Combined prediction method, system and equipment based on boundary model and program product

Abstract

The invention belongs to the technical field of combined prediction, and particularly discloses a combined prediction method, system, equipment and program product based on a boundary model, and aims at complex and uncertain prediction problems, weights of different prediction models are determined based on priori knowledge by changing common underlying logic of combined prediction. And constructing a corresponding boundary model to carry out model parameter estimation and model fitting degree calculation so as to traverse the boundary model fitting degree of each alternative optimal predicted value for the target prediction problem, and selecting the alternative optimal predicted value with the optimal fitting degree condition as a combined predicted value of the target prediction problem, thereby getting rid of the nature of pursuing consensus by an average method, and improving the prediction efficiency of the target prediction problem. The optimal prediction value can be searched by taking facts as target guidance, and the facts can be effectively prevented from being replaced by consensus. The method is different from an existing publication method and a Bayesian method, the optimal prediction value is searched by utilizing the data driving model, and a new thought is provided for the combined prediction method by taking facts as target orientation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of combination prediction, and particularly relates to a combination prediction method, system, device and program product based on a boundary model. BACKGROUND

[0002] Combination prediction has a wide range of applications in various fields, and the related research fields are numerous. Among them, the social choice theory and the expert judgment theory are closely related. Different research fields have different focuses, and the research contents intersect with each other. The social choice theory studies the process of aggregating individual preferences into group preferences. Unlike group facts, the social choice theory respects individual preferences and emphasizes the conflict of interests between individuals. Its goal is to propose a social choice mechanism, integrate individual preferences, coordinate conflicts of interest, and reach group consensus. Therefore, the social choice theory is aimed at consensus decision-making problems. For the problem of combination prediction, how to target the objective facts instead of replacing facts with group consensus has not been found in the social choice theory.

[0003] In order to improve the comprehensive benefits of economy, society and ecology, governments and organizations usually use expert judgment theory to make numerical prediction and probability prediction on uncertain events, and guide the formulation of corresponding policies according to the prediction results. Expert judgment belongs to group facts, and needs to aggregate the opinions of multiple experts to eliminate the influence of individual bias and random error. According to different aggregation methods, expert judgment can be divided into two forms: interactive aggregation and algorithmic aggregation.

[0004] (1) For interactive aggregation, there is interaction between experts, and experts are required to gradually form a consensus and provide a unified opinion in the interactive process. Typical interactive aggregation methods include the Delphi method, the nominal group method and the focus group method. Although the interactive process can effectively emerge the wisdom of crowds, the mutual influence between experts may also produce phenomena such as conformity and dictatorship, leading to the failure of decision-making. Therefore, the "pseudo-group" aggregation method using algorithms instead of the interactive process has gradually attracted attention.

[0005] (2) For algorithmic aggregation, there is no interaction between experts, and the organizer uses mathematical methods to aggregate the opinions of multiple experts. Algorithmic aggregation can weaken the mutual influence between experts, thereby reducing the group error and obtaining more accurate decisions. The mainstream research results of aggregation algorithm can be summarized into two categories: Bayesian aggregation method and axiomatic aggregation method. Bayesian aggregation method regards the aggregation process of expert opinions as a Bayesian inference process, which has a rigorous theoretical research framework. However, Bayesian aggregation method can only solve the problem of probability aggregation. In reality, the prediction model has great uncertainty in the cognition and estimation of probability, and most decision-making problems are presented in the form of numerical point estimation. Therefore, the application range of Bayesian aggregation method in practice is relatively narrow. In addition, since the prior probability of experts can only be approximately estimated, it is more difficult to obtain the likelihood function, so Bayesian aggregation method is difficult to be widely used in practice. The commonly used axiomatic aggregation method can be divided into two categories: average method and weighted average method. The average method is the most classic aggregation method, which can effectively weaken individual bias and emerge collective wisdom. The average value is the value that minimizes the sum of squared errors, so the process of averaging is the process of seeking consensus. There are many studies on the influence of interaction process on group decision-making based on average method, mainly in the field of behavioral science. However, there are few specific studies on average method. The research on axiomatic aggregation method mainly focuses on weighted average method, especially the weight quantification method. If part of the information of experts is known, such as research field and test performance, then according to the information, different weights are given to experts, and the weighted average of the opinions of experts is obviously a more accurate aggregation method. However, no matter how the weight is quantified, the final aggregation method is still the average method, which is still the process of group consensus.

[0006] In summary, the existing related research cannot be used to solve the problem of combined prediction with fact as the target. Social choice theory considers the relationship between individual preferences and group preferences, and the goal is to minimize the preference conflict between individuals and groups through aggregation method. Therefore, the research object of social choice theory is the group decision-making problem with consensus as the target, which is not applicable to combined prediction. Expert judgment theory takes aggregation method as the starting point, and the related research mainly involves Bayesian aggregation method and axiomatic aggregation method. Bayesian aggregation method can theoretically obtain facts, but it cannot be applied in practice due to its dependence on human uncertain information. The principle of axiomatic aggregation method is simple and operable, but its essence is the development and expansion of average method, which is a consensus-oriented aggregation method. Therefore, expert judgment theory is also not applicable to combined prediction. At present, there is no corresponding method that can better apply to combined prediction problem and effectively solve the problem of replacing fact with consensus. SUMMARY

[0007] The application aims to provide a boundary model-based combined prediction method, system, device and program product to solve the above problems in the prior art.

