A method, device and medium for analyzing dependence structure of interval quantile

Abstract

The application discloses a method, device and medium for analyzing the dependent structure of interval quantile, and relates to the technical field of computers.The method comprises the following steps: determining input data corresponding to a task scene, and determining a multi-dimensional covariate and a response variable according to the input data; dividing the response variable to obtain a plurality of sub-intervals; determining a projection correlation coefficient according to the multi-dimensional covariate and the response variable, wherein the projection correlation coefficient comprises a projection bias and a quantile projection correlation coefficient; determining the projection bias according to the projection correlation coefficient, determining a test statistic according to the projection bias, comparing the test statistic with a pre-set threshold, and determining data dependency. The application can adapt to multiple scenes because of the diverse input data sources; the response variable can be flexibly divided to obtain multiple sub-intervals; the projection correlation coefficient is determined by the multi-dimensional variable, which is scientific and reasonable; the test statistic is constructed by the projection bias and compared with the threshold, which can efficiently determine the data dependency, avoid complex approximation, and reduce the calculation cost.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a method, device and medium for dependency structure analysis of interval quantiles. Background Technology

[0002] With the rapid development of artificial intelligence technology, especially large foundation models, AI systems are facing increasingly higher demands on their ability to understand high-dimensional, heterogeneous, and unstructured data. From natural language processing and recommender systems to multimodal model training, model performance fundamentally depends on the accurate characterization of the complex relationships between input features. Especially when data distributions exhibit asymmetry, heavy tails, or structural abrupt changes, accurately modeling the dependencies between variables has become a critical problem that urgently needs to be solved in the current AI field. In traditional statistics, quantile regression, as an important tool for describing the dependencies between variables, has opened up new avenues for modeling heterogeneous data. Unlike mean regression, which focuses only on the average effect, quantile regression can characterize the conditional distribution information of the response variable at multiple locations, thereby revealing the influence of covariates on the target variable in different distribution intervals. This characteristic is particularly important in typical AI tasks such as financial risk control, medical prediction, and user behavior modeling. However, current mainstream quantile modeling methods have some key limitations that hinder their widespread application in modern artificial intelligence systems. On the one hand, traditional methods are often limited to fixed quantile modeling at a single or a few quantile levels, making it difficult to fully reveal the dependency structure of feature variables across the entire distribution range. This is especially true in tasks such as high-dimensional feature embedding or anomaly detection, where important dependency signals at the tail or under specific conditions are easily overlooked. On the other hand, most current quantile correlation methods are static correlation measures under low-dimensional settings, lacking the ability to adapt to the complex input structure of AI systems and making it difficult to deeply integrate with the preprocessing modules or attention mechanisms of deep learning models. Summary of the Invention

[0003] To address the aforementioned issues, this application proposes a dependency structure analysis method based on interval quantiles, comprising: determining input data corresponding to a task scenario, and determining multidimensional covariates and response variables based on the input data; dividing the response variable to obtain multiple sub-intervals; determining a projection correlation coefficient based on the multidimensional covariates and the response variable, wherein the projection correlation coefficient includes projection bias and quantile projection correlation coefficient; determining a projection bias based on the projection correlation coefficient; determining a test statistic based on the projection bias; and comparing the test statistic with a pre-set threshold to determine data dependency.

[0004] In one example, determining multidimensional covariates and response variables based on the input data specifically includes: the input data including at least one or more of the following: structured features, unstructured representations, image features, and text vectors; determining a high-dimensional feature space based on the input data, and determining covariates and response variables of arbitrary dimensions based on the high-dimensional feature space.

[0005] In one example, dividing the response variable specifically includes: determining multiple pre-set quantile intervals, including continuous quantile intervals and non-continuous quantile intervals, and dividing the response variable according to the pre-set quantile intervals.

[0006] In one example, determining the projected correlation coefficient based on the multidimensional covariates and the response variable specifically includes: determining the categories of the sub-intervals, the categories including unconditional quantiles and conditional quantiles; determining a similarity measure based on the unconditional quantiles and the conditional quantiles; determining quantile projection bias based on the similarity measure; determining quantile dependence based on the quantile projection bias; standardizing based on the quantile projection bias; and determining the projected correlation coefficient based on the standardized quantile projection bias and the quantile dependence.

