Irregular time series prediction method and device, medium and program product

Abstract

The invention provides an irregular time sequence prediction method and device, a medium and a program product, and the method comprises the steps: obtaining a to-be-predicted irregular time sequence, the irregular time sequence comprising time stamps with non-uniform time intervals and corresponding observation values; expanding the data on an orthogonal basis function set to respectively obtain a corresponding trend coefficient vector and a periodic coefficient vector, the orthogonal basis function set comprising a trend basis function set and a periodic basis function set; performing fusion modeling processing on the trend coefficient vector and the period coefficient vector to extract a depth feature vector reflecting a trend and period coupling relationship; and based on the depth feature vector, predicting a trend coefficient and a period coefficient corresponding to the target time period, and according to the trend coefficient and the period coefficient, combining a corresponding trend basis function set and a period basis function set, performing reconstruction to obtain a prediction sequence of the target time period. According to the method, through bistatic decomposition and fusion modeling, the precision and stability of irregular time sequence prediction are effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of time series data processing, and in particular to an irregular time series prediction method, device, medium and program product. BACKGROUND

[0002] Time series prediction is widely used in meteorological prediction, power load analysis, financial market fluctuation evaluation and other fields, especially when predicting trends in the future for a long time range, which belongs to the task of long-prediction-span time series modeling. This task puts forward higher requirements for the long-term dependence modeling capability, pattern recognition capability and adaptability to irregular data of the model.

[0003] In the prior art, recurrent neural networks (RNN) and their variants, convolutional neural networks (CNN) or self-attention mechanism driven Transformer models are commonly used to model time series. However, the existing methods generally have the following problems:

[0004] It is difficult to effectively process irregular time series data. In the actual collection process, due to factors such as sensor failure, network delay, etc., the time series often presents non-uniform sampling or data missing. Existing models usually assume that the input is an equal-time-interval sequence, and need to repair the data through interpolation and other preprocessing operations. However, such methods may introduce noise, distort the original time series structure, and thus affect the prediction accuracy of the model.

[0005] Long-term dependence modeling is inefficient. In some prediction tasks, the prediction result of the current time point depends on long-term historical information. Recurrent neural networks and their variants have difficulty in maintaining the stability of long-distance information transmission; while the Transformer model can alleviate this problem, but its self-attention mechanism has high time and space complexity when processing long sequences, resulting in large computational overhead in practical applications.

[0006] It is difficult to decouple and model complex patterns of time series structure. Real time series often contain long-term trends, multiple periodicities, short-term disturbances and other patterns. Existing methods only use a single decomposition technique (such as Fourier transform), which is difficult to accurately model long-term trends and complex periodic characteristics with different shapes at the same time, limiting the representation ability and generalization of the model.

[0007] The model has insufficient generalization ability and robustness. When the input time series has uneven sampling, missing values, external abnormal interference and other conditions, existing methods are prone to prediction performance fluctuations, have poor robustness, and are difficult to adapt to actual complex environments and other problems. SUMMARY

[0008] To address the problems existing in the prior art, the application provides an irregular time series prediction method, an electronic device, a storage medium and a program product, at least to solve the problem that in the prior art, when facing irregular time series with uneven time intervals, due to the lack of a strong adaptive modeling mechanism, it is difficult to directly extract effective features and make accurate prediction, thereby causing the prediction accuracy to be significantly reduced.

[0009] To achieve the above object and other advantages, some embodiments of the application provide the following aspects:

[0010] In a first aspect, some embodiments of the application provide an irregular time series prediction method, comprising:

[0011] Obtaining an irregular time series to be predicted, the irregular time series comprising time stamps with uneven time intervals and corresponding observation values;

[0012] Expanding the irregular time series on an orthogonal basis function set to obtain corresponding trend coefficient vectors and periodic coefficient vectors, respectively, the orthogonal basis function set comprising a trend basis function set and a periodic basis function set;

[0013] Fusing and modeling the trend coefficient vectors and the periodic coefficient vectors to extract a deep feature vector reflecting the coupling relationship between trend and period;

[0014] Based on the deep feature vector, predicting trend coefficients and periodic coefficients corresponding to a target time period, and according to the trend coefficients and the periodic coefficients, combining the corresponding trend basis function set and the periodic basis function set to reconstruct a prediction sequence of the target time period.

[0015] In a second aspect, some embodiments of the application also provide an electronic device, comprising:

[0016] One or more processors; and a memory storing computer program instructions which, when executed, cause the processor to perform the irregular time series prediction method as described in any of the above.

[0017] In a third aspect, some embodiments of the application also provide a computer-readable storage medium having stored thereon computer programs and / or instructions which, when executed by a processor, implement the irregular time series prediction method as described in any of the above.

[0018] In a fourth aspect, some embodiments of the application also provide a computer program product comprising computer programs and / or instructions which, when executed by a processor, implement the irregular time series prediction method as described in any of the above.

[0019] Compared with the related art, in the scheme provided by the embodiments of the present application, the irregular time series is expanded on the orthogonal basis function set composed of the trend basis function set and the periodic basis function set, so that a direct modeling method without interpolation is adopted, and the information loss caused by the interpolation preprocessing in the existing method is effectively avoided. Through the structured modeling and decomposition of the irregular time series containing long-term trend and multiple periodic patterns, the irregular sampling characteristics of uneven time intervals are effectively adapted, and the key features are extracted while the structure information of the original observation data is retained. On this basis, the trend coefficient vector and the periodic coefficient vector are fused for modeling and prediction, and the time series of the target time period is reconstructed by combining the corresponding basis function set, so that the long-term trend and periodic change can be accurately described, thereby improving the accuracy and stability of the irregular time series prediction. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other embodiments can be obtained by those skilled in the art without creative labor.