[0008] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0009] In a first aspect, a boundary model-based combined prediction method is provided, comprising:

[0010] A plurality of prediction models, a plurality of set test problems and a target prediction problem are determined, and test prediction values of each prediction model for each set test problem, factual optimal prediction values of each set test problem and a plurality of candidate optimal prediction values of the target prediction problem are obtained;

[0011] According to the test prediction values of each prediction model for each set test problem and the factual optimal prediction values of each set test problem, prediction deviation values of each prediction model for each set test problem are determined;

[0012] The weight values of each prediction model are determined based on the prediction deviation values of each prediction model for each set test problem;

[0013] The weight values of each prediction model are substituted into a preset initial boundary model function to obtain a first boundary model function under the weight values of each prediction model, and the initial boundary model function contains weight variables and model parameter variables;

[0014] A plurality of set model parameters are obtained, and based on each set model parameter, the prediction deviation values of each prediction model for each set test problem and the first boundary model function under the weight values of each prediction model, the fitting degrees of the first boundary model corresponding to each set model parameter under each set test problem are determined;

[0015] The average fitting degrees corresponding to each set model parameter are calculated according to the fitting degrees of the first boundary model corresponding to each set model parameter under each set test problem, and one of the set model parameters is selected as a model estimation parameter based on the average fitting degrees corresponding to each set model parameter;

[0016] The model estimation parameter is substituted into the initial boundary model function to obtain a second boundary model function, and the weight values of each prediction model are substituted into the second boundary model function for calculation to obtain the second boundary model function values under the weight values of each prediction model;

[0017] Actual prediction values of each prediction model for the target prediction problem are collected, and based on the actual prediction values of each prediction model for the target prediction problem, the candidate optimal prediction values and the second boundary model function values under the weight values of each prediction model, the fitting degrees of the second boundary model corresponding to each candidate optimal prediction value are determined;

[0018] The optimal prediction value corresponding to the second boundary model with the largest fitting degree is taken as the combined prediction value of the target prediction problem, and the combined prediction value of the target prediction problem is output.

[0019] In one possible design, the determination of the prediction deviation value of each prediction model for each set test problem according to the test prediction value of each prediction model for each set test problem and the factual optimal prediction value of each set test problem comprises:

[0020] The prediction deviation value of each prediction model for each set test problem is obtained by subtracting the factual optimal prediction value corresponding to the set test problem from the test prediction value of each prediction model for the set test problem.

[0021] In one possible design, the determination of the weight of each prediction model based on the prediction deviation value of each prediction model for each set test problem comprises:

[0022] The prediction deviation distance of each prediction model for each set test problem is obtained by substituting the prediction deviation value of each prediction model for each set test problem into a preset prediction deviation distance formula, and the prediction deviation distance formula is

[0023]

[0024] wherein ‖·‖2 represents a two-norm operation, i is a prediction model serial number, j is a set test problem serial number, represents the prediction deviation distance of the prediction model i for the set test problem j, represents the prediction deviation value of the prediction model i for the set test problem j;

[0025] The test performance index of each prediction model is obtained by substituting the prediction deviation distance of each prediction model for each set test problem into a prediction accuracy formula, and the prediction accuracy formula is

[0026]

[0027] wherein P i represents the test performance index of the prediction model i, and M is the number of set test problems;

[0028] The weight of each prediction model is obtained by substituting the test performance index of each prediction model into a preset weight formula, and the weight formula is

[0029]

[0030] wherein ω i represents the weight of the prediction model i, and N is the number of prediction models.

[0031] In a possible design, the initial boundary model function is

[0032]

[0033] where ω represents a weight variable, A represents a model parameter variable, and F represents the initial boundary model function with unknown weight variable ω and unknown model parameter variable A.

[0034] The first boundary model function is

[0035]

[0036] where ω i represents a weight of a prediction model i, i is a prediction model serial number, F(A) represents the first boundary model function with known weight ω i and unknown model parameter variable A.

[0037] The second boundary model function is

[0038]

[0039] where A' represents a model estimation parameter, and F(ω) represents the second boundary model function with unknown weight variable ω and known model estimation parameter A'.

[0040] In a possible design, the first boundary model function based on each set model parameter, a prediction deviation value of each prediction model for each set test question, and each prediction model weight is used to iteratively determine a first boundary model fitting degree corresponding to each set model parameter for each set test question, and the method comprises the following steps.

[0041] The first boundary model function based on each set model parameter, a prediction deviation value of each prediction model for each set test question, and each prediction model weight is substituted into a preset first boundary model fitting degree formula to perform iterative calculation, so as to obtain the first boundary model fitting degree corresponding to each set model parameter for each set test question, and the first boundary model fitting degree formula is

[0042]

[0043] where r j (A) represents the first boundary model fitting degree corresponding to the set model parameter A for the set test question j, i is a prediction model serial number, j is a set test question serial number, N is the number of prediction models, represents a prediction deviation value of a prediction model i for a set test question j, and min(·) represents a minimum value operator.

[0044] In a possible design, the second boundary model function value under the actual prediction value of each prediction model for the target prediction problem, each alternative optimal prediction value, and each prediction model weight is used to determine the second boundary model fitting degree corresponding to each alternative optimal prediction value, including:

[0045] The second boundary model function value under the actual prediction value of each prediction model for the target prediction problem, each alternative optimal prediction value, and each prediction model weight is substituted into a preset second boundary model fitting degree formula to perform traversal calculation, to obtain the second boundary model fitting degree corresponding to each alternative optimal prediction value, where the second boundary model fitting degree formula is

[0046]

[0047] where d° represents the alternative optimal prediction value, r(d°) represents the second boundary model fitting degree of the alternative optimal prediction value d°, i is the prediction model serial number, N is the number of prediction models, d i represents the actual prediction value of the prediction model i for the target prediction problem, min(·) represents a minimum value operator, F(ω i ) represents the weight ω i of the prediction model i, and F(d°) represents the corresponding second boundary model function value.

