estimates the posterior distribution of model parameters (including attribute weights, interaction coefficients, and correction coefficients). Finally, it uses the learned optimal parameters to calculate willingness to pay and selection probability, achieving accurate advertising recommendations with causal explanatory power.

[0137] In ad bidding, high bids are often strongly correlated with unrecorded high implicit quality (such as brand power), leading the model to incorrectly attribute users' choice of high quality to a preference for high prices. To address this, the proposed solution uses a control function method to derive a correction mechanism. It predicts the exogenous part of price using instrumental variables (IVs) that are unrelated to quality but affect price, thus removing the residuals related to the error term. These residuals are then added as independent terms to the utility function, mathematically blocking the endogenous correlation between the price variable and the error term, ensuring that the parameters learned by the model reflect users' true causal preferences. For the combinatorial explosion problem, where the entire ad combinatorial space grows exponentially, rendering the denominator of the traditional Softmax function incomputable, the proposed solution derives a conditional likelihood estimation method based on local competitive subsets. It constructs small subsets containing real and negative samples using signal functions satisfying equal-probability generation constraints, proving that optimizing the conditional probability on these subsets is equivalent to optimizing the global probability. This transforms unsolvable global computation into parallelizable local computation. Combined with variational Bayesian learning, this achieves rapid convergence of complex structured models on industrial-grade data.

[0138] Figure 3 This is a structural block diagram of an advertising combination recommendation system based on structured Bayesian learning and endogeneity correction, provided in one embodiment of this application. The device includes at least the following modules:

[0139] The vector extraction module is used to construct an observation dataset based on the acquired advertising transaction data, define the full set of advertising products, and obtain the observable feature vector and instrumental variable vector for each advertising product.

[0140] The residual calculation module is used to identify endogenous variables from the observable feature vectors and perform regression analysis based on the instrumental variable vectors to calculate the residual terms used for endogeneity correction.

[0141] The function building module is used to call observable feature vectors and residual terms to construct a structured combined utility function that includes nonlinear feature utility, interaction utility, and endogenous correction utility. The function is used to describe the user's choice behavior for the ad combination.

[0142] The probability calculation module is used to construct local competitive subsets using signal functions that satisfy equal probability constraints, and to calculate the conditional selection probability of the observed sample on the local competitive subset by combining the structured combination utility function.

[0143] The parameter optimization module is used to construct a global log-likelihood objective function based on the conditional choice probability and to obtain the optimal model parameters of the structured combined utility function using the stochastic gradient optimization method.

[0144] The ad recommendation module is used to call the structured utility function using the optimal model parameters obtained from training, calculate the selection probability of candidate ad combinations, and perform ad combination recommendations.

[0145] For relevant details, please refer to the above method implementation examples.

[0146] Figure 4 This is a block diagram of an electronic device provided in one embodiment of this application. The device includes at least a processor 401 and a memory 402.

[0147] Processor 401 may include one or more processing cores, such as a quad-core processor or an octa-core processor. Processor 401 may be implemented using at least one hardware form selected from DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). Processor 401 may also include a main processor and a coprocessor. The main processor, also known as a CPU (Central Processing Unit), is used to process data in the wake-up state; the coprocessor is a low-power processor used to process data in the standby state. In some embodiments, processor 401 may integrate a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the screen. In some embodiments, processor 401 may also include an AI (Artificial Intelligence) processor, which is used to handle computational operations related to machine learning.

[0148] Memory 402 may include one or more computer-readable storage media, which may be non-transitory. Memory 402 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments, the non-transitory computer-readable storage media in memory 402 is used to store at least one instruction, which is executed by processor 401 to implement the advertising combination recommendation method based on structured Bayesian learning and endogeneity correction provided in the method embodiments of this application.

[0149] In some embodiments, the electronic device may also optionally include: a peripheral device interface and at least one peripheral device. The processor 401, memory 402, and peripheral device interface can be connected via a bus or signal line. Each peripheral device can be connected to the peripheral device interface via a bus, signal line, or circuit board. Indicatively, peripheral devices include, but are not limited to: a touch display screen and a power supply.

[0150] Of course, electronic devices may also include fewer or more components, and this embodiment does not limit this.

[0151] Optionally, this application also provides a computer-readable storage medium storing a program that is loaded and executed by a processor to implement the advertising combination recommendation method based on structured Bayesian learning and endogeneity correction described in the above method embodiments.

[0152] Optionally, this application also provides a computer product including a computer-readable storage medium storing a program, which is loaded and executed by a processor to implement the advertising combination recommendation method based on structured Bayesian learning and endogeneity correction described in the above method embodiments.

