Anti-factual fair decision model based on data generation and intervention driven association

Abstract

The invention discloses an anti-fact fairness decision-making model based on data generation and intervention-driven correlation. The anti-fact fairness decision-making model includes estimating anti-fact fairness of a causal model based on intervention-driven correlation, and using intervention-driven correlation to reduce data of the generated anti-fact fairness model. Compared with the prior art, the method has the advantages that the method for solving the anti-fact fairness problem through fair data generation is directly suitable for non-binary pion feeling attributes and labels, has adjustable parameters to control the tradeoff between accuracy and fairness, can be used for generating data capable of realizing an anti-fact fairness model, and can be used for realizing the anti-fact fairness model. A fair decision model is provided.

Description

Technical Field

[0001] The present invention relates to the technical field of fairness research on machine learning models, and specifically refers to a counterfactual fair decision-making model based on data generation and intervention-driven association. Background Art

[0002] With the advancement of artificial intelligence (AI) technology, decision-making systems that once relied entirely on human judgment are gradually turning to AI-based decision-making. At the same time, the fairness issue in machine learning models has received increasing attention from society.

[0003] One of the first challenges in solving fairness problems in machine learning is to formalize people's perception of fairness. To address this challenge, many fairness standards have been proposed in recent years. However, most of these standards define fairness from a statistical perspective, which makes them lack universality and sometimes leads to contradictions between different standards. Unlike fairness standards defined by statistical methods, counterfactual fairness goes a step further and considers how their prediction results would change if individuals belonged to different populations. A major challenge in solving counterfactual fairness problems is that sensitive attribute information may be embedded in non-sensitive attributes, thereby inadvertently affecting the decision-making process of downstream models.

[0004] For example, a zip code may reveal racial demographics, and occupation may hint at gender. Excluding all attributes containing sensitive information could drastically reduce the accuracy of the model, thus affecting its utility.

[0005] To this end, the inventors proposed a new metric, called Intervention-Driven Correlation (IDC), to evaluate the counterfactual fairness of generative models. IDC evaluates fairness by randomly intervening on sensitive attributes and measuring the correlation between these interventions and label changes. This metric is applicable to discrete and continuous sensitive attributes and labels, and is more suitable as a fairness constraint in generative model training than metrics such as total effect.

[0006] Based on IDC, the inventors proposed IDC-Reduction, a two-stage training method that solves the "Utopia Problem", that is, counterfactual fair data may not guarantee that the model will make equally fair predictions in real scenarios. Summary of the invention

[0007] The technical problem to be solved by the present invention is to overcome the above technical defects and provide a counterfactual fair decision-making model based on data generation and intervention-driven association.

[0008] To solve the above technical problems, the technical solution provided by the present invention is: a counterfactual fairness decision-making model based on data generation and intervention-driven association, including the counterfactual fairness of the causal model estimated based on intervention-driven correlation, and the data for generating the counterfactual fairness model using intervention-driven correlation reduction.

[0009] Preferably, the causal model is expressed as in:

[0010] V is the set of endogenous variables, U is the set of exogenous variables, is a set of functions that determine v;

[0011] That is V i ←f i (pa(V i ), U i ),in:

[0012] pa(V i ) indicates V i The parent variable set, P U represents the distribution of U.

[0013] Preferably, the specific representation of the intervention-driven correlation includes: ΔA i =D A (a0, a i ), ΔY i =D Y (y0,y i ),in:

[0014] A is a variable, Y is the descendant variable of A, and (a, y) represents a sample;

[0015] (a, y)~P(A, Y). Perform n interventions on A, i.e. do(A=a i ), i=1, 2, ..., n;

[0016] y i represents the value of Y after the intervention, and the changes of A and Y before and after the intervention are expressed as ΔA and ΔY, respectively;

[0017] D A and D Y is a function that measures the difference between different values ​​of A and Y, while the correlation between ΔA and ΔY is the intervention-driven correlation;

[0018] IDC(A,Y)=Crr(ΔA,ΔY), where Crr is a function for evaluating the dependency between ΔA and ΔY;

[0019] When IDC(A,Y)=0, then Y is counterfactually fair to A.

[0020] Preferably, the Crr function includes Pearson correlation coefficient, distance correlation and mutual information.