[0048] In a possible design, the average fitting degree corresponding to each set model parameter is used to select one set model parameter as a model estimation parameter, including:

[0049] Each set model parameter whose average fitting degree reaches a set fitting degree threshold condition is selected as a preselected model parameter, and the preselected model parameter with the minimum value is selected as the model estimation parameter.

[0050] In a second aspect, a boundary model-based combined prediction system is provided, including a data acquisition unit, a deviation determination unit, a weight determination unit, a first construction unit, a first calculation unit, a parameter selection unit, a second construction unit, a second calculation unit, and a result output unit, where:

[0051] The data acquisition unit is configured to determine a plurality of prediction models, a plurality of set test problems, and a target prediction problem, and to acquire test prediction values of each prediction model for each set test problem, factual optimal prediction values of each set test problem, a plurality of alternative optimal prediction values of the target prediction problem, and a plurality of set model parameters.

[0052] The deviation determination unit is configured to determine prediction deviation values of each prediction model for each set test problem according to the test prediction values of each prediction model for each set test problem and the factual optimal prediction values of each set test problem.

[0053] a weight determination unit configured to determine a weight of each prediction model based on a prediction deviation value of each prediction model for each set test question;

[0054] a first construction unit configured to substitute the weight of each prediction model into a preset initial boundary model function to obtain a first boundary model function under the weight of each prediction model, the initial boundary model function containing a weight variable and a model parameter variable;

[0055] a first calculation unit configured to determine a first boundary model fitting degree corresponding to each set model parameter under each set test question based on each set model parameter, a prediction deviation value of each prediction model for each set test question, and the first boundary model function under the weight of each prediction model;

[0056] a parameter selection unit configured to calculate an average fitting degree corresponding to each set model parameter according to the first boundary model fitting degree corresponding to each set model parameter under each set test question, and select one of the set model parameters as a model estimation parameter based on the average fitting degree corresponding to each set model parameter;

[0057] a second construction unit configured to substitute the model estimation parameter into the initial boundary model function to obtain a second boundary model function, and substitute the weight of each prediction model into the second boundary model function to obtain a second boundary model function value under the weight of each prediction model;

[0058] a second calculation unit configured to collect an actual prediction value of each prediction model for a target prediction question, and determine a second boundary model fitting degree corresponding to each candidate optimal prediction value based on the actual prediction value of each prediction model for the target prediction question, each candidate optimal prediction value, and the second boundary model function value under the weight of each prediction model;

[0059] a result output unit configured to take the candidate optimal prediction value corresponding to the maximum second boundary model fitting degree as a combined prediction value of the target prediction question, and output the combined prediction value of the target prediction question.

[0060] In a third aspect, a combined prediction device based on a boundary model is provided, comprising:

[0061] a memory configured to store instructions;

[0062] a processor configured to read the instructions stored in the memory, and execute the method of any one of the first aspect according to the instructions.

[0063] In a fourth aspect, a computer readable storage medium is provided, and the computer readable storage medium has stored thereon instructions which, when executed on a computer, cause the computer to perform any of the methods of the first aspect. Also provided is a computer program product which, when executed on a computer, performs any of the methods of the first aspect.

[0064] Beneficial effects: The application proposes a combination prediction method based on a boundary model by changing the common underlying logic of combination prediction when facing complex uncertain prediction problems, breaks away from the essence of average method pursuing consensus, can find the optimal prediction value with the fact as the target, and can effectively avoid consensus instead of fact. The application is different from the existing axiomatic method and Bayesian method, finds the optimal prediction value by using a data-driven model, is oriented to the fact as the target, and provides a new idea for the combination prediction method. BRIEF DESCRIPTION OF DRAWINGS

[0065] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of these drawings.

[0066] Figure 1 The schematic diagram of the steps of the method in the embodiment 1 of the present application is shown in the figure;

[0067] Figure 2 The schematic diagram of the boundary model in the embodiment 1 of the present application is shown in the figure;

[0068] Figure 3 The schematic diagram of the boundary model corresponding to different model parameters in the embodiment 1 of the present application is shown in the figure;

[0069] Figure 4 The schematic diagram of the system in the embodiment 2 of the present application is shown in the figure;

[0070] Figure 5 The schematic diagram of the equipment in the embodiment 3 of the present application is shown in the figure. DETAILED DESCRIPTION

[0071] It should be noted that the description of these embodiments is used to help understand the present application, but does not constitute a limitation of the present application. The specific structure and function details disclosed herein are only used to describe the example embodiments of the present application. However, the present application can be embodied in many alternative forms, and should not be understood as limited in the embodiments set forth herein.

[0072] It should be understood that, unless specifically stated and limited otherwise, the term "connected" is used broadly and exemplarily, and can be fixedly connected, or detachably connected, or integrally connected; can be mechanically connected, or electrically connected; can be directly connected, or indirectly connected through an intermediate medium; and can be internal connection of two elements. Those skilled in the art can understand the specific meaning of the above-mentioned terms in the embodiments according to the specific circumstances.