[0153] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0154] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for recommending advertising combinations based on structured Bayesian learning and endogeneity correction, characterized in that, The method includes: An observation dataset is constructed based on the acquired advertising transaction data, the full set of advertising products is defined, and the observable feature vector and instrumental variable vector of each advertising product are obtained. The construction of the observation dataset based on the acquired advertising transaction data, defining the full set of advertising products and obtaining the observable feature vector and instrumental variable vector for each advertising product, includes: extracting historical advertising transaction data from the advertising log database to construct the observation dataset. ,in, The total number of samples, Indicates the first The combination of advertised products selected by the user in this display; the full set of advertised products is defined as follows: Extract the observable feature vector of each advertised product. and instrumental variable vector The observable feature vector The instrumental variable vector is used to describe the known characteristics of the advertised product in terms of content, price, and attributes. Exogenous auxiliary variables refer to those that can significantly influence the pricing strategy of advertised goods, but are not directly related to the unobserved potential quality attributes of the goods. Endogenous variables are identified from the observable feature vectors, and regression analysis is performed based on the instrumental variable vectors to calculate residual terms for endogeneity correction. The step of identifying endogenous variables from the observable feature vector and performing regression analysis based on the instrumental variable vector to calculate the residual term used for endogeneity correction includes: identifying endogenous variables from the observable feature vector. And by calling the instrumental variable vector, the linear regression equation is constructed as follows: in, This represents the identified endogenous variables. Represents an instrumental variable vector. The regression coefficients to be estimated are: For the residual term, The transpose of the vector is represented; the linear regression equation is fitted using the least squares method to obtain estimated values ​​of the regression coefficients. And based on the estimated value The residual term for each advertised product is calculated as follows: in, This refers to the residual term used for endogeneity correction; By calling the observable feature vector and residual terms, a structured combined utility function is constructed, which includes nonlinear feature utility, interaction utility and endogenous correction utility. The function is used to describe the user's selection behavior for the advertising combination. The step of calling the observable feature vector and residual terms to construct a structured combined utility function that includes nonlinear feature utility, interaction utility, and endogeneity correction utility includes: defining the combination of advertised products faced by the user. Composed of several advertised products, advertising mix The selection instructions for each item are as follows: When advertising products Included in the combination China Times, Otherwise, it is 0; based on the observable feature vectors of each item in the combination. The aggregate feature vector of the combination is calculated as follows: The structured composition utility function is constructed as follows: in, For nonlinear characteristic utility, For interactive utility, For endogenous modification effect; The complete expression for the structured composition utility function is shown below: in, For the set of parameters to be estimated, For the first The aggregated value of each feature, This represents the number of dimensions in each product feature vector. The coefficient of the linear term, The coefficient of the quadratic term, Let be a binary vector representing the co-occurrence relationship of each pair of items in the combination. For the interaction parameter vector, For the corresponding weight parameters, For the residuals used for endogeneity correction; A local competitive subset is constructed using a signal function that satisfies the equal probability constraint, and the conditional selection probability of the observed sample on the local competitive subset is calculated by combining the structured combination utility function. A global log-likelihood objective function is constructed based on the conditional selection probability, and the optimal model parameters of the structured combined utility function are obtained by using the stochastic gradient optimization method. The optimal model parameters obtained from training are used to call the structured utility function to calculate the selection probability of candidate ad combinations and perform ad combination recommendations.

2. The advertising combination recommendation method based on structured Bayesian learning and endogeneity correction according to claim 1, characterized in that, The step of constructing a local competitive subset using a signal function that satisfies equal probability constraints, and then combining it with the structured combination utility function to calculate the conditional selection probability of the observed sample on the local competitive subset, includes: For each observed true choice We introduce a random mapping as the signal function, denoted as . Based on observed real choices As the initial seed node, it is used to generate [various nodes] by performing a random perturbation operation. There are several different competing combinations, among which A local competitive subset is generated based on a preset number of negative samples. ; For the generated subset Any two combinations and The signal function generates this specific set. The probabilities are equal, meaning they satisfy the following symmetric equation: Construct the following formula for calculating the probability of conditional choice: in, This means that the known competition range is limited to a local subset. Under the premise that the user hits the true choice The probability of conditional choice. and Combinations With competing combinations The aggregated feature vector.

3. The advertising combination recommendation method based on structured Bayesian learning and endogeneity correction according to claim 2, characterized in that, The process of constructing a global log-likelihood objective function based on the conditional choice probability and obtaining the optimal model parameters of the structured combined utility function using a stochastic gradient optimization method includes: Based on the conditional selection probability, a global log-likelihood objective is constructed, and a variational inference framework is introduced, setting the approximate posterior distribution of the parameter to be estimated as an independent Gaussian distribution that satisfies the mean field assumption. A lower bound of evidence is constructed as the objective function for optimization. The lower bound of evidence is used to characterize the difference between the joint probability density of the observed data and parameters and the approximate posterior distribution. In the gradient calculation process, a reparameterization technique is introduced, which introduces a standard normal distribution noise variable and rewrites the parameter to be estimated as a differentiable function of the mean, variance and noise variable to support the backpropagation of the gradient. The stochastic gradient optimization process is performed, which draws samples from the observation dataset in batches and generates corresponding local competitive subsets in real time. The lower bound gradient of evidence for the current batch is calculated based on the reparameterized parameters, and the variational parameters of the approximate posterior distribution are iteratively optimized using the gradient update algorithm until the model converges and the optimal model parameters are output.