[0021] Figure 1 is a flow diagram of an irregular time series prediction method provided by the embodiments of the present application;

[0022] Figure 2 is a structural diagram of an electronic device provided by the embodiments of the present application. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be clearly and completely described below with reference to the drawings of the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0024] First embodiment

[0025] The first embodiment of the present application relates to an irregular time series prediction method, referring to Figure 1 The method can include the following steps:

[0026] Step S1: acquiring an irregular time series to be predicted, the irregular time series including time stamps with uneven time intervals and corresponding observation values.

[0027] For step S1, specifically, the irregular time series refers to an observation data sequence with uneven timestamp intervals, which is common in practical acquisition scenarios with missing data, asynchronous sampling, device abnormalities, etc. For example, satellite remote sensing data, medical monitoring data, industrial sensor data, etc. In this embodiment, no interpolation or completion operation is performed on the time series to retain the original irregular sampling characteristics as the subsequent modeling input.

[0028] Step S2: Expanding the irregular time series on the orthogonal basis function set to obtain corresponding trend coefficient vectors and periodic coefficient vectors, respectively. The orthogonal basis function set includes a trend basis function set and a periodic basis function set.

[0029] For step S2, specifically, the irregular time series obtained in step S1 is expanded on a set of constructed orthogonal basis functions to realize separate modeling of different components in the time series. The orthogonal basis function set refers to a set of mutually orthogonal (i.e. inner product is zero) and linearly independent basis functions. These basis functions can collectively span a function space for representing the structural components of any given time series in the space. The orthogonal basis function set includes two parts: one is a trend basis function set for modeling the overall trend of the time series, usually selecting polynomial functions arranged in ascending order of degree; the other is a periodic basis function set for modeling periodic components, usually selecting complex exponential functions or Fourier basis functions with different frequency components.

[0030] The above orthogonal basis function set plays a role similar to multi-dimensional coordinate axes in the function space, with each basis function representing a component in a different direction. By expanding the irregular time series on these basis functions, the original complex signal can be mapped into two independent but complementary substructures: the trend part and the periodic part. This decomposition method makes different components mutually independent in representation, facilitating subsequent separate solving of the trend coefficient vector and the periodic coefficient vector, and further realizing joint modeling and accurate extraction of the trend characteristics and periodic characteristics in the irregular time series.

[0031] Step S3: Fusion modeling of the trend coefficient vector and the periodic coefficient vector to extract a deep feature vector reflecting the coupling relationship between the trend and the periodicity.

[0032] For step S3, specifically, the trend coefficient vector and the period coefficient vector are derived from the expansion results of the irregular time series on the trend basis function set and the period basis function set, respectively, representing the explicit structural expression of the long-term trend and the periodic oscillation in the time series. To further model the potential coupling relationship between the two components, the embodiment adopts a fusion modeling mechanism in this step, which jointly inputs the trend and period information into a nonlinear feature extraction network to mine deep-level interactive features and output a deep feature vector representing the coupling relationship between the two. The deep feature vector retains the key features of the trend change and the period oscillation and enhances the representation ability of the collaborative mode, providing effective support for predicting the trend coefficient and the period coefficient of the target time period.

[0033] Step S4: Based on the deep feature vector, the trend coefficient and the period coefficient corresponding to the target time period are predicted, and according to the trend coefficient and the period coefficient, the corresponding trend basis function set and the period basis function set are combined to reconstruct the prediction sequence of the target time period.

[0034] For step S4, specifically, after completing the double basis expansion and trend-period fusion modeling of the irregular time series, the deep feature vector obtained contains the long-term trend features, periodic oscillation features and their coupling relationship of the sequence. In this step, based on the deep feature vector, regression inference of the trend coefficient and the period coefficient in the target time period is performed, and further used to reconstruct the prediction sequence. Specifically, the deep feature vector obtained by fusion modeling is input into a regression network (time series regression prediction model), and the corresponding trend coefficient and period coefficient in the future target time period are predicted through nonlinear mapping. The obtained coefficients are taken as the regression output results, and then linear combination is performed on the corresponding trend basis function and period basis function to realize the reconstruction of the observation values in the target time period, thereby generating the final prediction sequence.

[0035] Further, the overall architecture of the system applying the irregular time series prediction method mainly includes the following functional modules:

[0036] Data input module: used for receiving the original irregular time series, which contains time stamps with uneven time intervals and corresponding observation values. The system can perform standardization processing on the data and select valid observation points for subsequent modeling;

[0037] Double basis decomposition module: based on the pre-defined orthogonal basis function set, the function space expansion operation of the irregular time series is performed to extract the trend coefficient vector and the period coefficient vector, and complete the structured decomposition of the complex time series;

[0038] The fusion feature modeling module: the trend coefficient and the period coefficient are respectively subjected to nonlinear feature mapping, and the two types of features are subjected to fusion modeling through a deep perception structure (such as a multilayer perception machine), to generate a deep feature vector reflecting the coupling characteristics of long-term trends and periodicity;

[0039] The prediction and reconstruction module: based on the deep feature vector, the trend coefficient and the period coefficient of the target time period are respectively predicted, and the corresponding trend basis function set and the period basis function set are combined for numerical reconstruction, to output the complete prediction sequence of the target time period.

[0040] Through the cooperative work of the above modules, the application realizes a complete end-to-end prediction process. The end-to-end process integrates the whole process from the original irregular time series input to the prediction sequence output in the system, avoids the information loss in the intermediate steps, and guarantees the integrity and continuity of the prediction results. The prediction output not only serves as the final result for external calling, but also participates in the supervision feedback of the training process, is compared with the real observation data, the loss function is calculated, and the loss is used as a supervision signal to optimize the robustness and accuracy of the whole system in the irregular sampling scene.

