Multi-dimensional prediction ensemble method and apparatus, terminal device, and storage medium

Abstract

The application is suitable for the technical field of intelligent terminals, and provides a multi-dimensional prediction integration method, device, terminal equipment and storage medium. The method comprises the following steps: obtaining a target input; using at least two base models to respectively predict the target input, obtaining a multi-dimensional prediction vector output by each base model, and each multi-dimensional prediction vector containing prediction values of multiple dimensions; according to a preset weight parameter set, performing weighted fusion on the multi-dimensional prediction vectors output by the at least two base models, and generating a multi-dimensional integrated prediction result of the target input; wherein the preset weight parameter set is determined by using a verification set containing multiple verification samples and corresponding real multi-dimensional labels, and is optimized and determined with the aim of minimizing the weighted fusion prediction error. The application can improve the accuracy of multi-dimensional prediction.

Description

Technical Field

[0001] This application relates to the field of smart terminal technology, and in particular to a multidimensional prediction integration method, apparatus, terminal device, and storage medium. Background Technology

[0002] Multi-dimensional output prediction tasks are widespread in industries, scientific research, and data analysis, such as simultaneously predicting multiple performance parameters or experimental results. In multi-dimensional output prediction tasks, such as multi-output regression or multi-label classification, ensemble learning methods are often used to fuse multiple base models to improve prediction performance.

[0003] However, under small sample conditions, the number of samples available for training the base model is limited. To select a model and tune hyperparameters, a portion of the training data is typically allocated as a validation set, further compressing the available sample size for model learning. Furthermore, weights in ensemble fusion are often evenly distributed or set based on a single-dimensional evaluation metric. This method of weight determination fails to reflect the differences in the contribution of the base model to outputs across different dimensions, thus limiting the accuracy of multidimensional predictions.

[0004] Therefore, improving the accuracy of multidimensional prediction is a problem that needs to be solved. Summary of the Invention

[0005] This application provides a multidimensional prediction integration method, apparatus, terminal device, and storage medium, which can improve the accuracy of multidimensional prediction.

[0006] In a first aspect, embodiments of this application provide a multidimensional prediction ensemble method, including: Obtain the target input; At least two base models are used to predict the target input to obtain a multidimensional prediction vector output by each base model. Each multidimensional prediction vector contains prediction values ​​in multiple dimensions. Based on a preset set of weight parameters, the multidimensional prediction vectors output by the at least two base models are weighted and fused to generate a multidimensional integrated prediction result for the target input. The preset set of weight parameters is determined by optimizing a validation set containing multiple validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error.

[0007] Secondly, embodiments of this application provide a multidimensional prediction integration device, comprising: The input acquisition unit is used to acquire the target input; A prediction unit is used to predict the target input using at least two base models respectively, and to obtain a multidimensional prediction vector output by each base model, wherein each multidimensional prediction vector contains prediction values ​​of multiple dimensions. The prediction fusion unit is used to perform weighted fusion of the multidimensional prediction vectors output by the at least two base models according to a preset set of weight parameters to generate a multidimensional fusion prediction result of the target input; wherein, the preset set of weight parameters is optimized and determined by using a validation set containing multiple validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error.

[0008] Thirdly, embodiments of this application provide a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the multidimensional prediction integration method as described in the first aspect above.

[0009] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the multidimensional prediction integration method as described in the first aspect above.

[0010] Fifthly, embodiments of this application provide a computer program product that, when run on a terminal device, causes the terminal device to execute the multidimensional prediction integration method as described in the first aspect above.

[0011] In this embodiment, after obtaining the target input, at least two base models are used to predict it, resulting in multiple multidimensional prediction vectors. Each multidimensional prediction vector contains predicted values ​​in multiple dimensions. These multiple multidimensional prediction vectors are then weighted and fused according to a preset set of weight parameters to generate a multidimensional integrated prediction result. The preset set of weight parameters is obtained by optimizing a validation set containing validation samples and corresponding real multidimensional labels, with the goal of minimizing the weighted fusion prediction error. In this way, validation samples are transformed from passive evaluation roles into active optimization criteria for weight learning. The determination process of the weight parameter set directly aims to minimize the final fusion prediction error, ensuring that the fusion weight allocation of each base model in the multidimensional output space is tightly coupled with the prediction target. This allows for the active learning of better fusion strategies from limited validation samples, thereby fully utilizing validation samples in small-sample scenarios and effectively improving multidimensional prediction accuracy. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1This is a flowchart illustrating the implementation of the multidimensional prediction ensemble method provided in the embodiments of this application; Figure 2 This is a flowchart illustrating a specific implementation of the base model training and weight parameter set optimization in the multidimensional prediction ensemble method provided in this application embodiment; Figure 3 This is a flowchart illustrating a specific implementation of the multidimensional prediction ensemble method provided in this application for obtaining a preset set of weight parameters. Figure 4 This is a flowchart illustrating a specific implementation of step S103 in the multidimensional prediction ensemble method provided in this application embodiment; Figure 5 This is another specific implementation flowchart of step S103 in the multidimensional prediction integration method provided in the embodiments of this application; Figure 6 This is a structural block diagram of the multidimensional prediction integration device provided in the embodiments of this application; Figure 7 This is a schematic diagram of the terminal device provided in the embodiments of this application. Detailed Implementation

[0014] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0015] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0016] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0017] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0018] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0019] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0020] By way of example and not limitation, the multidimensional prediction integration method provided in this application is applicable to various types of terminal devices that need to perform multidimensional prediction integration. Specific terminal devices may include mobile phones, tablets, wearable devices, laptops, ultra-mobile personal computers (UMPCs), desktop computers, and servers, etc. This application does not impose any restrictions on the specific type of terminal device.

[0021] Figure 1 The implementation flow of the multidimensional prediction ensemble method provided in this application embodiment is illustrated. The method flow includes steps S101 to S103. The specific implementation principle of each step is as follows: Step S101: Obtain the target input.