4. The advertising combination recommendation method based on structured Bayesian learning and endogeneity correction according to claim 1, characterized in that, The step of using the optimal model parameters obtained from training to call the structured utility function, calculating the selection probability of candidate ad combinations, and performing ad combination recommendations includes: Extract a set of candidate ad combinations that are currently available for display from the ad delivery database. Each candidate combination consists of several ad products. For each candidate combination, the constructed structured combination utility function is invoked, and the optimal parameter set is substituted. Calculate the utility value of this combination; After obtaining the utility values ​​of all candidate ad combinations, the conditional selection probability model is invoked to perform normalization calculation on the utility results, and the selection probability of each candidate ad combination is obtained. The candidate ad combinations are sorted from high to low according to the selection probability, and the ad combination with the highest probability is selected as the preferred placement plan.

5. An advertising combination recommendation system based on structured Bayesian learning and endogeneity correction, characterized in that, include: The vector extraction module is used to construct an observation dataset based on the acquired advertising transaction data, define the full set of advertising products, and obtain the observable feature vector and instrumental variable vector for each advertising product. The construction of the observation dataset based on the acquired advertising transaction data, defining the full set of advertising products and obtaining the observable feature vector and instrumental variable vector for each advertising product, includes: extracting historical advertising transaction data from the advertising log database to construct the observation dataset. ,in, The total number of samples, Indicates the first The combination of advertised products selected by the user in this display; the full set of advertised products is defined as follows: Extract the observable feature vector of each advertised product. and instrumental variable vector The observable feature vector The instrumental variable vector is used to describe the known characteristics of the advertised product in terms of content, price, and attributes. Exogenous auxiliary variables refer to those that can significantly influence the pricing strategy of advertised goods, but are not directly related to the unobserved potential quality attributes of the goods. The residual calculation module is used to identify endogenous variables from the observable feature vector and perform regression analysis based on the instrumental variable vector to calculate residual terms for endogeneity correction. The step of identifying endogenous variables from the observable feature vector and performing regression analysis based on the instrumental variable vector to calculate the residual term used for endogeneity correction includes: identifying endogenous variables from the observable feature vector. And by calling the instrumental variable vector, the linear regression equation is constructed as follows: in, This represents the identified endogenous variables. Represents an instrumental variable vector. The regression coefficients to be estimated are: For the residual term, The transpose of the vector is represented; the linear regression equation is fitted using the least squares method to obtain estimated values ​​of the regression coefficients. And based on the estimated value The residual term for each advertised product is calculated as follows: in, This refers to the residual term used for endogeneity correction; The function construction module is used to call the observable feature vector and residual terms to construct a structured combined utility function that includes nonlinear feature utility, interaction utility and endogeneity correction utility. The function is used to describe the user's choice behavior for the advertising combination. The step of calling the observable feature vector and residual terms to construct a structured combined utility function that includes nonlinear feature utility, interaction utility, and endogeneity correction utility includes: defining the combination of advertised products faced by the user. Composed of several advertised products, advertising mix The selection instructions for each item are as follows: When advertising products Included in the combination China Times, Otherwise, it is 0; based on the observable feature vectors of each item in the combination. The aggregate feature vector of the combination is calculated as follows: The structured composition utility function is constructed as follows: in, For nonlinear characteristic utility, For interactive utility, For endogenous modified utility; the complete expression of the structured combined utility function is shown below: in, For the set of parameters to be estimated, For the first The aggregated value of each feature, This represents the number of dimensions in each product feature vector. The coefficient of the linear term, The coefficient of the quadratic term, Let be a binary vector representing the co-occurrence relationship of each pair of items in the combination. For the interaction parameter vector, For the corresponding weight parameters, For the residuals used for endogeneity correction; The probability calculation module is used to construct a local competitive subset using a signal function that satisfies the equal probability constraint, and to calculate the conditional selection probability of the observed sample on the local competitive subset in combination with the structured combination utility function. The parameter optimization module is used to construct a global log-likelihood objective function based on the conditional selection probability, and to obtain the optimal model parameters of the structured combined utility function using a stochastic gradient optimization method. The ad recommendation module is used to call the structured utility function using the optimal model parameters obtained from training, calculate the selection probability of candidate ad combinations, and perform ad combination recommendations.

6. An electronic device, characterized in that, The device includes a processor and a memory; the memory stores a program that is loaded and executed by the processor to implement an advertising combination recommendation method based on structured Bayesian learning and endogeneity correction as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The storage medium stores a program that, when executed by a processor, is used to implement an advertising combination recommendation method based on structured Bayesian learning and endogeneity correction as described in any one of claims 1 to 4.

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