[0041] Compared with the related art, in the scheme provided by the application, the irregular time series is expanded on the orthogonal basis function set composed of the trend basis function set and the period basis function set, so that a direct modeling method without interpolation is adopted, and the information loss caused by the interpolation preprocessing in the existing method is effectively avoided. Through the structured modeling and decomposition of the irregular time series containing long-term trends and multiple periodic patterns, the irregular sampling characteristics of uneven time intervals are effectively adapted, and the key features are extracted while the structure information of the original observation data is retained. On this basis, the trend coefficient vector and the period coefficient vector are subjected to fusion modeling and prediction, and the time series of the target time period is reconstructed by combining the corresponding basis function set, so that the long-term trend and the periodic change can be accurately described, and the accuracy and stability of the irregular time series prediction are improved.

[0042] Second embodiment

[0043] The second embodiment of the application relates to an irregular time series prediction method. The second embodiment is an improvement based on the first embodiment, and the specific improvement is that in the second embodiment of the application, a specific implementation mode of expanding the orthogonal basis function set based on a linear equation set and a joint least square optimization model is provided, that is, step S2 can further include the following steps:

[0044] Step S201: constructing a first linear equation set for trend modeling, representing the irregular time series as a first linear combination of trend coefficients on the trend basis function set, and the trend basis function set adopts a polynomial basis function arranged in ascending order of degree.

[0045] In this step, within any finite time interval [t0, t1], a subsequence of an irregular time series can be considered as a time series segment f(t), which can be represented on its domain as a superposition of the trend basis function g(t) and the periodic basis function p(t):

[0046] f(t) = g(t) + p(t)

[0047] To model the long-term trend component in irregular time series, a first set of linear equations for trend modeling is constructed. Specifically, a set of polynomial basis functions arranged in ascending order is selected as the trend basis function set, which is defined as:

[0048] φ k (t)=t k k = 0, 1, ..., K

[0049] Where K is the highest order of the basis function, used to adjust the complexity of trend modeling; t represents the timestamp, and φ k (t) represents the basis function of the k-th order polynomial.

[0050] By projecting the observation points of the original time series onto this set of basis functions, a trend modeling formula in the form of a linear combination can be established as follows:

[0051]

[0052] Where g(t) is a function representing the trend term, and c k The trend coefficient vector to be determined reflects the projection intensity of the original time series onto the k-th order polynomial.

[0053] Substituting the N observation points into the above equation yields the first system of linear equations, which is used to solve for the unknown trend coefficient vector, and takes the following form:

[0054]

[0055] These N observation points constitute N linear equations, where the unknowns are c0, c1, ..., c K Write these equations in matrix form:

[0056] T·c=f

[0057] in, This is a trend basis function matrix, where each row corresponds to a polynomial basis function value at a given time point. c = [c0, c1, ..., c K ], where f is the trend coefficient vector to be determined; f = [f(t1), f(t2), ..., f(t)] N)], which is a vector consisting of corresponding observation values.

[0058] Therefore, each observation point of the irregular time series is brought into the trend modeling formula, that is, its corresponding time stamp is substituted into the trend modeling expression composed of polynomial basis functions as an independent variable, to construct the first linear equation set for trend modeling. The linear equation set establishes an explicit algebraic relationship between the original observation data and the trend basis functions, so that the entire trend modeling problem is converted into a linear solution problem of the trend coefficient vector, facilitating subsequent parameter estimation by optimization methods such as least squares, thereby realizing the structured modeling of long-term change trends in the original time series.

[0059] Step S202: Constructing a second linear equation set for periodic modeling, representing the irregular time series as a second linear combination of periodic coefficients on a periodic basis function set, and the periodic basis function set adopts complex exponential basis functions with different frequency components.

[0060] In this step, in order to effectively capture various periodic components in the time series, a set of complex exponential basis functions with different frequencies can be selected as the periodic basis function set. Each basis function corresponds to a specific frequency component and is used to model the periodic fluctuation characteristics of the time series at that frequency. Preferably, the periodic basis function set can be constructed using Fourier basis functions, which are a family of functions composed of multiple sine and cosine functions with different frequencies and amplitudes, and have good periodicity and spectral representation capability. By weighting and superimposing multiple Fourier basis functions with different frequencies, the complex periodic variation pattern formed by the superposition of multiple periodic components in the time series can be effectively represented, thereby realizing effective decomposition and reconstruction of the periodic variation pattern.

[0061] In the modeling process, the observation points of the original time series are projected onto these periodic basis functions to calculate the corresponding weighting coefficients, i.e., the periodic coefficient vector. For this purpose, the periodic basis functions can be defined as follows:

[0062] j = 0, 1, …, J

[0063] where ω j represents the frequency component of the jth periodic basis function; ψ j (t) is the jth periodic basis function, used to model the periodic fluctuation characteristics at the corresponding frequency.

[0064] Based on the periodic basis function set, the periodic function p(t) that describes the periodic components in the time series can be represented as the following periodic function expression:

[0065]

[0066] where dj is the to-be-solved periodic coefficient, reflecting the projection intensity of the original time series in the jth frequency dimension; Re(·) represents taking the real part of a complex number to ensure that the final modeling result is a real-valued function, and the output is a real-valued time series.

[0067] For the N observation points contained in the irregular time series, each observation time point t n is substituted into the above periodic function expression to obtain the following second linear equation group:

[0068]

[0069] The unknowns in this equation group are the periodic coefficient vector d = [d0, d1, …, d J ], which can be solved by the least squares method to minimize the residual sum of squares between the predicted value and the actual observation value.