[0022] The target input refers to the raw data to be used for multidimensional prediction, and its specific form depends on the actual prediction scenario. For example, in a wind power generation prediction scenario, the target input could be historical meteorological and power data of the target wind farm, including features such as wind speed, wind direction, temperature, and humidity; in an industrial fault diagnosis scenario, the target input could be multi-channel signal data collected from sensors in industrial equipment; in a cloud resource load prediction scenario, the target input could be data such as the number of virtual machines, CPU usage, and memory usage over a historical period; in a material performance prediction scenario, the target input could be a vector describing material formulations or process parameters; and in an image multi-attribute regression scenario, the target input could be an image to be analyzed. The form of the target input is not limited to the examples above and is determined according to the specific multidimensional prediction task.

[0023] In one possible implementation, the dimension of the target input is consistent with the feature dimension used during the training of the base model, eliminating the need for additional dimension adaptation processing.

[0024] Step S102: Use at least two base models to predict the target input respectively, and obtain the multidimensional prediction vectors output by each base model. Each multidimensional prediction vector contains prediction values ​​of multiple dimensions.

[0025] After acquiring the target input, at least two base models are used to predict the target input. The base models are pre-trained multidimensional prediction models, and their outputs are multidimensional prediction vectors, each containing prediction values ​​in multiple dimensions.

[0026] In one possible implementation, the at least two base models can be base models selected from multiple pre-trained heterogeneous multidimensional base models that meet preset performance conditions, or they can be multiple pre-trained homogeneous multidimensional base models. Specifically, the at least two base models can be of the same or different types. For example, multiple heterogeneous base models can include any combination of different types such as neural network models, support vector regression models, random forest regression models, and gradient boosting decision tree models, or they can include models of the same type but with different hyperparameter settings. The introduction of multiple heterogeneous base models helps to capture patterns in different aspects of the data, providing diverse predictive information for subsequent fusion.

[0027] Each base model can independently map from the input to a multidimensional output; that is, each base model can output a multidimensional prediction vector for the same target input. The dimension of this multidimensional prediction vector is d, where d is an integer greater than 1, representing the number of output dimensions in the multidimensional prediction task.

[0028] For example, assuming the output dimension d of a multidimensional prediction task is 3, then for the same target input, the multidimensional prediction vector output by any base model contains prediction values ​​in 3 dimensions, corresponding to 3 different prediction targets. The number of dimensions in the multidimensional prediction vector is the same as the number of dimensions in the output of the multidimensional prediction task.

[0029] By distributing the target input to multiple base models, different base models can make parallel predictions of the target input from different perspectives, thus providing diverse sources of prediction information for multidimensional ensemble prediction.

[0030] As one possible implementation of this application Figure 2 This paper illustrates a specific implementation process of base model training and weight parameter set optimization in the multidimensional prediction ensemble method provided in this application, detailed below: A1: Train multiple heterogeneous base models.

[0031] Heterogeneous base models refer to predictive models that differ in model structure, type, or hyperparameter configuration. For example, base models can be different types such as neural network models, decision tree models, and support vector regression models, or they can be the same type of neural network model but with different numbers of hidden layers or different learning rates. Heterogeneous base models can be combined randomly, meaning there are no restrictions on the specific model types; different types and hyperparameters can be arbitrarily combined. The heterogeneity of base models helps capture patterns in data from multiple perspectives, providing diverse predictive results for subsequent integration and fusion.

[0032] One possible implementation involves acquiring an imbalanced dataset and using it to train multiple heterogeneous base models. An imbalanced dataset refers to a data set where the number of samples from different classes is unevenly distributed; for example, the number of simulated or analog samples is far greater than the number of experimental or real samples. In an imbalanced dataset, the samples with a larger number are called simulated samples, and the samples with a smaller number are called experimental samples. Simulated samples can be data samples generated through computer simulation or numerical simulation, while experimental samples can be real data samples obtained through actual measurement or experimentation. Each sample in the imbalanced dataset corresponds to a multidimensional ground truth label, and the dimension of this multidimensional ground truth label is consistent with the output dimension of the multidimensional prediction task.

[0033] In one possible implementation, when the training data is an imbalanced dataset, the imbalanced dataset is divided into multiple subsets. Each subset contains some simulation samples and some or all experimental samples. The partitioning can be achieved using various sampling methods, such as random sampling, stratified sampling, or bootstrap sampling. Sample weights are assigned to the samples in each subset, forming multiple weighted subsets. Each weighted subset contains both sample data and the corresponding sample weights, which characterize the importance of the sample in subsequent model training. A base model is then trained using each weighted subset, resulting in multiple heterogeneous base models.

[0034] One possible implementation is that the method of assigning sample weights can be set according to actual needs. For example, different weight values ​​can be set for simulation samples and experimental samples, so that the fewer experimental samples receive higher weights during model training, thereby improving the model's predictive ability for experimental samples. When training the base model using weighted subsets, the loss calculation during model training is adjusted according to the sample weights of each sample in the weighted subset, so that samples with higher weights have a greater impact during training. By training the base model on different weighted subsets, different base models can learn different prediction patterns from different sample distributions.

[0035] A2: Evaluate the performance of the plurality of heterogeneous base models using a validation set, and determine at least two base models from the plurality of heterogeneous base models that meet the performance conditions.

[0036] The validation set is a collection of samples independent of the training dataset, containing multiple validation samples and their corresponding ground truth labels. Validation samples are data samples selected from the known dataset for validation, and the ground truth labels for each validation sample are its true values ​​in each output dimension. Multiple heterogeneous base models, trained separately, are used to predict the values ​​of each validation sample in the validation set, resulting in the multidimensional prediction vectors for each base model on each validation sample. The predictive performance of each base model is evaluated based on the differences between its predictions and the ground truth labels of the validation samples.

[0037] In one possible implementation, the performance of the base model prediction can be evaluated using various metrics, such as mean squared error, mean absolute error, or coefficient of determination R². For multidimensional output tasks, the evaluation metrics can be calculated holistically for all output dimensions, or they can be calculated separately for each output dimension and then averaged.