[0021] Preferably, the intervention-driven correlation reduction includes causal discovery training and counterfactual fairness training, wherein the data of the counterfactual fairness model includes using CausalGAN as a causal perception generator,

[0022] in:

[0023] G i is a subnetwork, representing a conditional GAN, G i Enter as a vector (pa(V i ), z i ), where pa(V i ) indicates V i The parent node value, z i is the noise part of the conditional GAN;

[0024] The loss function in the causal-aware generator And the discriminator loss function The definition is as follows:

[0025]

[0026] Among them, P G is the distribution of samples generated from G(z), D(·) is the discriminator function;

[0027]

[0028] P r represents the observed data distribution, P G Represents the data distribution generated by the generator. represents the distribution of interpolated samples between real data samples and generated samples, λ g is the gradient penalty coefficient.

[0029] Preferably, the CausalGAN generates tabular data using the formula:

[0030] G(Z)={G I (C I )|I∈V}

[0031]

[0032] Z~P Z

[0033] Among them, G I (·) represents the conditional generator used to generate variable I, C I is input to G IThe conditional vector of variable I, pa(I) is the parent node set of variable I, Z I is noise and plays the role of an exogenous variable of I.

[0034] Preferably, in the counterfactual fairness training, the subnetwork responsible for generating data labels is called G Y During this period, the loss function for:

[0035]

[0036] Among them, λ f (0<λ f <1) denotes a hyperparameter used to control the trade-off between fairness and data utility.

[0037] The advantages of the present invention over the prior art are that the technical solution provided by the present invention solves the counterfactual fairness problem by generating fair data, is directly applicable to non-binary sensitive attributes and labels, has adjustable parameters to control the trade-off between accuracy and fairness, and can be used to generate data that can realize a counterfactual fairness model. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a schematic diagram of intervention-driven correlation.

[0039] Figure 2 is a schematic diagram of the IDC reduction overview for generating counterfactual fair data.

[0040] Figure 3 It is a schematic diagram of the experimental results of downstream model sensitivity.

[0041] Figure 4 Schematic diagram of the utility-fairness trade-off curve of the intervention-driven relevance reduction method.

[0042] Figure 5 Pseudocode diagram. DETAILED DESCRIPTION

[0043] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0044] Combined with Figure 1-5 shown.

[0045] Structural Causal Models:

[0046] A structural causal model (SCM) M can be expressed as: in:

[0047] V is a set of endogenous variables, which are determined by the variables in V∪U;

[0048] U is the set of exogenous variables, which are determined by factors outside the scope of the model;

[0049] is the set of functions that determine V, i.e., V i ← f i (pa(V i ), U i ), where pa(V i ) represents the set of parent variables of V; i

[0050] P U represents the distribution of U.

[0051] A structural causal model provides a structured way to represent and study causal relationships in complex systems. In an SCM, variables are connected by a directed acyclic graph (DAG), which is called the causal graph of M, where each node represents a variable and the edges represent causal dependencies.

[0052] Counterfactual fairness is a fairness criterion that addresses bias in the decision-making process by considering counterfactual scenarios of an individual's sensitive attributes. Denote the sensitive attribute as A, the label as Y, and each individual as <A, X, Y>. Counterfactual fairness requires that for individuals with the same X = x and A = a, intervening on A to a' should result in equal probabilities of the decision.

[0053] If for any background X = x and A = a, holds for all y and any possible value a' of A, then the predictor is counterfactually fair.

[0054] Given an observed dataset Construct a generator G that generates a dataset with the same structure as and ensure that:

[0055]

[0056] holds for all y and any possible value a' of A, where σ represents the allowed difference between and and ∈ is the allowed unfairness. A well-trained downstream model on

[0057]

[0058] where η represents the allowed fairness loss.

[0059] Utopian Problem:

[0060] set up The SCM followed by real-world data is if The decision made is not counterfactually fair, that is:

[0061]

[0062] in is The function that determines the label variable Y in , pa a (Y) represents the value of pa(Y) after the intervention do(A=a).

[0063] The above inequality can be further divided into two cases:

[0064]

[0065] For the case represented by formula (3), this is a direct discrimination against sensitive attributes, which is easy to detect and eliminate, so only the case of formula (2) is considered. In the following analysis, it is assumed that

[0066] Let the counterfactual fair SCM be More specifically, represents the SCM followed by a generator that generates counterfactual fair data, namely:

[0067]

[0068] A sufficient condition for the above properties is:

[0069]

[0070] However, if If counterfactual fairness is achieved in the case of equation (4), then its downstream model will not be able to maintain counterfactual fairness in the real world.