[0070] By constructing the second linear equation group for periodic modeling, the structural expression of the periodic fluctuation characteristics in the irregular time series is realized. This process uses a set of complex exponential basis functions with different frequency components as the periodic basis function set, models the periodic components in the time series through linear combination, and effectively captures the periodic patterns at different frequency scales in the signal. At the same time, the complex exponential basis function has good orthogonality and frequency resolution, which can improve the interpretability and controllability of the modeling process while ensuring the modeling accuracy.

[0071] Step S203: Based on the first linear equation group and the second linear equation group, a joint least squares optimization model is constructed to minimize the residual sum of squares between the predicted value of the basis function combination at each time point and the original observation value. By solving the weighted coefficients in the first linear combination and the second linear combination, the trend coefficient vector and the periodic coefficient vector are obtained, respectively, as the structured representation of the irregular time series in the orthogonal function subspace.

[0072] In this step, the basis function expansion of the trend item and the periodic item is substituted to obtain the following joint fitting model:

[0073]

[0074] where t i represents the timestamp of the irregular time series. The joint least squares loss function is constructed as:

[0075]

[0076] where g(t i ) is the trend item, representing the linear projection of the original time series on the trend basis function set; p(t i) is a periodic term, representing the linear projection of the original time series onto the set of periodic basis functions; vectors c, d represent the trend coefficient vector and the periodic coefficient vector, respectively.

[0077] The loss function measures the fitting error between the reconstructed sequence value and the original observation value. By optimizing the loss function, the optimal trend coefficient vector c = [c0, c1, …, c K ] and the periodic coefficient vector d = [d0, d1, …, d J ] can be jointly solved. The reconstructed value at each time point is as close as possible to the original observation data by combining the trend basis function and the periodic basis function.

[0078] Further, the embodiment also includes:

[0079] The column vectors of each basis function in the set of trend basis functions and the set of periodic basis functions are constructed into basis function matrices, and each basis function matrix is normalized to improve the numerical stability of the coefficient fitting.

[0080] Specifically, the function values of each basis function in the set of trend basis functions and the set of periodic basis functions at different time stamps are regarded as column vectors, and are arranged to form a basis function matrix. Specifically, for the polynomial basis function set {φ k (t) = t k} used for trend modeling, the values of all trend basis functions can be calculated at each original time stamp t i , to construct a trend basis function matrix where each column corresponds to the value of a basis function at all time points, N is the length of the time series, and K is the order of the trend basis function. Similarly, for the complex exponential basis function set used in periodic modeling, the real part of the value at each time point is calculated as the value of the periodic basis function, to construct a periodic basis function matrix where J is the number of periodic basis functions.

[0081] In actual modeling, the value range of the trend basis function and the periodic basis function at different time scales may differ greatly, for example, the polynomial basis function will amplify rapidly as the time increases, while the periodic basis function generally fluctuates in the range of [-1, 1]. This will result in a significant difference in numerical scale of different columns in the constructed trend basis function matrix Φ and periodic basis function matrix Ψ, thereby increasing the condition number when solving the linear equation system, causing numerical instability or even solution drift. Therefore, for the trend basis function matrix Φ and the periodic basis function matrix Ψ constructed above, the columns of each are normalized to have a uniform numerical scale. Specifically, the standardization method with mean zero and standard deviation one, or unit norm normalization (for example, normalizing each column vector to unit L2 norm) can be used.

[0082] The normalization processing helps to alleviate the interference of the differences in the value range and scale of different basis functions on the fitting result, makes the fitting solution closer to the global optimum, improves the numerical stability and convergence speed of the subsequent coefficient solving process, and obtains more accurate and more explainable modeling coefficients.

[0083] As can be seen, in the scheme provided by the embodiments of the application, by introducing the bilinear equation structure of trend modeling and periodic modeling, and based on the joint least square optimization mechanism to solve the coefficients, not only the decoupling and structured expression of the long-term trend and periodic components in the irregular time series are realized, but also the accuracy of coefficient estimation and the robustness of model expression are further improved.

[0084] Third embodiment

[0085] The third embodiment of the application relates to an irregular time series prediction method. The third embodiment is an improvement based on the first embodiment, and the specific improvement is that in the third embodiment of the application, a deep fusion mechanism based on joint modeling of the trend coefficient vector and the periodic coefficient vector is provided, that is, step S3 can further include the following steps:

[0086] Step S301: performing nonlinear feature mapping on the trend coefficient vector and the periodic coefficient vector respectively, and constructing a first feature representation tensor for representing the trend component and a second feature representation tensor for representing the periodic component.

[0087] In this step, the trend coefficient vector c and the periodic coefficient vector d obtained from the linear modeling stage are respectively subjected to nonlinear feature mapping operations to extract higher-order structure patterns and potential semantic information therefrom. The mapping results are respectively constructed as a first feature representation tensor T1 for representing the trend component and a second feature representation tensor T2 for representing the periodic component.

[0088] To achieve the above nonlinear mapping process, the embodiment adopts a network architecture of MLP-Mixer (Multi-Layer Perceptron Mixer). Unlike the attention mechanism used in the Transformer model or the convolution kernel used in the traditional neural network, the MLP-Mixer network architecture is modeled only with fully connected layers. The architecture regards each input coefficient vector (trend coefficient vector or cycle coefficient vector) as a two-dimensional feature matrix, alternately applies fully connected layers in the channel dimension (representing feature types) and the coefficient dimension (representing time or position), and deeply mixes the internal information of the trend coefficient vector or the cycle coefficient vector to output a higher-order nonlinear feature representation tensor. Specifically, modeling in the channel dimension helps to explore the potential semantic association between different features, while modeling in the coefficient dimension enhances the model's perception and representation ability of time series structure. In this way, the semantic information can be fully mixed within the feature dimension, while the structural pattern can be captured in the time series dimension, thereby improving the internal modeling ability of the trend feature or the cycle feature and ensuring the expression accuracy and richness of each type of feature.