[0038] Based on the evaluation results, at least two base models that meet the performance conditions are determined from multiple heterogeneous base models. The performance conditions can be preset evaluation index thresholds.

[0039] For example, the performance condition can be set as follows: the mean squared error (MSE) of the base model on the validation and test sets is lower than a preset threshold; or, the M base models with the smallest MSE are selected; or, the coefficient of determination (R²) is higher than a preset threshold. The base models are ranked according to the evaluation metrics, and the top M base models with the best performance are selected as the base models that meet the performance condition, where M is an integer greater than or equal to 2. Alternatively, base models whose evaluation metrics exceed the preset threshold can be selected.

[0040] By running validation set samples on each base model and calculating the prediction error, at least two base models that meet the performance conditions are selected as base models to participate in subsequent weighted fusion, thereby improving the overall accuracy of the integrated prediction.

[0041] A3: Using the validation set, with the goal of minimizing the weighted fusion prediction error, the initial weight parameter set is optimized to obtain the preset weight parameter set.

[0042] The initial weight parameter set is the initial value assigned to the weight parameters before the optimization process begins. It is the starting point for weight parameter optimization. This initial weight parameter set can be set based on preset rules, such as random values, zero values, or equally distributed values.

[0043] For example, when the number of base models is M and the output dimension is d, if the weight parameter set consists of M d×d weight matrices that correspond one-to-one with the M base models, the initial weight parameter set can be set as M d×d matrices, where the diagonal elements of each matrix are 1 / M and the off-diagonal elements are 0, meaning that each base model has equal initial weights in the corresponding output dimension.

[0044] The initial weight parameter set is optimized using a validation set, with the optimization objective being to minimize the weighted fusion prediction error. The weighted fusion prediction error refers to the error between the predicted result obtained after weighting and fusing the multidimensional prediction vectors of the validation samples according to the current weight parameter set and the true multidimensional label corresponding to the validation sample. By continuously adjusting the weight parameters in the weight parameter set, this weighted fusion prediction error is gradually reduced until it reaches a minimized state, thus determining the preset weight parameter set. The optimization process can be achieved by iteratively updating the weight parameters until the convergence condition is met, thereby adjusting the initial weight parameter set to the preset weight parameter set. After optimization, the preset weight parameter set is saved for subsequent weighted fusion operations when predicting the target input.

[0045] By using the validation set to optimize the initial weight parameter set with the goal of minimizing the weighted fusion prediction error, the preset weight parameter set is directly optimized to minimize the fusion prediction error. This achieves direct coupling between the weight parameter set and the multidimensional prediction objective, allowing the weight parameters to be rationally allocated according to the prediction contributions of each base model in different output dimensions. In this embodiment, multiple heterogeneous base models are first trained, enabling them to learn diverse prediction patterns from different model structures or training data distributions. A validation set is used to evaluate the performance of each base model, and at least two base models that meet the performance criteria are selected from the heterogeneous models. This ensures that the base models participating in subsequent weighted fusion have good predictive performance. Based on this, the initial weight parameter set is optimized using the validation set with the goal of minimizing the weighted fusion prediction error. This allows the validation set to not only perform base model performance evaluation but also participate in the optimization and determination of the weight parameter set, eliminating the need for an additional independent sample subset for weight determination. This improves the utilization efficiency of validation samples under limited sample conditions. Simultaneously, the optimization process of the weight parameter set directly aims to minimize the fusion prediction error, allowing the optimized weight parameters to be differentiated according to the prediction contributions of each base model in different output dimensions, thereby improving the accuracy of multidimensional ensemble prediction.

[0046] As one possible implementation of this application Figure 3 The following is a detailed implementation process of obtaining a preset set of weight parameters in the multidimensional prediction ensemble method provided in this application: B1: Construct an objective function with a set of weight parameters as decision variables. The objective function is configured to measure the error between the prediction result obtained by weighted fusion of the prediction vectors of the validation samples based on the set of weight parameters and the corresponding true multidimensional labels.

[0047] The weight parameter set is the decision variable to be determined during the optimization process. The objective function is optimized by adjusting the values ​​of the decision variables. The objective function is a function of the weight parameter set, and its value reflects the deviation between the weighted fusion prediction result obtained from all validation samples and the true multidimensional label under the current weight parameter set. The specific form of the objective function can be set according to actual needs. For example, the objective function can be set as the sum of squared prediction errors of all validation samples on the validation set, or as the mean absolute error of all validation samples on the validation set, or as maximizing the sum of the determination coefficients R² of all output dimensions. The smaller the value of the objective function, the closer the weighted fusion prediction result is to the true value.

[0048] In one possible implementation, the bias can be quantified using the sum of squared errors (SSE). Suppose the validation set has N validation samples. Let j be the true multidimensional label vector of the j-th validation sample. The prediction result obtained by weighting and fusing the prediction vector of the j-th validation sample according to the weight parameter set is as follows: The SSE calculation formula is as follows (1): (1) in, Let represent the Euclidean norm. For the j-th validation sample, its prediction matrix is ​​a d-row, M-column matrix, where the i-th column represents the d-dimensional prediction vector output by the base model i. Let the weight matrix corresponding to the base model i be . ,but ,in Let i be the prediction vector of the base model i for the j-th validation sample.

[0049] In one possible implementation, the objective function further includes a regularization term. The regularization term can be a penalty term on the L1 or L2 norm of the weight parameters. This regularization term is used to prevent the weight parameter set from overfitting the validation samples during the optimization process, constrain the range of weight parameter values, avoid the weight parameters overfitting the noise of the validation set, and improve the generalization ability of the preset weight parameter set to new samples.

[0050] B2: Determine the constraints of the weight parameter set.

[0051] Constraints are restrictions imposed on the range or relationship of values ​​in the weight parameter set, ensuring that the optimization solution satisfies predetermined physical meanings or mathematical properties. Constraints can be set according to the specific form of the weight parameter set, or determined based on actual needs. Setting constraints ensures that the obtained weight parameter set has reasonable physical meanings or mathematical properties, avoiding meaningless negative weights or divergent weights. By determining constraints, the effective search space of the weight parameter set is limited, thereby guiding the optimization process to generate weights that conform to the expected structure.