[0073] In the following description, specific details are provided to facilitate a full understanding of the example embodiments. However, one skilled in the art will understand that the example embodiments can be implemented without these specific details. For example, devices can be shown in block diagrams to avoid obscuring the examples with unnecessary detail. In other examples, well-known processes, structures, and techniques can not be shown in detail to avoid obscuring the embodiments.

[0074] Embodiment 1:

[0075] For the prediction problem of complex uncertainty, the combination prediction method is an effective way to find the optimal prediction value (fact). Compared with a single prediction method, it can effectively reduce random error and improve prediction accuracy. However, researchers in this field have long focused on consensus-oriented combination prediction, and there is little systematic theoretical research, resulting in a lack of matching theoretical guidance in problem prediction such as epidemic judgment, natural disaster prediction, and ecological environment prediction. At the same time, the rapid development of big data and artificial weight technology in recent years makes it possible to combine knowledge-driven and data-driven combination prediction methods, which provides an important basis for the theoretical analysis of combination prediction and the proposal of model-based combination prediction methods in this embodiment. This embodiment provides a combination prediction method based on boundary model, as shown in Figure 1 The method comprises the following steps:

[0076] S1. Determine a plurality of prediction models, a plurality of set test problems, and a target prediction problem, and obtain test prediction values of each prediction model for each set test problem, optimal prediction values of each set test problem, and a plurality of candidate optimal prediction values of the target prediction problem.

[0077] In specific implementation, a plurality of prediction models for combination prediction, a plurality of set test problems (which can be set in combination with historical information / prior knowledge), and a target prediction problem are determined, and at the same time, the optimal prediction values (i.e. factual values) of each set test problem and a plurality of candidate optimal prediction values (such as a plurality of candidate prediction temperature values within a certain temperature range for a temperature prediction problem) for the target prediction problem are determined. Each prediction model can be used to predict each set test problem in advance to obtain test prediction values of each prediction model for each set test problem.

[0078] S2. Determine the prediction deviation value of each prediction model for each set test question according to the test prediction value of each prediction model for each set test question and the fact optimal prediction value of each set test question.

[0079] In particular implementation, the prediction deviation value of each prediction model for each set test question can be obtained by subtracting the fact optimal prediction value of each set test question from the test prediction value of each prediction model for each set test question.

[0080] S3. Determine the weight of each prediction model based on the prediction deviation value of each prediction model for each set test question.

[0081] In particular implementation, at present, compared with the average method, the weighted average method can obtain a better decision by using the difference between the prediction models, which is an effective method of combined prediction. Existing research results start from factors such as professional knowledge, thinking mode and cultural background, and theoretically analyze and experimentally verify the quantification of the weight, that is, research from the perspective of mechanism. However, the measurement of the weight involves multiple disciplines such as psychology and management, and it is difficult to conduct comprehensive and logically rigorous mechanism research, so there is no universal conclusion yet. The present embodiment quantifies the weight from the perspective of decision optimality by data, and the goal of prediction is to approach the optimal prediction value (fact) and reduce the prediction deviation. Therefore, the present embodiment sets the quantification index of the weight as the inverse of the expectation of the historical prediction deviation, starting from the prediction result and combining prior knowledge such as test data or historical data.

[0082] Suppose there are N prediction models, and each prediction model has M set test questions (i.e. each prediction model has done a test question). First, substitute the prediction deviation value of each prediction model for each set test question into the preset prediction deviation distance formula to obtain the prediction deviation distance of each prediction model for each set test question, and the prediction deviation distance formula is

[0083]

[0084] where ‖·‖2 represents the two norm operation, i is the prediction model serial number, j is the set test question serial number, represents the prediction deviation distance of prediction model i for set test question j, represents the prediction deviation value of prediction model i for set test question j;

[0085] Then substitute the prediction deviation distance of each prediction model for each set test question into the prediction accuracy formula to obtain the test performance index of each prediction model, and the prediction accuracy formula is

[0086]

[0087] wherein, P i the test performance index of the prediction model i, and M is the number of set test problems;

[0088] The test performance of each prediction model is then normalized to obtain the weight of each prediction model, i.e., the test performance index of each prediction model is substituted into the preset weight calculation formula to calculate the weight of each prediction model, and the weight calculation formula is

[0089]

[0090] wherein, ω i the weight of the prediction model i, and N is the number of prediction models.

[0091] S4. Substituting the weight of each prediction model into the preset initial boundary model function to obtain the first boundary model function under the weight of each prediction model, and the initial boundary model function contains a weight variable and a model parameter variable.

[0092] In specific implementation, the hyperbolic model is an ideal form of the boundary model, i.e., an ideal model under the condition that the number of prediction models is sufficient. In actual prediction, since the number of single prediction models is limited, the boundary model is only a part of the hyperbolic model, as shown in Figure 2 The hyperbolic model is shown in the figure, the horizontal axis represents the weight, the vertical axis represents the prediction deviation, and the hyperbolic curve is an ideal boundary model, Figure 2 The part of the curve selected in the middle frame represents the actual initial boundary model, and the initial boundary model function is set as

[0093]

[0094] wherein, ω represents the weight variable; A is a model parameter variable, representing the complexity of the prediction problem, which determines the slope of the boundary model function, and the determination of the boundary model is the process of estimating the model parameter A, which can be estimated by a data-driven method, i.e., using the data of the weight and the deviation to estimate the parameter, as shown in Figure 3 i.e., different boundary models corresponding to different model parameters A, and the parameter estimation process is the process of selecting a suitable boundary function so that the weight and the deviation of the prediction model meet the boundary; F represents the initial boundary model function in which the weight variable ω is unknown and the model parameter variable A is unknown. Substituting the weight of each prediction model into the initial boundary model function can obtain the first boundary model function under the weight of each prediction model, and the first boundary model function is

[0095]

[0096] wherein, ω i the weight of the prediction model i, i is the serial number of the prediction model, and F(A) represents the weight ωi the first boundary model function with the unknown model parameter variable A being known.