[0089] Formally, the mapping process can be recorded as:

[0090] T1=F trend (c),T2=F period (d)

[0091] wherein F trend (·) represents a nonlinear mapping function for trend modeling, F period (·) represents a nonlinear mapping function for cycle modeling, and T1 and T2 are the first feature representation tensor and the second feature representation tensor, respectively.

[0092] Step S302: The first feature representation tensor and the second feature representation tensor are spliced along a preset dimension, and the spliced feature representation tensor is input into a multi-layer perceptron network to perform cross-dimension modeling and information fusion, thereby obtaining a fusion feature vector reflecting the coupling relationship between the trend and the cycle.

[0093] In this step, the first feature representation tensor T1 and the second feature representation tensor T2 are spliced according to a preset dimension to form a spliced feature representation tensor Tconcat, which is used for subsequent coupling modeling. The splicing operation can be carried out in the channel dimension or the time dimension, depending on the specific task configuration and feature space structure.

[0094] The concatenated feature representation tensor Tconcat is input into a shared-parameter multi-layer perceptron network to perform nonlinear interaction and cross-dimensional modeling operations. The multi-layer perceptron network is composed of several fully connected layers, and activation functions (such as ReLU or GELU) and normalization mechanisms (such as LayerNorm or BatchNorm) can be inserted between layers to enhance representation capability and numerical stability. The multi-layer perceptron network has the characteristic of sharing parameters in the trend and cycle fusion process, which means that the same set of network weight parameters is repeatedly used for forward propagation in different positions of the fusion feature tensor, i.e., the same MLP structure is applied in multiple channel dimension positions, effectively reducing the total number of network parameters and improving the generalization ability and training stability of the model. Unlike traditional independent MLP networks, the parameter sharing mechanism ensures consistency and symmetry in the processing of each sub-position during fusion, avoiding information redundancy and overfitting problems.

[0095] Step S303: The fusion feature vector is processed in parallel on multiple preset cycle scales to extract cycle features of different frequency components, and a deep feature vector representing multi-scale cycle patterns is generated based on an adaptive aggregation mechanism.

[0096] In this embodiment, step S303 specifically includes:

[0097] Step S3031: Based on the preset cycle scale, a corresponding feature modeling branch structure is constructed respectively, and the cycle scale has different frequency resolutions for covering periodic change patterns in multiple time ranges;

[0098] Step S3032: The fusion feature vector is input into each feature modeling branch structure in parallel to extract feature representation vectors under different cycle scales;

[0099] Step S3033: Based on an adaptive fusion mechanism, the feature representation vectors corresponding to each cycle scale are combined by weighting to generate a deep feature vector representing the coupling relationship of multiple cycle scales.

[0100] Specifically, the cycle scale is used to describe the periodic changes of different frequency levels in the time series, covering short cycles (such as daily or hourly), medium cycles (such as weekly or monthly), and long cycles (such as quarterly or annual) in different time ranges.

[0101] According to modeling requirements, the feature modeling branch structure can include but is not limited to: convolutional neural network, recurrent neural network, frequency domain filter and multi-head attention mechanism module, etc. According to the frequency characteristics of the corresponding period scale, each feature modeling branch structure flexibly configures the modeling method, for example: when modeling short periods, a convolutional neural network (CNN) with a small receptive field can be used to capture local changes; when modeling medium periods, a gated recurrent unit (GRU) or a long short-term memory network (LSTM) can be combined for time series modeling; when modeling long periods, a frequency domain filter or windowed Fourier transform can be used to extract low-frequency trend components; if necessary, a multi-head self-attention mechanism can be introduced to capture periodic dependency structures across time ranges. The output of each feature modeling branch structure is a feature representation vector corresponding to its target period scale.

[0102] To integrate the feature representations extracted under each period scale, the present embodiment introduces an adaptive fusion mechanism. According to the context importance of the output features of each period scale branch, the corresponding weight coefficients are calculated, and a weighted combination operation is performed, finally generating a unified deep feature vector to represent the coupling relationship and periodic behavior pattern of the fused features under multiple period scales. This fusion mechanism can be implemented using attention weight distribution strategies, gating mechanisms or learning-based scoring functions, etc. to achieve adaptive modeling of the importance of different period scales. The final generated deep feature vector will be used as the input of the subsequent prediction module, improving the model's ability to model periodic trend changes and prediction accuracy.

[0103] As can be seen, in the scheme provided by the embodiments of the present application, by constructing a multi-stage modeling mechanism for decoupling and fusion of trends and periods, accurate modeling and deep coupling expression of trend changes and periodic components can be achieved when facing the complex dynamic characteristics of irregular time series, significantly improving the recognition ability and generalization performance of multi-scale time series patterns, thereby improving the accuracy and stability of the overall prediction.

[0104] It should be noted that the third embodiment of the present application can also be an improvement based on any one or more of the first embodiment to the second embodiment.

[0105] Fourth Embodiment

[0106] The fourth embodiment of the present application relates to an irregular time series prediction method. The fourth embodiment is an improvement based on the first embodiment, and the specific improvement is that in the fourth embodiment of the present application, a prediction output mechanism based on trend and period coefficient decoupling modeling is provided, that is, step S4 can further include the following steps:

[0107] Step S401: input the deep feature vector into the pre-trained linear regression prediction model to predict the trend coefficient and the period coefficient corresponding to the target time period, respectively;

[0108] Step S402: Based on the timestamp information of the target time period, each basis function in the trend basis function set and the periodic basis function set is called respectively, and numerical expansion is performed in timestamp order to construct a trend basis function matrix and a periodic basis function matrix;

[0109] Step S403: Linearly combining the trend coefficient with the trend basis function matrix to generate a trend component sequence;

[0110] Step S404: Linearly combining the periodic coefficient with the periodic basis function matrix to generate a periodic component sequence;

[0111] Step S405: Adding the trend component sequence and the periodic component sequence to obtain the prediction sequence of the target time period.