[0007] In one example, determining the test statistic based on the projection bias specifically includes: determining pre-set random sample data; performing sample estimation on the projection correlation coefficient based on the random sample data to determine the bias-reduction test statistic; and determining that the bias-reduction test statistic asymptotically follows a normal distribution with zero mean and finite variance when the input feature dimension tends to infinity.

[0008] In one example, the test statistic is compared with a pre-set threshold to determine data dependency. Specifically, this includes: determining the asymptotic variance associated with the quantile interval based on the pre-set quantile interval; determining the threshold of the test statistic based on the characteristics of the asymptotic variance and the normal distribution; comparing the test statistic with the threshold; and if the test statistic is greater than the threshold, it is determined that there is a dependency between the covariate and the response variable within the quantile interval.

[0009] In one example, the division of the response variable specifically includes: when using a uniform segmentation strategy, generating continuous quantile intervals according to a preset equal-width rule; when using an adaptive segmentation strategy, dynamically adjusting the interval boundaries according to the data distribution density of the response variable.

[0010] In one example, the standardization process based on the quantile projection deviation specifically includes: standardizing the quantile projection deviation according to a pre-set variance normalization factor to obtain the quantile projection correlation coefficient; calculating the conditional quantile function of the covariate and the response variable, and defining a random vector similarity measure based on a geometric perspective; when the probability measure is a Lebesgue measure, calculating the square of the interval projection correlation coefficient through numerical integration; when the probability measure is a counting measure, calculating the square of the countable set projection correlation coefficient through discrete summation.

[0011] On the other hand, this application also proposes a dependency structure analysis device for interval quantiles, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the dependency structure analysis device for interval quantiles to perform: the method described in any of the examples above.

[0012] On the other hand, this application also proposes a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured to be the method described in any of the examples above.

[0013] This application provides input data covering various types, including structured and unstructured data, enabling the identification of covariates and response variables of arbitrary dimensions in high-dimensional space, making it suitable for complex and diverse task scenarios. When partitioning the response variable, it can use uniform segmentation to generate continuous intervals, adaptively adjust boundaries based on data distribution density, and also support discontinuous intervals to meet different data feature requirements. Similarity measures are determined through unconditional and conditional quantiles, leading to the projected correlation coefficient, which scientifically measures the degree of dependency between variables. The standardization process is diverse, considering different probability measures. Based on random sample data, a biased test statistic is determined. When the input feature dimension approaches infinity, it asymptotically follows a normal distribution. The threshold is determined by combining the asymptotic variance to judge data dependency, avoiding the complex threshold approximation of traditional methods, reducing computational costs, and improving the reliability and efficiency of the test. Attached Figure Description

[0014] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0015] Figure 1 This is a flowchart illustrating a dependency structure analysis method for interval quantiles in an embodiment of this application.

[0016] Figure 2This is a schematic diagram of a dependency structure analysis device for interval quantiles in an embodiment of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0019] like Figure 1 As shown, in order to solve the above problems, this application provides a method for dependency structure analysis of interval quantiles, the method comprising:

[0020] S101. Determine the input data corresponding to the task scenario, and determine the multidimensional covariates and response variables based on the input data. Divide the response variables to obtain multiple sub-intervals.

[0021] This system acquires input data from any AI task scenario. This data can encompass various types, including structured features such as form data, unstructured representations such as embedded vectors and graph representations, as well as image features and text vectors. It also supports input processing of covariates x and response variables Y of arbitrary dimensions within a high-dimensional feature space Rp. For simplicity, the response variable will be denoted as Y, and the covariate as x, where x can be a vector of any dimension.

[0022] By pre-setting a series of continuous or discontinuous quantile intervals, such as 0.1 to 0.3, 0.3 to 0.7, 0.7 to 0.9, the distribution of the response variable is divided into multiple sub-intervals, thereby capturing the dependencies between variables in different regions. This step has low requirements for the assumptions of the marginal distribution, and is therefore suitable for data analysis scenarios with complex distribution structures such as non-Gaussian distributions and heteroscedasticity.