[0052] In one possible implementation, when the weight parameter set includes weight matrices that correspond one-to-one with the base models, the constraints are fixed constraints or flexible constraints. The dimension of each weight matrix is ​​consistent with the dimension of the multidimensional prediction vector, both being d×d, where d is the dimension of the multidimensional prediction vector.

[0053] The fixed constraint is that the sum of the weight matrices of all base models equals the identity matrix, and the diagonal elements of each weight matrix are non-negative. This fixed constraint requires that for each output dimension, the sum of the weights of all base models in that dimension equals 1, and there is no weight flow between different output dimensions. The identity matrix is ​​a d×d matrix with diagonal elements of 1 and off-diagonal elements of 0. Non-negative diagonal elements mean that the value of the element in the i-th row and i-th column of each weight matrix is ​​greater than or equal to 0. The physical meaning of the fixed constraint is that the final predicted value for each output dimension is obtained only by weighted summation of the predicted values ​​of each base model in that output dimension, unaffected by the predicted values ​​of other output dimensions. Under the fixed constraint, all off-diagonal elements of the weight matrix are 0. The fixed constraint guarantees that the sum of the self-contribution weights of all base models for any dimension is 1, the sum of the cross-interference weights between different dimensions is 0, and the non-negative diagonal elements guarantee that the self-contribution weights are non-negative.

[0054] The flexible constraint requires that the sum of the traces of the weight matrices of all base models equals the dimension of the multidimensional prediction vector, the sum of the off-diagonal elements of all weight matrices equals zero, and the diagonal elements of each weight matrix are non-negative. The trace of a matrix refers to the sum of its diagonal elements. The flexible constraint requires that the sum of the traces of the weight matrices of all base models equals d, and the sum of all off-diagonal elements of all weight matrices equals 0. The flexible constraint allows off-diagonal elements to be non-zero, meaning that the prediction result of one output dimension can be corrected using prediction information from other output dimensions, thereby achieving information flow between output dimensions, i.e., allowing weights to be transferred between different dimensions, achieving the effect of weight mobility. The requirement that the diagonal elements of each weight matrix are non-negative is the same as the fixed constraint.

[0055] For example, suppose there are M base models in total. Let i be the weight matrix corresponding to the base model i. for A 3D identity matrix. Fixed constraints are represented as: ,and ,That , express The Line 1 Column elements. Fixed constraints ensure that the sum of the self-contribution weights of all base models for any one dimension is 1, the sum of the cross-interference weights between different dimensions is 0, and the non-negativity of diagonal elements ensures that the self-contribution weights are non-negative. Flexible constraints are expressed as: ,and , Flexible constraints no longer force the sum of self-contribution weights on each dimension to be strictly 1. Instead, they require the sum of self-contribution weights across all dimensions to be d, and the sum of cross-interference to be zero. This allows weights to be transferred between the same dimension in different models, providing a more flexible weight allocation space than fixed constraints.

[0056] In one possible implementation, when the initial weight parameter set includes weight vectors corresponding one-to-one with the predicted values ​​of the multiple dimensions, the constraint condition includes that the sum of the elements of the weight vector corresponding to each dimension is equal to one. This ensures that the weighted fusion of the base model predictions in each dimension is a convex combination, and the fusion result will not exceed the range of the base model predictions.

[0057] For example, with an output dimension of d and a base model number of M, the weight parameter set includes d M-dimensional weight vectors, each corresponding to an output dimension. For the i-th output dimension, the sum of the elements of its corresponding M-dimensional weight vector is equal to 1, that is, the final prediction value of this output dimension is the weighted sum of the prediction values ​​of each base model on this output dimension, and each weight is a non-negative value.

[0058] B3: Under the constraints, the objective function is optimized to obtain the preset set of weight parameters.

[0059] After applying constraints, the objective function is optimized. Optimization means finding the optimal value (minimum or maximum value) of the decision variable among all feasible solutions that satisfy the constraints.

[0060] In one possible implementation, when the objective function is convex and the constraints are linear, a quadratic programming algorithm or a convex optimization algorithm can be used to solve it; when the objective function or constraints are non-convex or nonlinear, a heuristic algorithm can be used. After optimization, the set of weight parameters that makes the objective function optimal is obtained, and this set is used as the preset set of weight parameters.

[0061] In this embodiment, by constructing an objective function, determining and applying constraints on the weight parameter set, and performing optimization, the preset weight parameter set is determined directly to minimize the fusion prediction error. The verification sample changes from a passive evaluation role to an active participation in the optimization basis of weight learning. The weight allocation and multidimensional prediction objective are tightly coupled, thereby making full use of limited verification samples in small sample scenarios and effectively improving the accuracy of multidimensional prediction.

[0062] Step S103: According to the preset weight parameter set, the multidimensional prediction vectors output by the at least two base models are weighted and fused to generate the multidimensional integrated prediction result of the target input; wherein, the preset weight parameter set is optimized and determined by using a validation set containing multiple validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error.

[0063] After obtaining the multidimensional prediction vectors output by each base model, the multidimensional prediction vectors output by each base model are weighted and fused according to a preset set of weight parameters to generate a multidimensional integrated prediction result for the target input. The dimension of this multidimensional integrated prediction result is the same as the dimension of the multidimensional prediction vectors output by each base model.

[0064] The preset weight parameter set is a pre-determined and stored set of weight parameters that corresponds to the base models. It is used to weight and fuse the multidimensional prediction vectors output by each base model, controlling the contribution of each base model in the fusion process and the way information is exchanged between dimensions. Weighted fusion refers to using the preset weight parameter set to combine the multidimensional prediction vectors output by multiple base models with weights to generate a comprehensive multidimensional integrated prediction result. The specific method of weighted fusion is determined by the structure of the preset weight parameter set.