[0112] Specifically, the deep feature vector is input into the linear regression prediction model which is trained in advance. The model can include multiple linear regression layers to output the trend coefficient and the periodic coefficient of the target time period, respectively. The prediction process does not depend on uniform sampling of time, but directly constructs a vector representation based on a specific timestamp, realizing joint prediction of future trend changes and periodic structures.

[0113] The linear regression prediction model is trained by supervised learning. Specifically, in the training phase, the historical time series data is used as the training data set. First, the trend coefficient and the periodic coefficient corresponding to the time period are extracted as the training label, and the deep representation vector containing multi-scale features is constructed as the input feature. The input and output constitute a set of supervised training samples. The model is internally set with multiple linear regression layers, which are used to predict the trend coefficient and the periodic coefficient, respectively. The parameters of the regression layer are optimized by minimizing the mean square error loss function between the predicted coefficient and the real coefficient. During the training process, batch gradient descent or its variants can be used for iterative update until the model converges. The trained prediction model can output the trend coefficient and the periodic coefficient corresponding to the target time period according to any given deep feature vector.

[0114] In the prediction scenario, the prediction result is not a single value, but a time series, i.e., the values of multiple future time points t∈[t L+1 ,t L+H ] are predicted. Since the trend basis function set {φ k (t)} and the periodic basis function set {ψ j (t)} are defined on a continuous time domain or a discrete point set. In order to realize efficient reconstruction in the form of matrix multiplication, these functions need to be expanded at all future time points to form the corresponding trend basis function matrix and the periodic basis function matrix where H is the number of predicted steps, i.e., the number of future timestamps.

[0115] In generating the trend component sequence, the trend basis functions can be expanded point by point in numerical value at each timestamp within the prediction period, so as to construct a corresponding trend basis function matrix, wherein each row represents the value of a basis function at all prediction time points. Then, by performing matrix multiplication operation on the predicted trend coefficients and the basis function matrix, the trend component sequence within the entire prediction period can be efficiently generated. Similarly, in generating the periodic component sequence, the periodic basis functions can be expanded at the target timestamp to form a periodic basis function matrix, and matrix multiplication operation is performed on the predicted periodic coefficients to efficiently generate the periodic component sequence within the entire prediction period.

[0116] After the trend component sequence and the periodic component sequence are constructed, further addition operation is performed to add the numerical values of the two at each prediction time point, to obtain the final prediction sequence. That is, for any time point t ∈ [t L+1 ,t L+H ] within the prediction period, the prediction value can be expressed as:

[0117]

[0118] where, φk(t) represents the value of the kth trend basis function at time t; φk represents the kth trend coefficient predicted by the model; k φk(t) represents the value of the kth trend basis function at time t; φk represents the kth trend coefficient predicted by the model; ψj(t) represents the value of the jth periodic basis function at time t; ψj represents the jth periodic coefficient predicted by the model; j ψj(t) represents the value of the jth periodic basis function at time t; ψj represents the jth periodic coefficient predicted by the model; ψj(t) represents the value of the jth periodic basis function at time t; ψj represents the jth periodic coefficient predicted by the model;

[0119] Through the above addition operation, the prediction sequence can not only cover the long-term change direction reflected by the trend term, but also capture the short-term oscillation or repeated pattern embodied by the periodic term, so as to improve the description ability of the prediction model to behaviors of different time scales, and realize the organic combination of trend and periodicity. In addition, it also has good interpretability: the trend part is composed of a group of definable polynomial basis functions, which can correspond to linear growth or slow change behavior in economic, environmental and other backgrounds; the periodic part is expressed by periodic basis functions (such as Fourier basis), which can reflect seasonal and periodic fluctuation characteristics. Through observation and analysis of each coefficient, further causal explanation or sensitivity analysis can be carried out.

[0120] As can be seen, in the scheme provided by the embodiments of the present application, the decoupling prediction and reconstruction mechanism based on the trend coefficient and the period coefficient is introduced, which can make full use of the trend and periodic information contained in the aforementioned deep fusion features, and realize efficient prediction of the trend coefficient and the period coefficient at multiple future time points. At the same time, by constructing the trend basis function matrix and the period basis function matrix, the trend component sequence and the period component sequence are respectively generated in a linear combination manner, and the complete predicted time sequence is reconstructed by summation calculation, which not only improves the interpretability of the prediction process, but also realizes the separable modeling of the prediction structure, which is beneficial to the flexibility and robustness of the model when processing complex time structure, thereby improving the overall prediction accuracy and generalization ability.

[0121] It should be noted that the fourth embodiment of the present application can also be an improvement based on any one or more of the first to third embodiments.

[0122] In addition, some embodiments of the present application also provide an electronic device. The electronic device can be various forms of digital computers, such as laptops, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, etc. The electronic device can also be various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices.

[0123] The electronic device includes one or more processors, and a memory storing computer program instructions which, when executed, cause the processor to perform an irregular time series prediction method provided by any one or more of the above embodiments. Figure 2 An exemplary structural diagram of the electronic device is disclosed. The electronic device includes one or more processors 1101, a memory 1102, and an interface for connecting components, including a high-speed interface and a low-speed interface. Various components are connected to each other by different buses, and can be installed on a common motherboard or in other ways as needed. The processor can process instructions executed within the electronic device, including graphical information stored in the memory or on the memory to display a GUI on an external input / output device, such as a display device coupled to the interface. In some other embodiments, multiple processors and / or multiple buses can be used with multiple memories and multiple memories, if necessary. Similarly, multiple electronic devices can be connected, each providing part of the necessary operations. Among them, the components shown herein, their connections and relationships, and their functions are only examples, and are not intended to limit the implementation of the present application described and / or claimed herein.