[0023] S102. Determine the projection correlation coefficient based on the multidimensional covariates and the response variable, wherein the projection correlation coefficient includes projection bias and quantile projection correlation coefficient.

[0024] Under the aforementioned assumptions, Y is a univariate response variable, and the covariate x is a p-dimensional vector, where p is greater than or equal to 1. Let... and Let represent the unconditional τ quantile of Y and the conditional τ quantile of given x, respectively, where 0 is less than τ and less than 1.

[0025] In the field of statistics, the definition is... ,in is the cumulative distribution function of Y, and inf represents taking the minimum value in the set. Y is the cumulative distribution function conditionally with respect to x. Let T be the quantile interval, where T is a subset of (0,1). Definition , where τ is the quantile level, with a value range of (0,1), and I represents the indicator function.

[0026] Next, two random vectors based on geometric angles are defined. and Similarity measures between them: Among them, the relevant random variables and the independent and identically distributed cases are based on pre-set literature suggestions, and the smoothing term is included. Take as The median is used to avoid instability caused by vectors that are too short, i.e., norms close to 0.

[0027] For a fixed τ belonging to (0,1), the quantile projection deviation is defined as denoted as τ is used to measure the dependence of Y on x at the τ quantile level. Its mathematical formula is:

[0028]

[0029] Here, E represents the expected value of the random variable.

[0030] To standardize this projection bias, a quantile projection correlation coefficient, denoted as PQcor(Y|x;τ), is further introduced. Its mathematical formula is:

[0031]

[0032] in, express variance

[0033]

[0034] here , , and They are all random variables that are independent and identically distributed with x.

[0035] In each given quantile interval Within this interval, define and calculate the projected correlation coefficient between the covariate and the response variable. The squared form of the interval quantile projected correlation coefficient is:

[0036]

[0037] Where μ depends on the quantile interval The probability measure. When When μ is an interval or the union of intervals, it can take the Lebesgue measure; when When the set is countable, μ can take the counting measure. If The quantile interval, under the Lebesgue measure, can be represented as:

[0038]

[0039] like For a countable set, it can be represented in counting measure as:

[0040]

[0041] S103. Determine the projection deviation based on the projection correlation coefficient, determine the test statistic based on the projection deviation, and compare the test statistic with a preset threshold to determine the data dependency.

[0042] set up Given a set of n independent and identically distributed random samples, estimate the projective correlation coefficient using the sample data. Definition The sample τ quantile is:

[0043]

[0044] in, It is the empirical distribution function of Y. Furthermore, it is defined as follows: Sample estimate is , i=1,2,…,n.

[0045] In higher-dimensional cases, The items are centralized, that is, using Alternative ,in Thus, a biased test statistic is constructed. The estimate of the square of the correlation coefficient after bias correction of the interval quantile projection is expressed as:

[0046]

[0047] in,

[0048]

[0049]

[0050] When μ is a count measure, the integral of the square of the correlation coefficient projected by the interval quantiles is relatively simple to calculate. However, when μ is a Lebesgue measure, the calculation becomes more difficult due to the integral of τ. It is important to note that when... hour, The estimate remains unchanged. At this point, the square of the sample quantile projection deviation... It can be represented as:

[0051]

[0052] Furthermore, the square of the quantile projection correlation coefficient of the sample interval It can be represented as:

[0053]

[0054] in, This represents the k / n sample quantile of Y, i.e. =k / n. Represents quantile intervals The intersection of the interval [(k-1) / n, k / n).

[0055] Therefore, if For the Lebesgue measure, then ,So The calculation can be made more convenient based on the following known integral results:

[0056] ,

[0057] Under certain regularization conditions, when the dimension p of the input feature / covariate x tends to infinity as the sample size n increases, if Y and x are quantile-independent within a given quantile interval Γ, then the partial pass statistic is... It asymptotically follows a normal distribution with zero mean and finite variance, and its form is as follows:

[0058]

[0059] The asymptotic variance is defined as follows:

[0060]

[0061] Here, min() represents taking the minimum value. () represents a probability measure, and here we take the Lebesgue measure.