[0065] In this embodiment, the preset weight parameter set is determined by optimization using a validation set. The specific process for optimizing and determining the preset weight parameter set can be found in the descriptions of steps A3 and B1 to B3 above, and will not be repeated here.

[0066] For example, assume the number of base models M is 3, the validation set contains 100 validation samples, and the output dimension d of each validation sample is 2. For any validation sample, prediction is performed using the three base models respectively, resulting in three 2D prediction vectors. These three 2D prediction vectors are then weighted and fused according to the current weight parameter set to obtain a 2D fused prediction result. The error between this 2D fused prediction result and the 2D true multidimensional label of the validation sample is calculated. The errors of all 100 validation samples are accumulated to obtain the overall weighted fused prediction error. The weight parameter set is adjusted by an optimization algorithm to minimize this overall weighted fused prediction error, thereby determining the preset weight parameter set.

[0067] The weight parameter set, which is proactively optimized through the validation set in advance, integrates the prediction information of multiple base models in the optimal way. This allows the weight parameter set to be optimized directly to minimize the fusion prediction error. The weight parameters can be reasonably allocated according to the prediction contribution of each base model in different output dimensions, so that the multidimensional fusion prediction result is closer to the true value than the prediction result of any single base model, and higher prediction accuracy is obtained in the multidimensional output space.

[0068] As one possible implementation of this application, the preset weight parameter set includes weight matrices that correspond one-to-one with the at least two base models, wherein the number of rows and columns of each weight matrix are equal to the dimension of the multidimensional prediction vector; Figure 4 A specific implementation flow of step S103 in the multidimensional prediction ensemble method provided in this application embodiment is shown below: C1: Multiply the weight matrix corresponding to each base model with the multidimensional prediction vector of that base model to obtain the weighted prediction vector of each base model.

[0069] The preset weight parameter set includes M weight matrices, where M is the number of base models and is an integer greater than or equal to 2. Each weight matrix corresponds to one base model. The number of rows and columns of each weight matrix is ​​equal to the dimension d of the multidimensional prediction vector, i.e., each weight matrix is ​​a d×d dimensional matrix. For any base model, the weight matrix corresponding to that base model is multiplied by the multidimensional prediction vector output by that base model. The weight matrix is ​​a d×d dimensional matrix, and the multidimensional prediction vector is a d-dimensional column vector; multiplying them yields a d-dimensional vector, which is the weighted prediction vector of that base model.

[0070] C2: The weighted prediction vectors of each base model are summed to obtain the multidimensional integrated prediction result.

[0071] After obtaining the weighted prediction vectors of each base model, the weighted prediction vectors of all base models are accumulated. The accumulation method is vector addition, that is, the components of all weighted prediction vectors in the same dimension are added separately. Since each weighted prediction vector is a d-dimensional vector, the vector obtained after accumulation is also a d-dimensional vector. This accumulation result is the multidimensional ensemble prediction result, and its dimension is d.

[0072] For example, for base model i, its weight matrix is... Its output d-dimensional prediction vector Performing matrix multiplication yields a d-dimensional weighted prediction vector. In matrix multiplication, the p-th component of the weighted prediction vector is equal to the weight matrix. The elements in row p and the prediction vector The sum of the products of each component. Through this multiplication, the original prediction information of base model i is redistributed and combined by the weight matrix, and the prediction information of all input dimensions of the base model is fused into each output dimension. If M=3, that is, a total of 3 base models, and the output dimension d=2, after obtaining the weighted prediction vectors of the 3 base models, the 3 weighted prediction vectors are added together. The weighted prediction vector of the 1st base model is... The weighted prediction vector of the second base model is The weighted prediction vector of the third base model is Then, after summing, we get This 2D vector is the result of the multidimensional integrated prediction.

[0073] In this embodiment, the multidimensional prediction vector of the base model is linearly transformed by the weight matrix, so that the weight matrix can not only independently weight the predicted values ​​of each output dimension, but also realize the cross-fusion of prediction information between different output dimensions. This fully utilizes the potential correlation between each output dimension in the multidimensional output task, thereby realizing the coupling and fusion of information between dimensions. Then, the prediction information of multiple base models after being weighted by the weight matrix is ​​integrated to obtain the final prediction result, which can effectively improve the overall accuracy of the multidimensional prediction task.

[0074] As one possible implementation of this application, the preset weight parameter set includes weight vectors that correspond one-to-one with the predicted values ​​of the multiple dimensions, and the dimension of each weight vector is the same as the number of the base models. Figure 5 Another specific implementation flow of step S103 in the multidimensional prediction ensemble method provided in the embodiments of this application is shown below: D1: Based on the predicted values ​​of the base model in each dimension, a predicted value vector is constructed, and the weight vector corresponding to each dimension is multiplied by the predicted value vector to obtain the integrated predicted value for each dimension.

[0075] When the preset weight parameter set includes weight vectors that correspond one-to-one with the predicted values ​​of multiple dimensions, each weight vector corresponds to one output dimension, that is, the i-th weight vector corresponds to the i-th output dimension, where i takes any integer from 1 to d. For example, each dimension k corresponds to an independent weight vector. The dimension of the weight vector is the same as the number of base models M, and the i-th component in the weight vector represents the fusion weight of base model i in dimension k.

[0076] The weight vector corresponding to each output dimension is multiplied by the predicted value vector. The dot product operation involves multiplying corresponding elements of two vectors with the same dimension and summing the results to obtain a scalar value, which is the ensemble predicted value for that output dimension. By performing the dot product operation between the weight vector and the predicted value vector for each output dimension, the ensemble predicted value for each output dimension is obtained.

[0077] For example, for dimension k, the predicted values ​​of all base models in dimension k are extracted to form an M-dimensional predicted value vector. The i-th component in the predicted value vector is the predicted value of base model i in dimension k. The weight vector vk corresponding to dimension k is then multiplied by the predicted value vector. The result of the dot product is a scalar, which is the ensemble predicted value for dimension k. The dot product operation is equivalent to multiplying the predicted value of each base model by its corresponding weight coefficient and then summing the results.