[0071] Downstream models in Train on the generated data and Make predictions on the generated data.

[0072] The SCM followed to obtain the decisions made by the downstream model is: If the downstream model is If we learn decision patterns from the generated data, then:

[0073]

[0074] Due to formula (1), In, then:

[0075]

[0076] Therefore, due to equations (1) and (3), middle,

[0077]

[0078] This means that the downstream model is not counterfactually fair in real-world predictions, i.e., there is a utopian problem.

[0079] Intervention drives relevance:

[0080] Intervention-Driven Correlation, IDC. Let A be a variable, and Y be the descendant variable of A, that is, Y∈de(A). Let (a, y) represent a sample: (a, y) ~ P(A, Y). Perform n interventions on A, that is, do(A=a i ), i=1, 2,...,n. Let y i represents the value of Y after some intervention. The changes in A and Y before and after the intervention are expressed as ΔA and ΔY, respectively, that is:

[0081] ΔA i =D A (a0, a i ), ΔY i =D Y (y0,y i )

[0082] Where D A and D Y is a function that measures the difference between different values ​​of A and Y. The correlation between ΔA and ΔY under multiple interventions is called the intervention-driven correlation:

[0083] IDC(A,Y)=Crr(ΔA,ΔY)

[0084] where Crr is a function used to evaluate the dependence between ΔA and ΔY.

[0085] IDC does not directly quantify the causal effect as the change in Y after the intervention. Instead, it measures the correlation between the degree of intervention in A and the change in Y, making IDC applicable to scenarios where labels and sensitive attributes are not binary. Unlike the direct calculation method of the total effect expressed in equation (5), IDC does not provide a direct calculation method. It is necessary to define D separately. A, D Y and Crr(A, Y). However, the process is not complicated. For commonly involved sensitive attributes (such as age, gender, and race), simple arithmetic operations such as subtraction are sufficient. In addition, widely accepted correlation measures such as Pearson correlation coefficient, distance correlation, and mutual information can be used as Crr functions. When using a neural network as a causal model, IDC can be calculated through two forward propagations. In the first forward propagation, the neural network randomly generates a batch of data. In the second forward propagation, random interventions are imposed on the sensitive attributes to generate data reflecting these interventions. By combining and analyzing these two batches of data, the IDC of the current neural network can be determined.

[0086] In this framework, assuming that the Crr function value is 0, indicating that the two variables are independent of each other, it has been shown that when IDC equals 0, the causal model is counterfactually fair.

[0087] If IDC(A,Y)=0, then Y is counterfactually fair to A.

[0088] Proof. Let (a0, y0) be the initial sample, and (a0, y0) ~ P(A, Y|X). Perform multiple interventions on A, that is, do(A=a i ), a i ~P(A), i=1, 2,...,n. Let y i is the value of Y after intervention, that is, y i ~P(Y|do(A=a i ), X).

[0089] When IDC(A,Y)=0, it means ΔA⊥ΔY. Therefore, for any a i ,have

[0090] P(Y|do(A=a i ), X)=P(Y|A=a0,

[0091] Therefore, for all interventions on A, we have

[0092] P(Y|do(A=a i ), X) = P(Y|do(A = a j ), x) = P(Y|A = a0, X),

[0093] where i = 1, 2, ..., n, j = 1, 2, ..., n. Therefore, Y is counterfactually fair to A.

[0094] Intervention-related reduction:

[0095] Intervention correlation reduction consists of two stages. The first stage is dedicated to enabling the causal-aware generator to learn causal relationships in the observed data, thereby preparing for intervention operations in subsequent steps. The second stage introduces IDC-based fairness constraints based on the first stage, enabling the generator to generate counterfactually fair data. This two-stage training method helps the generator avoid the utopian problem, thereby ensuring the counterfactual fairness of the downstream model.

[0096] In specific usage, CausalGAN is used as the causal-aware generator, but any generator that can support intervention operations can be trained using intervention correlation reduction.

[0097] CausalGAN is a generative model designed to model and manipulate causal relationships in data. It consists of several conditional generators that are interconnected according to a causal graph. Each subnetwork G i , which represents a conditional GAN ​​in CausalGAN and can be regarded as learning the function f in SCM i The model is responsible for generating V i The value of G i Enter as a vector (pa(V i ), z i ), where pa(V i ) indicates V i The value of the parent node, z i It is regarded as the noise part of the conditional GAN ​​and plays the role of exogenous variables. CausalGAN generates all variables one by one according to the topological ordering of the variables in the causal graph.