[0062] If, within a given quantile interval, Y and x have a linear or non-linear quantile dependency, and as n approaches infinity, but .

[0063] In particular, we would like to point out here that asymptotic variance The joint distribution is independent of (x, Y). When Γ is an interval, the asymptotic variance can be approximated by numerical integration. In Γ=(0,1) and In special cases, according to Anderson and Darling (1952), it can be proven that... Therefore, the asymptotic variance can be calculated explicitly.

[0064] The results above show that when the input feature / covariate dimension p is sufficiently large, the threshold of the debiased statistic we constructed for testing the correlation between Y and x within a given quantile interval does not depend on the joint distribution of (Y,x), but only on the quantile interval of interest. This avoids the threshold approximation of bootstrap or random permutation in traditional methods and significantly reduces computational costs.

[0065] like Figure 2 As shown in the embodiment of this application, a dependency structure analysis device for interval quantiles is also provided, including:

[0066] At least one processor; and,

[0067] A memory that is communicatively connected to at least one processor; wherein,

[0068] The memory stores instructions executable by at least one processor, which enable a dependency structure analysis device for interval quantiles to perform the following:

[0069] Determine the input data corresponding to the task scenario, and determine the multidimensional covariates and response variables based on the input data. Divide the response variables to obtain multiple sub-intervals.

[0070] The projection correlation coefficient is determined based on the multidimensional covariates and the response variable, and the projection correlation coefficient includes projection bias and quantile projection correlation coefficient.

[0071] The projection bias is determined based on the projection correlation coefficient, and a test statistic is determined based on the projection bias. The test statistic is then compared with a pre-set threshold to determine data dependency.

[0072] This application embodiment also provides a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured as follows:

[0073] Determine the input data corresponding to the task scenario, and determine the multidimensional covariates and response variables based on the input data. Divide the response variables to obtain multiple sub-intervals.

[0074] The projection correlation coefficient is determined based on the multidimensional covariates and the response variable, and the projection correlation coefficient includes projection bias and quantile projection correlation coefficient.

[0075] The projection bias is determined based on the projection correlation coefficient, and a test statistic is determined based on the projection bias. The test statistic is then compared with a pre-set threshold to determine data dependency.

[0076] In the 1990s, improvements to a technology could be clearly distinguished as either hardware improvements (e.g., improvements to the circuit structure of diodes, transistors, switches, etc.) or software improvements (improvements to the methodology). However, with technological advancements, many methodological improvements today can be considered direct improvements to the hardware circuit structure. Designers almost always obtain the corresponding hardware circuit structure by programming the improved methodology into the hardware circuit. Therefore, it cannot be said that a methodological improvement cannot be implemented using hardware physical modules. For example, a Programmable Logic Device (PLD) (such as a Field Programmable Gate Array (FPGA)) is such an integrated circuit whose logic function is determined by the user programming the device. Designers can program and "integrate" a digital system onto a PLD themselves, without needing chip manufacturers to design and manufacture dedicated integrated circuit chips. Furthermore, nowadays, instead of manually manufacturing integrated circuit chips, this programming is mostly implemented using "logic compiler" software. Similar to the software compiler used in program development, the original code before compilation must also be written in a specific programming language, called a Hardware Description Language (HDL). There are many HDLs, such as ABEL (Advanced Boolean Expression Language), AHDL (Altera Hardware Description Language), Confluence, CUPL (Cornell University Programming Language), HDCal, JHDL (Java Hardware Description Language), Lava, Lola, MyHDL, PALASM, and RHDL (Ruby Hardware Description Language). Currently, the most commonly used are VHDL (Very-High-Speed ​​Integrated Circuit Hardware Description Language) and Verilog. Those skilled in the art should also understand that by simply performing some logic programming on the method flow using one of these hardware description languages ​​and programming it into an integrated circuit, the hardware circuit implementing the logical method flow can be easily obtained.