[0078] D2: The integrated prediction values ​​of each dimension are concatenated to obtain the multidimensional integrated prediction result.

[0079] After obtaining the ensemble prediction value for each output dimension, the ensemble prediction values ​​for all output dimensions are concatenated according to the order of the output dimensions. The concatenation method is vector concatenation, that is, the ensemble prediction values ​​of each dimension are arranged in dimensional order to form a d-dimensional vector, which is the multidimensional ensemble prediction result.

[0080] In this embodiment, the predicted values ​​of each base model in a single dimension are weighted and summed using a dot product method. This allows the integrated predicted value in that dimension to incorporate the prediction information from multiple base models. The results of the independent fusion of each dimension are then integrated into a complete multidimensional output, forming a multidimensional integrated prediction result consistent with the task dimension. Each dimension has an independent weight vector, enabling the allocation of appropriate weights based on the performance of different base models in each dimension, achieving fine-grained, dimension-wise weight control. Because each dimension is independently weighted and fused, this implementation can naturally degenerate into a single-dimensional prediction scenario, thus possessing broad applicability.

[0081] In one possible implementation, the weight vector scheme and the aforementioned weight matrix scheme are parallel and independent implementations. In the weight vector scheme, each output dimension independently corresponds to a weight vector, and the weight optimizations between output dimensions are independent of each other, making it suitable for multidimensional prediction scenarios where the correlation between output dimensions is weak. In the weight matrix scheme, the prediction information between different output dimensions is cross-weighted through the off-diagonal elements of the weight matrix, making it suitable for multidimensional prediction scenarios where there is a strong correlation between output dimensions. The choice between the two parallel schemes can be made based on the correlation between output dimensions in the actual application scenario.

[0082] In one possible implementation, when the multidimensional prediction ensemble method is applied to a classification task, multiple heterogeneous base models are multidimensional classification models, and the multidimensional prediction vector is the probability vector or log-odds vector output by the classification model.

[0083] Classification tasks refer to prediction tasks that divide input data into one or more predefined categories. When multidimensional prediction ensemble methods are applied to classification tasks, the base model is a multidimensional classification model. The output of a multidimensional classification model is a multidimensional prediction vector, where the dimension 'd' is the same as the number of predefined categories in the classification task, and 'd' is an integer greater than 1. For example, a neural network model that classifies c categories will have an output dimension 'd' equal to the number of categories 'c'.

[0084] A probability vector is the probability distribution vector output by a multidimensional classification model after processing with a normalized exponential function (softmax function). Each element in the probability vector has a value between 0 and 1, and the sum of all elements equals 1. Each element represents the predicted probability that the target input belongs to the corresponding category.

[0085] For example, for a classification task involving three categories, the multidimensional prediction vector output by the classification model is a 3-dimensional probability vector, where each component represents the probability that the input sample belongs to category 1, category 2, and category 3, respectively. After weighting and fusing the multidimensional prediction vectors output by at least two base models according to a preset set of weight parameters, a 3-dimensional weighted fused probability vector is obtained. This weighted fused probability vector is then normalized so that the sum of its components is 1, yielding the final multidimensional ensemble prediction result.

[0086] The log-odds vector is the original vector of predicted values ​​output by a multidimensional classification model before processing with the normalized exponential function; it is also called the logits vector. Each element in the log-odds vector is a real value, and the range of values ​​for each component is unaffected by external variables. The range can be limited to positive numbers, negative numbers, or zero.

[0087] In one possible implementation, the true multidimensional label corresponding to each training or validation sample is represented using one-hot encoding. One-hot encoding refers to representing a category label as a vector with the same number of dimensions as the number of categories, where the component corresponding to the true category has a value of 1, and the remaining components have values ​​of 0. The validation samples and their corresponding one-hot encoded true labels constitute the validation set, which is used to optimize a preset set of weight parameters. The optimization process is consistent with the regression task, constructing an objective function with the weight parameter set as the decision variable. The objective function measures the error between the result obtained by weighting and fusing the probability vector or log odds vector of the validation samples according to the weight parameter set and the one-hot encoded true label. Under constraints, the optimal weight parameter set is solved to obtain the preset weight parameter set.

[0088] For example, in a classification task with three categories, if the true category of a sample is the second category, then its corresponding true multidimensional label is: The 3D vector. The classification task is processed in a multi-dimensional output form, so that the processing method for multi-dimensional prediction vectors in the previous steps is also applicable to the classification task.

[0089] In one possible implementation, when the multidimensional prediction vector output by the multidimensional classification model is a probability vector, after performing the steps of acquiring the target input, predicting the target input using at least two base models respectively, and weighting and fusing the multidimensional prediction vectors output by each base model according to a preset set of weight parameters, the resulting multidimensional integrated prediction result is also a probability vector. Since the sum of the components of the multidimensional integrated prediction result obtained after weighted fusion may not be equal to 1, the probability vector is normalized to ensure that the sum of the components is 1, thereby enabling each component to correctly represent the prediction probability of the target input belonging to each category. Normalization can be achieved by dividing each component by the sum of all components.

[0090] In one possible implementation, when the multidimensional prediction vector output by the multidimensional classification model is a log-odds vector, since the components of the log-odds vector are raw values ​​without normalization exponential function processing, the sum of its components is not necessarily equal to 1, and each component can be directly used as input for weighted fusion. After performing the weighted fusion step, the multidimensional integrated prediction result obtained by fusion can be processed by normalization exponential function to convert it into a probability vector form, thereby obtaining the predicted probability that the target input belongs to each category.

[0091] In this embodiment, the multidimensional prediction ensemble method is applied to the classification task, which transforms the classification problem into a weighted fusion problem of multidimensional output vectors. The schemes for weight matrix coupling fusion and weight vector dimensional fusion in the regression task can be directly applied to the classification scenario. This broadens the application field of the multidimensional prediction ensemble method and enables the mechanism of active weight optimization of the validation set to play a role in the classification task, effectively improving the classification prediction accuracy in small sample classification scenarios.