[0124] The electronic device can further include an input device 1103 and an output device 1104. The processor 1101, the memory 1102, the input device 1103, and the output device 1104 can be connected through a bus or other means, Figure 2 The connection through the bus is taken as an example.

[0125] The input device 1103 can receive input digital or character information, and generate key signal input related to user settings and function control of the electronic device, such as a touch screen, a keypad, a mouse, a trackpad, a touchpad, a pointing stick, one or more mouse buttons, a trackball, a joystick, and the like. The output device 1104 can include a display device, an auxiliary lighting device (for example, an LED), a tactile feedback device (for example, a vibration motor), and the like. The display device can include, but is not limited to, a liquid crystal display, a light-emitting diode display, and a plasma display. In some embodiments, the display device can be a touch screen.

[0126] To provide interaction with the user, the electronic device can be a computer. The computer has a display device (for example, a cathode ray tube or an LCD monitor) for displaying information to the user, and a keyboard and a pointing device (for example, a mouse) through which the user can provide input to the computer. Other kinds of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (for example, visual feedback, auditory feedback); and input from the user can be received in any form (for example, voice input or tactile input).

[0127] In the embodiments of the present application, the computer program / instructions are stored on the computer readable medium, and the computer program / instructions are executed by the processor to implement the irregular time series prediction method provided by any one or more of the above embodiments. The computer readable medium can be included in the electronic device described in the above embodiments; or can exist separately without being assembled into the device. The above computer readable medium carries one or more computer readable instructions.

[0128] The memory 1102 can be used as a non-transitory computer readable storage medium for storing non-transitory software programs, non-transitory computer executable programs, and modules. The processor 1101 executes various function applications and data processing of the server by running the non-transitory software programs, instructions, and modules stored in the memory 1102, so as to implement the program instructions / modules corresponding to the method provided by any one or more of the above embodiments in the embodiments of the present application.

[0129] The memory 1102 can include a program region and a data region, where the program region can store an operating system, an application required by at least one function, and the like, and the data region can store data created according to use of the electronic device, and the like. In addition, the memory 1102 can include a high-speed random access memory, and can further include a non-transitory memory such as at least one of a magnetic disk storage device, a flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory 1102 can optionally include a memory disposed remotely with respect to the processor 1101, and these remote memories can be connected to the electronic device through a network. Examples of the network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and a combination thereof.

[0130] It should be noted that the computer-readable medium described in the present application can be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable medium may, for example, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or apparatus, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the computer-readable medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or apparatus.

[0131] The computer-readable medium includes permanent and non-permanent, removable and non-removable media, and can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory, static random access memory, dynamic random access memory, other types of random access memory, read-only memory, electrically erasable programmable read-only memory, flash memory or other memory technology, read-only optical disc, digital versatile disc or other optical storage, magnetic cassette tape, magnetic tape disc storage or other magnetic storage device, or any other non-transmission medium that can be used to store information accessible by a computing device.

[0132] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network ("LAN") or a wide area network ("WAN"), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0133] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware or any combination thereof. For example, the embodiments can be implemented by an application specific integrated circuit, a general purpose computer or any other similar hardware device. In some embodiments, the software programs of the embodiments can be executed by a processor to implement the above steps or functions. Similarly, the software programs of the embodiments (including related data structures) can be stored in a computer readable recording medium, such as a RAM memory, a magnetic or optical drive or a floppy disk and the like. In addition, some steps or functions of the embodiments can be implemented by hardware, such as a circuit cooperating with a processor to perform the steps or functions.

[0134] The computer program product provided by the embodiments of the present application includes one or more computer programs / instructions, which, when executed by a processor, generate all or part of the processes or functions described in the embodiments of the present application. The computer can be a general purpose computer, a special purpose computer, a computer network or other programmable device. The computer instructions can be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center through wired (such as coaxial cable, optical fiber, digital subscriber line) or wireless (such as infrared, wireless, microwave, etc.) mode. The computer readable storage medium can be any available medium accessible by a computer or a data storage device such as a server, data center and the like integrated with one or more available media. The available media can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk) and the like.

[0135] The computer program product of the present application can be a computer program including a plurality of program instructions that control at least one processing unit of a computer to implement the method according to the embodiments of the present application. The computer program product of the present application can be stored in a computer readable storage medium (media), including but not limited to: optical read only memory (ROM), RAM, soft disc, and the like, which is coupled to the computer system bus via a coupling means, which enables the computer to read information in the computer program product, so as to implement the methods or achieve the device according to the embodiments of the present application.

[0136] The scope of the present application is defined by the appended claims rather than the description preceding it, therefore, all changes and modifications that come within the meaning and range of equivalency of the claims are to be embraced by the application. No feature of the application should be considered critical unless expressly stated in the claims. In addition, no single feature or combination of features should be considered essential unless expressly stated in the claims. Further, the mention herein of certain terms in the description and / or the claims should not be considered limiting, unless expressly stated to that effect. Specifically, any use of the terms "include", "have", "with", or the like, is not meant to exclude the presence of other elements or steps. It should be further noted that the terms "comprise", "comprising", "have", "has", "including", "including", "containing", "including" or any other variation thereof, are not meant to exclude other elements or steps. The terms "first", "second", "third", "fourth", "fifth" or the like are used merely to distinguish one element from another, and do not require a particular order or sequence. The use of the terms "first", "second", "third", "fourth", "fifth" or the like does not indicate relative importance.