[0077] The controller can be implemented in any suitable manner. For example, it can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code form, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included therein for implementing various functions can also be considered as structures within the hardware component. Alternatively, the means for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0078] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0079] For ease of description, the above devices are described in terms of function, divided into various units. Of course, in implementing this specification, the functions of each unit can be implemented in one or more software and / or hardware components.

[0080] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the device and medium embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the description of the method embodiments.

[0081] The devices and media provided in this application are one-to-one with the methods. Therefore, the devices and media also have similar beneficial technical effects as their corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the devices and media will not be repeated here.

[0082] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0083] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0084] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0085] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0086] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0087] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0088] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0089] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0090] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for dependency structure analysis of interval quantiles, characterized in that, include: Determine the input data corresponding to the task scenario, and determine the multidimensional covariates and response variables based on the input data. Divide the response variables to obtain multiple sub-intervals. The projection correlation coefficient is determined based on the multidimensional covariates and the response variable, and the projection correlation coefficient includes projection bias and quantile projection correlation coefficient. The projection bias is determined based on the projection correlation coefficient, and a test statistic is determined based on the projection bias. The test statistic is then compared with a pre-set threshold to determine data dependency. The projection correlation coefficient is determined based on the multidimensional covariates and the response variable, specifically including: The categories of the sub-intervals are determined, including unconditional quantiles and conditional quantiles, and a similarity measure is determined based on the unconditional quantiles and the conditional quantiles. The quantile projection bias is determined based on the similarity metric, and the degree of quantile dependence is determined based on the quantile projection bias. The projection deviation is standardized based on the quantile projection deviation, and the projection correlation coefficient is determined based on the standardized quantile projection deviation and the quantile dependence. The test statistic is determined based on the projection bias, specifically including: Determine pre-set random sample data, and perform sample estimation on the projection correlation coefficient based on the random sample data to determine the bias removal test statistic; When the input feature dimension approaches infinity, the bias removal test statistic is determined to asymptotically follow a normal distribution with zero mean and finite variance. The test statistic is compared with a pre-set threshold to determine data dependencies, specifically including: Determine the asymptotic variance associated with the quantile intervals based on the pre-set quantile intervals; The threshold of the test statistic is determined based on the characteristics of the asymptotic variance and normal distribution, and the test statistic is compared with the threshold. If the test statistic is greater than the threshold, it is determined that there is a dependency between the covariate and the response variable within the quantile interval.

2. The method according to claim 1, characterized in that, The multidimensional covariates and response variables are determined based on the input data, specifically including: The input data includes at least one or more of the following: structured features, unstructured representations, image features, and text vectors; A high-dimensional feature space is determined based on the input data, and covariates and response variables of arbitrary dimensions are determined based on the high-dimensional feature space.

3. The method according to claim 1, characterized in that, The response variables are divided, specifically including: Multiple pre-defined quantile intervals are determined, including continuous quantile intervals and non-continuous quantile intervals, and the response variable is divided according to the pre-defined quantile intervals.

4. The method according to claim 3, characterized in that, The response variables are divided, specifically including: When using a uniform segmentation strategy, continuous quantile intervals are generated according to a preset equal-width rule; When using an adaptive segmentation strategy, the interval boundaries are dynamically adjusted based on the data distribution density of the response variables.

5. The method according to claim 1, characterized in that, The standardization process based on the quantile projection deviation specifically includes: The quantile projection bias is standardized according to the pre-set variance normalization factor to obtain the quantile projection correlation coefficient. Calculate the conditional quantile function between the covariate and the response variable, and define a similarity measure of random vectors from a geometric perspective; When the probability measure is the Lebesgue measure, the square of the interval projection correlation coefficient is calculated by numerical integration; When the probability measure is a counting measure, the square of the projected correlation coefficient of the countable set is calculated by discrete summation.

6. A dependency structure analysis device for interval quantiles, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the interval quantile dependency structure analysis device to perform the method as described in any one of claims 1-5.

7. A non-volatile computer storage medium storing computer-executable instructions, characterized in that, The computer-executable instructions are configured to be the method as described in any one of claims 1-5.

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