[0092] As can be seen from the above, in this embodiment, after obtaining the target input, at least two base models are used to predict it respectively, resulting in multiple multidimensional prediction vectors. Each multidimensional prediction vector contains prediction values ​​in multiple dimensions. Then, the multiple multidimensional prediction vectors are weighted and fused according to a preset weight parameter set to generate a multidimensional integrated prediction result. The preset weight parameter set is obtained by optimizing a validation set containing validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error. In this way, the validation samples are transformed from passive evaluation to active participation in the optimization of weight learning. The determination process of the weight parameter set is directly aimed at minimizing the final fusion prediction error, so that the fusion weight allocation of each base model in the multidimensional output space is closely coupled with the prediction target. It can actively learn a better fusion strategy in a limited number of validation samples, thereby making full use of validation samples in small sample scenarios and effectively improving the multidimensional prediction accuracy.

[0093] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0094] Corresponding to the multidimensional prediction ensemble method described in the above embodiments, Figure 6 A structural block diagram of the multidimensional prediction integration device provided in the embodiments of this application is shown. For ease of explanation, only the parts related to the embodiments of this application are shown.

[0095] Reference Figure 6 The multidimensional prediction integration device includes: a question-answer pair acquisition unit 61, a mapping strategy determination unit 62, an index value calculation unit 63, and a model evaluation unit 64, wherein: Input acquisition unit 61 is used to acquire target input; The prediction unit 62 is used to predict the target input using at least two base models respectively, and obtain a multi-dimensional prediction vector output by each base model, wherein each multi-dimensional prediction vector contains prediction values ​​of multiple dimensions. The prediction fusion unit 63 is used to perform weighted fusion of the multidimensional prediction vectors output by the at least two base models according to a preset set of weight parameters to generate a multidimensional fusion prediction result of the target input; wherein, the preset set of weight parameters is optimized and determined by using a validation set containing multiple validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error.

[0096] As one possible implementation of this application, the preset weight parameter set includes weight matrices that correspond one-to-one with the at least two base models, wherein the number of rows and columns of each weight matrix is ​​equal to the dimension of the multidimensional prediction vector; the prediction integration unit 63 includes: The first integration module is used to multiply the weight matrix corresponding to each base model with the multidimensional prediction vector of that base model to obtain the weighted prediction vector of each base model; and to sum the weighted prediction vectors of each base model to obtain the multidimensional integrated prediction result.

[0097] As one possible implementation of this application, the preset weight parameter set includes weight vectors that correspond one-to-one with the predicted values ​​of the multiple dimensions, and the dimension of each weight vector is the same as the number of the base models; the prediction ensemble unit 63 includes: The second integration module is used to construct a prediction value vector based on the predicted values ​​of the base model in each dimension, and to perform a dot product operation between the weight vector corresponding to each dimension and the prediction value vector to obtain the integrated prediction value of each dimension; and to concatenate the integrated prediction values ​​of each dimension to obtain the multidimensional integrated prediction result.

[0098] As one possible implementation of this application, the multidimensional prediction ensemble device further includes a model building and training unit, used for: Train multiple heterogeneous base models; The performance of the plurality of heterogeneous base models is evaluated using a validation set, and at least two base models that satisfy the performance conditions are determined from the plurality of heterogeneous base models. Using the validation set, the initial weight parameter set is optimized with the goal of minimizing the weighted fusion prediction error to obtain the preset weight parameter set.

[0099] As one possible implementation of this application, the step of optimizing the weight parameter set using the validation set with the goal of minimizing the weighted fusion prediction error to obtain the preset weight parameter set includes: Construct an objective function with a set of weight parameters as decision variables. The objective function is configured to measure the error between the prediction result obtained by weighted fusion of the prediction vectors of the validation samples based on the set of weight parameters and the corresponding true multidimensional labels. Determine the constraints for the set of weight parameters; Under the constraints, the objective function is optimized to obtain the preset set of weight parameters.

[0100] As one possible implementation of this application, when the weight parameter set includes a weight matrix that corresponds one-to-one with the base model, the constraint condition is a fixed constraint or a flexible constraint. The fixed constraint is that the sum of the weight matrices of all base models is equal to the identity matrix, and the diagonal elements of each weight matrix are non-negative. The flexible constraints are that the sum of the traces of the weight matrices of all base models is equal to the dimension of the multidimensional prediction vector, the sum of the off-diagonal elements of all weight matrices is equal to zero, and the diagonal elements of each weight matrix are non-negative.

[0101] As one possible implementation of this application, when the multidimensional prediction ensemble method is applied to a classification task, the multiple heterogeneous base models are multidimensional classification models, and the multidimensional prediction vector is the probability vector or log-odds vector output by the multidimensional classification model.

[0102] As can be seen from the above, in this embodiment, after obtaining the target input, at least two base models are used to predict it respectively, resulting in multiple multidimensional prediction vectors. Each multidimensional prediction vector contains prediction values ​​in multiple dimensions. Then, the multiple multidimensional prediction vectors are weighted and fused according to a preset weight parameter set to generate a multidimensional integrated prediction result. The preset weight parameter set is obtained by optimizing a validation set containing validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error. In this way, the validation samples are transformed from passive evaluation to active participation in the optimization of weight learning. The determination process of the weight parameter set is directly aimed at minimizing the final fusion prediction error, so that the fusion weight allocation of each base model in the multidimensional output space is closely coupled with the prediction target. It can actively learn a better fusion strategy in a limited number of validation samples, thereby making full use of validation samples in small sample scenarios and effectively improving the multidimensional prediction accuracy.

[0103] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0104] This application embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements... Figures 1 to 5 The steps of any multidimensional prediction ensemble method are represented.

[0105] This application embodiment also provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements... Figures 1 to 5 The steps of any multidimensional prediction ensemble method are represented.

[0106] This application also provides a computer program product that, when run on a terminal device, causes the terminal device to execute the implementation of... Figures 1 to 5 The steps of any multidimensional prediction ensemble method are represented.