[0097] S5. Obtain a plurality of set model parameters, and based on each set model parameter, a predicted deviation value of each prediction model for each set test question, and the first boundary model function under the weight of each prediction model, iteratively determine the first boundary model fitting degree corresponding to each set model parameter under each set test question.

[0098] In a specific implementation, a plurality of set model parameters A can be obtained in advance. For example, each set model parameter A can be set to be between 0.1 and 50 based on prior knowledge. Then, each set model parameter, a predicted deviation value of each prediction model for each set test question, and the first boundary model function under the weight of each prediction model are substituted into a preset first boundary model fitting degree formula to iteratively calculate a first boundary model fitting degree corresponding to each set model parameter under each set test question. The first boundary model fitting degree formula is

[0099]

[0100] wherein, r j (A) represents the first boundary model fitting degree corresponding to the set model parameter A under the set test question j, i represents the serial number of the prediction model, j represents the serial number of the set test question, N represents the number of prediction models, represents the predicted deviation value of the prediction model i for the set test question j, and min(·) represents a minimum value operator.

[0101] The boundary model fitting degree refers to a ratio of distances from all boundary inner deviations to the boundary to distances from all deviations to the boundary, and can be understood as a proportion of reasonable predictions within the boundary to all predictions. The boundary model fitting degree ∈ [0, 1]. When the boundary model fitting degree is equal to 0, it indicates that, based on the boundary model, predicted deviations of all prediction models are all beyond the boundary, and the model parameter A is unreasonable. When the boundary model fitting degree is equal to 1, it indicates that, based on the boundary model, predicted deviations of all prediction models are all within the boundary, and the model parameter A is reasonable. Therefore, the higher the boundary model fitting degree, the more reasonable the model parameter A.

[0102] S6. Calculate an average fitting degree corresponding to each set model parameter according to the first boundary model fitting degree corresponding to each set model parameter under each set test question, and select one from the set model parameters as the model estimation parameter based on the average fitting degree corresponding to each set model parameter.

[0103] In implementation, the preset first boundary model fitting degree formula is used to traverse calculation by substituting the set model parameters, the prediction deviation values of each prediction model for each set test question and the first boundary model function under each prediction model weight, to obtain the first boundary model fitting degree corresponding to each set model parameter under each set test question, and the first boundary model fitting degree formula is

[0104]

[0105] wherein, r j (A) represents the first boundary model fitting degree corresponding to the set model parameter A under the set test question j, i represents the prediction model serial number, j represents the set test question serial number, N represents the number of prediction models, represents the prediction deviation value of the prediction model i for the set test question j, and min(·) represents the minimum value operator.

[0106] Finally, each set model parameter whose average fitting degree reaches the set fitting degree threshold is taken as a preselected model parameter, and the one with the minimum value is selected from the preselected model parameters as the model estimation parameter. Since the prediction model will always be inaccurate, the boundary model fitting degree equal to 1 will not always appear, and therefore, the parameter A that can make the boundary model fitting degree reach the maximum value is generally selected as the model parameter. In addition, as the parameter A continuously increases, the boundary model fitting degree continuously increases, but the increasing speed continuously decreases, and when the boundary model fitting degree reaches a certain threshold r T , it is meaningless to further increase the parameter A, and blindly increasing the parameter A will cause the prediction model to be under-fitted. Therefore, in the embodiment, the minimum value of all set model parameters A whose boundary model fitting degree reaches the threshold r T is taken as the model estimation parameter A', that is, the model estimation parameter A' = arg min A (r(A) > r T ).

[0107] S7. The model estimation parameter is substituted into the initial boundary model function to obtain a second boundary model function, and the weight of each prediction model is substituted into the second boundary model function to obtain the second boundary model function value under the weight of each prediction model.

[0108] In implementation, after the model estimation parameter is determined, the model estimation parameter is substituted into the initial boundary model function to obtain a second boundary model function, and the weight of each prediction model is substituted into the second boundary model function to obtain the second boundary model function value under the weight of each prediction model.

[0109]

[0110] wherein A' is a model estimation parameter, and F(ω) represents a second boundary model function with unknown weight variable ω and known model estimation parameter A'. Then, the weight of each prediction model is substituted into the second boundary model function for calculation, to obtain the second boundary model function value F(ω i ) of each prediction model.

[0111] S8. Collecting actual prediction values of each prediction model for the target prediction problem, and based on the actual prediction values of each prediction model for the target prediction problem, each candidate optimal prediction value, and the second boundary model function value of each prediction model under the weight, traversing to determine the second boundary model fitting degree corresponding to each candidate optimal prediction value.

[0112] In specific implementation, each prediction model can be used to predict the target prediction problem, to obtain actual prediction values of each prediction model for the target prediction problem. Then, the actual prediction values of each prediction model for the target prediction problem, each candidate optimal prediction value, and the second boundary model function value of each prediction model under the weight are substituted into the preset second boundary model fitting degree formula for traversal calculation, to obtain the second boundary model fitting degree corresponding to each candidate optimal prediction value. In the case of less candidate optimal prediction values, the traversal calculation can be performed in the manner of Table 1 as follows:

[0113] Table 1

[0114]

[0115] In the case of more candidate optimal prediction values, intelligent algorithms such as particle swarm and genetic algorithm can be used for calculation and solution. The second boundary model fitting degree formula is

[0116]

[0117] wherein d° represents a candidate optimal prediction value, r(d°) represents the second boundary model fitting degree of the candidate optimal prediction value d°, i is a prediction model serial number, N is the number of prediction models, d i represents an actual prediction value of prediction model i for the target prediction problem, min(·) represents a minimum value operator, F(ω i ) represents a second boundary model function value of prediction model i under the weight ω i .