[0137] The above description is merely illustrative of the application, and is not intended to limit the scope of the application. Any modification or equivalent arrangement of the application, which falls within the scope of the application, should be encompassed by the scope of the application. Therefore, the scope of the application should be defined by the scope of the claims. The above examples are intended to be exemplary and non-limiting.

Claims

1. A method for predicting irregular time series, characterized in that, include: Obtain the irregular time series to be predicted, wherein the irregular time series includes timestamps with uneven time intervals and corresponding observations; The irregular time series is expanded on an orthogonal basis function set to obtain the corresponding trend coefficient vector and period coefficient vector, respectively. The orthogonal basis function set includes a trend basis function set and a period basis function set. The trend coefficient vector and the period coefficient vector are fused and modeled to extract a deep feature vector that reflects the coupling relationship between trend and period. Based on the deep feature vector, the trend coefficient and period coefficient corresponding to the target time period are predicted, and the predicted sequence of the target time period is reconstructed according to the trend coefficient and the period coefficient, combined with the corresponding trend basis function set and the period basis function set.

2. The irregular time series prediction method according to claim 1, characterized in that, The step of expanding the irregular time series on an orthogonal basis function set to obtain the corresponding trend coefficient vector and period coefficient vector includes: Construct a first set of linear equations for trend modeling, representing the irregular time series as a first linear combination of trend coefficients on the set of trend basis functions, wherein the set of trend basis functions adopts polynomial basis functions arranged in ascending order of order; A second set of linear equations is constructed for periodic modeling, which represents the irregular time series as a second linear combination of periodic coefficients on the set of periodic basis functions, wherein the set of periodic basis functions adopts complex exponential basis functions with different frequency components; Based on the first and second linear equations, a joint least squares optimization model is constructed. The objective is to minimize the sum of squared residuals between the predicted values ​​and the original observed values ​​at each time point of the basis function combination. By solving the weighting coefficients in the first and second linear combinations, the trend coefficient vector and the period coefficient vector are obtained respectively, which serve as the structured representation of the irregular time series on the orthogonal function subspace.

3. The irregular time series prediction method according to claim 2, characterized in that, The step of expanding the irregular time series on an orthogonal basis function set to obtain the corresponding trend coefficient vector and period coefficient vector further includes: The trend basis function set and the column vectors of each basis function in the periodic basis function set are used to construct a basis function matrix, and each basis function matrix is ​​normalized to improve the numerical stability of the coefficient fitting.

4. The irregular time series prediction method according to claim 1, characterized in that, The step of fusing the trend coefficient vector and the period coefficient vector to extract a deep feature vector reflecting the coupling relationship between trend and period includes: Nonlinear feature mapping is performed on the trend coefficient vector and the period coefficient vector respectively to construct a first feature representation tensor for characterizing the trend component and a second feature representation tensor for characterizing the period component. The first feature representation tensor and the second feature representation tensor are concatenated along a preset dimension, and the concatenated feature representation tensor is input into a multilayer perceptron network to perform cross-dimensional modeling and information fusion, thereby obtaining a fused feature vector that reflects the coupling relationship between trends and cycles. The fused feature vector is processed in parallel on multiple preset periodic scales to extract periodic features of different frequency components, and a deep feature vector representing multi-scale periodic patterns is generated based on an adaptive aggregation mechanism.

5. The irregular time series prediction method according to claim 4, characterized in that, The step of processing the fused feature vector in parallel across multiple preset periodic scales to extract periodic features of different frequency components, and generating a deep feature vector representing a multi-scale periodic pattern based on an adaptive aggregation mechanism, includes: Based on a preset periodic scale, corresponding feature modeling branch structures are constructed respectively. The periodic scale has different frequency resolutions to cover periodic change patterns in multiple time ranges. The fused feature vectors are input in parallel into each feature modeling branch structure to extract feature representation vectors at different periodic scales. Based on the adaptive fusion mechanism, the feature representation vectors corresponding to each periodic scale are weighted and combined to generate a deep feature vector representing the coupling relationship of multiple periodic scales.

6. The irregular time series prediction method according to claim 1, characterized in that, The step of predicting the trend coefficient and periodic coefficient corresponding to the target time period based on the deep feature vector, and reconstructing the predicted sequence of the target time period based on the trend coefficient and the periodic coefficient, combined with the corresponding trend basis function set and periodic basis function set, includes: The deep feature vector is input into the pre-trained linear regression prediction model to predict the trend coefficient and periodic coefficient corresponding to the target time period, respectively. Based on the timestamp information of the target time period, each basis function in the trend basis function set and the period basis function set is called respectively, and the values ​​are expanded in the order of timestamps to construct the trend basis function matrix and the period basis function matrix; The trend coefficient is linearly combined with the trend basis function matrix to generate a trend component sequence; The periodic coefficients are linearly combined with the periodic basis function matrix to generate a periodic component sequence; The trend component sequence and the periodic component sequence are summed to obtain the prediction sequence for the target time period.

7. The irregular time series prediction method according to any one of claims 1-6, characterized in that, The set of periodic basis functions is constructed using Fourier basis functions, which consist of multiple sine and cosine functions with different frequencies and amplitudes. These functions are used to characterize the periodic change patterns formed by the superposition of multiple periodic components in the irregular time series through weighted superposition, so as to achieve effective decomposition and reconstruction of the periodic change patterns.

8. An electronic device, characterized in that, The electronic device includes: One or more processors; and a memory storing computer program instructions that, when executed, cause the processors to perform the irregular time series forecasting method as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program and / or instructions stored thereon, characterized in that, When the computer program and / or instructions are executed by the processor, they implement the irregular time series prediction method as described in any one of claims 1-7.

10. A computer program product comprising a computer program and / or instructions, characterized in that, When the computer program and / or instructions are executed by the processor, they implement the irregular time series forecasting method as described in any one of claims 1-7.

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