[0107] Figure 7 This is a schematic diagram of a terminal device provided in an embodiment of this application. For example... Figure 7 As shown, the terminal device 7 in this embodiment includes: a processor 70, a memory 71, and a computer program 72 stored in the memory 71 and executable on the processor 70. When the processor 70 executes the computer program 72, it implements the steps in the various multidimensional prediction integration method embodiments described above, for example... Figure 1 Steps S101 to S103 are shown. Alternatively, when the processor 70 executes the computer program 72, it implements the functions of each module / unit in the above-described device embodiments, for example... Figure 6 The functions of units 61 to 63 are shown.

[0108] For example, the computer program 72 may be divided into one or more modules / units, which are stored in the memory 71 and executed by the processor 70 to complete this application. The one or more modules / units may be a series of computer-readable instruction segments capable of performing a specific function, which describe the execution process of the computer program 72 in the terminal device 7.

[0109] The terminal device 7 may include, but is not limited to, a processor 70 and a memory 71. Those skilled in the art will understand that... Figure 7 This is merely an example of terminal device 7 and does not constitute a limitation on terminal device 7. It may include more or fewer components than shown, or combine certain components, or different components. For example, terminal device 7 may also include input / output devices, network access devices, buses, etc.

[0110] The processor 70 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0111] The memory 71 can be an internal storage unit of the terminal device 7, such as a hard disk or memory of the terminal device 7. The memory 71 can also be an external storage device of the terminal device 7, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the terminal device 7. Furthermore, the memory 71 can include both internal and external storage units of the terminal device 7. The memory 71 is used to store the computer program and other programs and data required by the terminal device. The memory 71 can also be used to temporarily store data that has been output or will be output.

[0112] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0113] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0114] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a device / terminal equipment, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0115] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0116] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multidimensional prediction ensemble method, characterized in that, include: Obtain the target input; At least two base models are used to predict the target input to obtain a multidimensional prediction vector output by each base model. Each multidimensional prediction vector contains prediction values ​​in multiple dimensions. Based on a preset set of weight parameters, the multidimensional prediction vectors output by the at least two base models are weighted and fused to generate a multidimensional integrated prediction result for the target input. The preset set of weight parameters is determined by optimizing a validation set containing multiple validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error.

2. The method according to claim 1, characterized in that, The preset set of weight parameters includes weight matrices that correspond one-to-one with the at least two base models, and the number of rows and columns of each weight matrix is ​​equal to the dimension of the multidimensional prediction vector. The step of weighting and fusing the multidimensional prediction vectors output by the at least two base models according to a preset set of weight parameters to generate a multidimensional integrated prediction result for the target input includes: Multiply the weight matrix corresponding to each base model with the multidimensional prediction vector of that base model to obtain the weighted prediction vector of each base model; The weighted prediction vectors of each base model are summed to obtain the multidimensional integrated prediction result.

3. The method according to claim 1, characterized in that, The preset weight parameter set includes weight vectors that correspond one-to-one with the predicted values ​​of the multiple dimensions, and the dimension of each weight vector is the same as the number of the base models; The step of weighting and fusing the multidimensional prediction vectors output by the at least two base models according to a preset set of weight parameters to generate a multidimensional integrated prediction result for the target input includes: Based on the predicted values ​​of the base model in each dimension, a predicted value vector is constructed, and the weight vector corresponding to each dimension is multiplied by the predicted value vector to obtain the integrated predicted value for each dimension. The integrated prediction values ​​from each dimension are concatenated to obtain the multidimensional integrated prediction result.

4. The method according to claim 1, characterized in that, Before predicting the target input using at least two base models, the method further includes: Train multiple heterogeneous base models; The performance of the plurality of heterogeneous base models is evaluated using a validation set, and at least two base models that satisfy the performance conditions are determined from the plurality of heterogeneous base models. Using the validation set, the initial weight parameter set is optimized with the goal of minimizing the weighted fusion prediction error to obtain the preset weight parameter set.

5. The method according to claim 4, characterized in that, The step of optimizing the weight parameter set using the validation set, with the goal of minimizing the weighted fusion prediction error, to obtain the preset weight parameter set includes: Construct an objective function with a set of weight parameters as decision variables. The objective function is configured to measure the error between the prediction result obtained by weighted fusion of the prediction vectors of the validation samples based on the set of weight parameters and the corresponding true multidimensional labels. Determine the constraints for the set of weight parameters; Under the constraints, the objective function is optimized to obtain the preset set of weight parameters.

6. The method according to claim 5, characterized in that, When the set of weight parameters includes a weight matrix that corresponds one-to-one with the base model, the constraint condition is a fixed constraint or a flexible constraint. The fixed constraint is that the sum of the weight matrices of all base models is equal to the identity matrix, and the diagonal elements of each weight matrix are non-negative. The flexible constraints are that the sum of the traces of the weight matrices of all base models is equal to the dimension of the multidimensional prediction vector, the sum of the off-diagonal elements of all weight matrices is equal to zero, and the diagonal elements of each weight matrix are non-negative.

7. The method according to claim 4, characterized in that, When the multidimensional prediction ensemble method is applied to a classification task, the multiple heterogeneous base models are multidimensional classification models, and the multidimensional prediction vector is the probability vector or log-odds vector output by the multidimensional classification model.

8. A multidimensional prediction integrated device, characterized in that, include: The input acquisition unit is used to acquire the target input; A prediction unit is used to predict the target input using at least two base models respectively, and to obtain a multidimensional prediction vector output by each base model, wherein each multidimensional prediction vector contains prediction values ​​of multiple dimensions. The prediction fusion unit is used to perform weighted fusion of the multidimensional prediction vectors output by the at least two base models according to a preset set of weight parameters to generate a multidimensional fusion prediction result of the target input; wherein, the preset set of weight parameters is optimized and determined by using a validation set containing multiple validation samples and corresponding real multidimensional labels with the goal of minimizing the weighted fusion prediction error.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the multidimensional prediction integration method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the multidimensional prediction integration method as described in any one of claims 1 to 7.

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