[0118] S9. Taking the candidate optimal prediction value corresponding to the maximum second boundary model fitting degree as the combined prediction value of the target prediction problem, and outputting the combined prediction value of the target prediction problem.

[0119] In implementation, according to the definition of the boundary model fitting degree, when r(d°) = 0, it indicates that the prediction deviations of all prediction models exceed the boundary, and the alternative optimal prediction value d° is unreasonable; when r(d°) = 1, it indicates that the prediction deviations of all prediction models based on the alternative optimal prediction value d° are within the boundary, and the alternative optimal prediction value d° is reasonable. Therefore, the greater the second boundary model fitting degree is, the more reasonable the alternative optimal prediction value d° is. Meanwhile, according to the characteristics of the boundary model, the greater the weight is, the smaller the prediction deviation is, and when the weight is 1, the corresponding prediction value is equal to the alternative optimal prediction value. Therefore, the alternative optimal prediction value d° corresponding to the maximum second boundary model fitting degree can be selected as the combined prediction value, that is, the combined prediction value d * = argmax d° {r(d°)}.

[0120] For the method of the present embodiment, specific application scenarios can be taken as examples, such as weather prediction scenarios. The prediction models include three kinds of meteorological expert prediction, cloud analysis prediction and scientific instrument prediction. It is assumed that the three prediction models have predicted the highest temperature of each day in the past year, that is, M = 365 set test problems have been predicted. According to the answers of the prediction models to the set test problems and the true answers (the actual highest temperature of each day in the past year) of the set test problems, the weights ω1, ω2, ω3 of the prediction models are obtained, the model estimation parameter A' is determined based on the first boundary model fitting degree, and the corresponding boundary model is obtained. Then, for a target prediction problem, such as predicting the highest temperature tomorrow, the meteorological expert prediction, cloud analysis prediction and scientific instrument prediction give three actual prediction values d1, d2, d3. Since the alternative prediction range of the highest temperature tomorrow is small, for example, 10-15 degrees, 0.1 degrees can be taken as the sampling interval, and all alternative optimal prediction values d° are traversed. For each alternative optimal prediction value d°, the second boundary model fitting degree is calculated, and the alternative optimal prediction value d° corresponding to the maximum second boundary model fitting degree is selected as the combined prediction value d * of the target prediction problem.

[0121] For the prediction of uncertain events, the existing technology is mostly realized based on axiomatic method and Bayesian method. The axiomatic method mainly refers to the average and weighted method, and the internal logic thereof is to obtain a prediction value that minimizes the mean square error (MSE). The prediction value that minimizes the mean square error (MSE) more reflects the consensus factors of multiple prediction models. The Bayesian method is target-oriented to facts, but the implementation process thereof requires a relatively accurate understanding and estimation of probability and conditional probability, and thus is mostly difficult to realize in practice. The embodiment method changes the common bottom logic of combination prediction, proposes a combination prediction method based on a boundary model, gets rid of the essence of the average method to pursue consensus, can be target-oriented to facts to find an optimal prediction value, can effectively avoid consensus instead of facts, and provides a new idea for the combination prediction method.

[0122] Embodiment 2:

[0123] The embodiment provides a combination prediction system based on a boundary model, as shown in Figure 4 The combination prediction system based on the boundary model comprises a data acquisition unit, a deviation judgment unit, a weight determination unit, a first construction unit, a first calculation unit, a parameter selection unit, a second construction unit, a second calculation unit and a result output unit, and wherein:

[0124] The data acquisition unit is configured to determine a plurality of prediction models, a plurality of set test problems and a target prediction problem, and acquire test prediction values of the prediction models for the set test problems, factual optimal prediction values of the set test problems, a plurality of candidate optimal prediction values of the target prediction problem, and a plurality of set model parameters.

[0125] The deviation judgment unit is configured to determine prediction deviation values of the prediction models for the set test problems according to the test prediction values of the prediction models for the set test problems and the factual optimal prediction values of the set test problems.

[0126] The weight determination unit is configured to determine weights of the prediction models based on the prediction deviation values of the prediction models for the set test problems.

[0127] The first construction unit is configured to substitute the weights of the prediction models into a preset initial boundary model function to obtain a first boundary model function under the weights of the prediction models, and the initial boundary model function comprises a weight variable and a model parameter variable.

[0128] The first calculation unit is configured to determine, based on the set model parameters, the prediction deviation values of the prediction models for the set test problems and the first boundary model function under the weights of the prediction models, a first boundary model fitting degree corresponding to the set model parameters under the set test problems.

[0129] The parameter selecting unit is configured to calculate an average fitting degree corresponding to each set model parameter according to the first boundary model fitting degrees corresponding to the set model parameters under each set test question, and select one of the set model parameters as a model estimation parameter based on the average fitting degrees corresponding to the set model parameters.

[0130] The second constructing unit is configured to substitute the model estimation parameter into the initial boundary model function to obtain a second boundary model function, and substitute the weight of each prediction model into the second boundary model function to obtain a second boundary model function value under the weight of each prediction model.

[0131] The second calculating unit is configured to collect actual prediction values of each prediction model for the target prediction question, and determine the second boundary model fitting degrees corresponding to each candidate optimal prediction value based on the actual prediction values of each prediction model for the target prediction question, the candidate optimal prediction values, and the second boundary model function values under the weight of each prediction model.

[0132] The result output unit is configured to take the candidate optimal prediction value corresponding to the maximum second boundary model fitting degree as a combined prediction value of the target prediction question, and output the combined prediction value of the target prediction question.

[0133] Embodiment 3

[0134] This embodiment provides a combined prediction device based on a boundary model, as shown in Figure 5 At the hardware level, the device includes:

[0135] The data interface is configured to establish data connection between the processor and an external data terminal.

[0136] The memory is configured to store instructions.

[0137] The processor is configured to read the instructions stored in the memory, and execute the combined prediction method based on the boundary model in Embodiment 1 according to the instructions.

[0138] Optionally, the device further includes an internal bus, and the processor, the memory and the data interface are connected to each other through the internal bus. The internal bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, an EISA (Extended Industry Standard Architecture) bus, or the like. The bus can be divided into an address bus, a data bus, a control bus, and the like.

[0139] The memory can include, but is not limited to, a random access memory (RAM), a read only memory (ROM), a flash memory, a first in first out memory (FIFO), a first in last out memory (FILO), and / or the like. The processor can be a general purpose processor, including a central processing unit (CPU), a network processor (NP), and / or the like; and can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic, a discrete hardware component.

[0140] Embodiment 4:

[0141] The embodiment provides a computer readable storage medium, and instructions are stored on the computer readable storage medium. When the instructions are run on a computer, the computer executes the combined prediction method based on the boundary model in the embodiment 1. The computer readable storage medium is a carrier for storing data, and can include, but is not limited to, a floppy disk, a compact disc, a hard disk, a flash memory, a USB flash disk, a memory stick, and / or the like. The computer can be a general purpose computer, a special purpose computer, a computer network, or other programmable devices.

[0142] The embodiment also provides a computer program product, and when the computer program product is run on a computer, the combined prediction method based on the boundary model in the embodiment 1 is executed. The computer can be a general purpose computer, a special purpose computer, a computer network, or other programmable devices.

[0143] Finally, it should be noted that: the above only describes the preferred embodiments of the present application and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, and / or the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A combined prediction method based on boundary models, characterized in that, include: Several prediction models, several set test problems, and a target prediction problem are identified, and the test prediction values ​​of each prediction model for each set test problem, the factual optimal prediction values ​​of each set test problem, and several alternative optimal prediction values ​​for the target prediction problem are obtained. Based on the test prediction values ​​of each prediction model for each set test problem and the actual optimal prediction values ​​of each set test problem, determine the prediction deviation value of each prediction model for each set test problem. The weights of each prediction model are determined based on the prediction deviation values ​​of each prediction model for each set test question. Substitute the weights of each prediction model into a preset initial boundary model function to obtain the first boundary model function under each prediction model weight. The initial boundary model function includes weight variables and model parameter variables. Obtain several set model parameters, and based on each set model parameter, the prediction deviation value of each prediction model for each set test problem, and the first boundary model function under the weight of each prediction model, traverse and determine the first boundary model fit degree corresponding to each set model parameter under each set test problem. Calculate the average goodness of fit of each set model parameter according to the first boundary model goodness of fit of each set model parameter under each set test problem, and select one of the set model parameters as the model estimation parameter based on the average goodness of fit of each set model parameter. Substitute the model estimation parameters into the initial boundary model function to obtain the second boundary model function, and then substitute the weights of each prediction model into the second boundary model function for calculation to obtain the second boundary model function value under each prediction model weight. Collect the actual predicted values ​​of each prediction model for the target prediction problem, and based on the actual predicted values ​​of each prediction model for the target prediction problem, each candidate optimal prediction value, and the second boundary model function value under the weight of each prediction model, iterate to determine the second boundary model fit degree corresponding to each candidate optimal prediction value. The candidate optimal prediction value with the highest model fit corresponding to the second boundary is used as the combined prediction value of the target prediction problem, and the combined prediction value of the target prediction problem is output.

2. The combined prediction method based on boundary models according to claim 1, characterized in that, The step of determining the prediction deviation of each prediction model for each set test problem based on the test prediction values ​​of each prediction model for each set test problem and the factual optimal prediction values ​​of each set test problem includes: The prediction bias of each prediction model for the given test problem is obtained by subtracting the actual optimal prediction value for the corresponding test problem from the test prediction value of each prediction model for the given test problem.

3. The combined prediction method based on boundary models according to claim 1, characterized in that, The determination of the weights of each prediction model based on the prediction deviation values ​​of each prediction model for each set test problem includes: The prediction deviation values ​​of each prediction model for each set test problem are substituted into a preset prediction deviation distance formula for calculation to obtain the prediction deviation distance of each prediction model for each set test problem. The prediction deviation distance formula is as follows: Where ||·||2 represents the L2 norm operation, i is the prediction model index, and j is the set test question index. The distance between the prediction bias of prediction model i and the given test problem j is used to characterize the prediction deviation. This represents the prediction bias of prediction model i for the given test problem j; The prediction deviation distance of each prediction model for each set test problem is substituted into the prediction accuracy formula for calculation to obtain the test performance index of each prediction model. The prediction accuracy formula is as follows: Among them, P i The test performance index characterizes the prediction model i, where M is the number of test questions. The test performance indicators of each prediction model are substituted into a preset weighting formula to calculate the weights of each prediction model. The weighting formula is as follows: Where, ω i The weights represent the prediction model i, and N is the number of prediction models.

4. The combined prediction method based on boundary models according to claim 1, characterized in that, The initial boundary model function is: Where ω represents the weight variable, A is the model parameter variable, and F represents the initial boundary model function where the weight variable ω and the model parameter variable A are unknown; The first boundary model function is Where, ω i F(A) represents the weights ω of prediction model i, where i is the prediction model index. i The first boundary model function is known, but the model parameter variable A is unknown; The second boundary model function is Where A' is the model estimation parameter, and F(ω) represents the second boundary model function where the weight variable ω is unknown but the model estimation parameter A' is known.

5. The combined prediction method based on boundary models according to claim 4, characterized in that, The process of determining the first boundary model fit degree corresponding to each set model parameter under each set test problem, based on each set model parameter, the prediction deviation value of each prediction model for each set test problem, and the first boundary model function under each prediction model weight, includes: Substituting the set model parameters, the prediction deviation of each prediction model for each set test problem, and the first boundary model function under the weights of each prediction model, into a preset first boundary model fit formula, we perform iterative calculations to obtain the first boundary model fit corresponding to each set model parameter under each set test problem. The first boundary model fit formula is: Where, r j (A) Characterizes the first boundary model fit of the given test problem j and corresponding model parameters A, where i is the prediction model index, j is the given test problem index, and N is the number of prediction models. The prediction deviation of prediction model i for given test problem j is represented by min(·), which represents the minimum value operator.

6. The combined prediction method based on boundary models according to claim 4, characterized in that, The process of determining the goodness of fit of the second boundary model corresponding to each candidate optimal prediction value by iterating through the actual predicted values ​​of each prediction model for the target prediction problem, each candidate optimal prediction value, and the second boundary model function value under the weights of each prediction model includes: The actual predicted values ​​of each prediction model for the target prediction problem, the optimal predicted values ​​of each candidate model, and the second boundary model function values ​​under the weights of each prediction model are substituted into a preset second boundary model fit formula for iterative calculation to obtain the second boundary model fit degree corresponding to each optimal predicted value. The second boundary model fit degree formula is as follows: Where d° represents the candidate optimal predicted value, r(d°) represents the second boundary model fit of the candidate optimal predicted value d°, i is the prediction model index, N is the number of prediction models, and d i The min(·) characterizes the actual predicted value of prediction model i for the target prediction problem, and represents the minimum value operator, F(ω). i The weights ω of the prediction model i are represented. i The corresponding second boundary model function value.

7. The combined prediction method based on boundary models according to claim 1, characterized in that, The step of selecting one of the set model parameters as the model estimation parameter based on the average goodness of fit corresponding to each set model parameter includes: Each set model parameter whose average goodness of fit reaches the set goodness of fit threshold is used as a pre-selected model parameter, and the one with the smallest value among the pre-selected model parameters is selected as the model estimation parameter.

8. A combined prediction system based on boundary models, characterized in that, It includes a data acquisition unit, a deviation determination unit, a weight determination unit, a first construction unit, a first calculation unit, a parameter selection unit, a second construction unit, a second calculation unit, and a result output unit, wherein: The data acquisition unit is used to determine several prediction models, several set test problems and target prediction problems, and to acquire the test prediction values ​​of each prediction model for each set test problem, the factual optimal prediction values ​​of each set test problem, several alternative optimal prediction values ​​of the target prediction problem, and several set model parameters. The deviation determination unit is used to determine the prediction deviation of each prediction model for each set test problem based on the test prediction value of each prediction model for each set test problem and the actual optimal prediction value of each set test problem. The weight determination unit is used to determine the weight of each prediction model based on the prediction deviation value of each prediction model for each set test problem. The first construction unit is used to substitute the weights of each prediction model into a preset initial boundary model function to obtain the first boundary model function under the weights of each prediction model. The initial boundary model function includes weight variables and model parameter variables. The first calculation unit is used to determine the first boundary model fit degree corresponding to each set model parameter under each set test problem based on each set model parameter, the prediction deviation value of each prediction model for each set test problem and the first boundary model function under each prediction model weight. The parameter selection unit is used to calculate the average fit of each set model parameter according to the first boundary model fit of each set model parameter under each set test problem, and select one of the set model parameters as the model estimation parameter based on the average fit of each set model parameter. The second building unit is used to substitute the model estimation parameters into the initial boundary model function to obtain the second boundary model function, and to substitute the weights of each prediction model into the second boundary model function for calculation to obtain the second boundary model function value under each prediction model weight. The second calculation unit is used to collect the actual prediction values ​​of each prediction model for the target prediction problem, and based on the actual prediction values ​​of each prediction model for the target prediction problem, each candidate optimal prediction value, and the second boundary model function value under the weight of each prediction model, it iterates to determine the second boundary model fitting degree corresponding to each candidate optimal prediction value. The result output unit is used to take the candidate optimal prediction value with the highest fitting degree to the second boundary model as the combined prediction value of the target prediction problem, and output the combined prediction value of the target prediction problem.

9. A combined prediction device based on boundary models, characterized in that it comprises: Memory, used to store instructions; A processor is configured to read instructions stored in the memory and execute the combined prediction method according to any one of claims 1-7.

10. A computer program product, characterized in that, When the computer program product is run on a computer, it performs the combined prediction method according to any one of claims 1-7.

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