[0098] Phase 1: Causal discovery training.

[0099] CausalGAN is constructed based on the structure of the causal graph and trained without considering fairness issues, such as Figure 2 As shown. The goal is to capture the causal relationship in the data. The WGAN-GP method is used to enhance the stability of the CausalGAN training process. The generator loss function And the discriminator loss function The definition is as follows:

[0100]

[0101] Among them, P G is the distribution of samples generated from G(z) and D(·) is the discriminator function.

[0102]

[0103] In the discriminator loss function, P rrepresents the distribution of observed data, P G Represents the data distribution generated by the generator. represents the distribution of interpolated samples between real data samples and generated samples, λ g is the gradient penalty coefficient. This penalty term encourages Lipschitz continuity of the discriminator function.

[0104] The formula for generating tabular data through CausalGAN is as follows:

[0105] G(Z)={G I (C I )|I∈V}

[0106]

[0107] Z~P Z

[0108] Among them, G I (·) represents the conditional generator used to generate variable I. All variables will be generated one by one according to the topological order in the causal graph. I is input to G I The conditional vector of variable I, pa(I) is the parent node set of variable I, Z I is noise and plays the role of an exogenous variable of I.

[0109] Phase 2: Counterfactual fairness training. In the second phase, the parameters of all subnetworks in the generator except the subnetwork responsible for generating labels will retain the values ​​at the end of the first phase. This approach helps avoid the Utopia problem and minimizes the impact of fairness constraints on the quality of generated data. For ease of explanation, the subnetwork responsible for generating data labels is called GY. In the second phase, the loss function The definition is as follows:

[0110]

[0111] Among them, λ f (0<λ f <1) represents a hyperparameter used to control the trade-off between fairness and data utility. By adopting this type of loss function, the generator can effectively handle the issues of data utility and data fairness during the second stage of training.

[0112] In a specific implementation, distance correlation is used to calculate IDC. ΔA and ΔY are calculated by subtraction.

[0113]

[0114] dVar(ΔA)=dCov 2 (ΔA, ΔA)

[0115]

[0116] IDC(A, Y)=DCrr(ΔA, ΔY)

[0117] Before calculating the loss of the generator each time, data needs to be generated twice. The first time is to generate normal data. Then the generated data is input into the discriminator to obtain an item of the generator loss. The second time is to intervene in A to make its value become a r , and then generate data again based on the same noise Z. r is randomly sampled from the marginal distribution of A. Through these two sets of generated data, the generator loss of the second stage is calculated. The second data generation process can be expressed as follows:

[0118] G(Z)=(G I (C I )|I∈V}

[0119]

[0120] Z~P Z

[0121] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

[0122] Comparative Experiments of the Present Invention In order to comprehensively evaluate the performance of the method proposed in the present invention, it is compared with several proposed baseline methods.

[0123] Original method: A predictor trained using the original dataset.

[0124] CausalGAN: First, the original dataset is used to train CausalGAN. Then, the predictor is trained using the data generated by CausalGAN. This ablation experiment aims to prove that the fairness achieved by the data generated by the method of the present invention is not inherent in CausalGAN itself.

[0125] DECAF: DECAF trains a causal-aware generator and tries to remove the causal influence of sensitive attributes on labels during the inference phase. It uses the causal-aware generator to randomize the parts related to sensitive attributes and ensures that labels are d-separated from sensitive attributes when generating labels.

[0126] Distance Correlation GAN: Distance Correlation GAN introduces the distance correlation between sensitive attributes and labels as a fairness constraint in the loss function of GAN. For ease of explanation, it is abbreviated as DCGAN.

[0127] CLAIRE: CLAIRE combines pre-processing and processing techniques to learn a causal model of the data using a variational autoencoder (VAE) and perform counterfactual augmentation. During training, the predictor needs to make consistent predictions for both the actual and counterfactual samples generated by the VAE.

[0128] In the experiments, three widely recognized datasets are used: the Law School dataset, the Adult dataset, and the COMPAS dataset.

[0129] For all datasets, discrete variables were encoded using one-hot encoding, continuous variables were encoded using quantile transformation, a linear regression model was used for the law school dataset, and a multilayer perceptron model was used for the adult dataset and COMPAS dataset. All downstream models were implemented using the default parameters of the scikit-learn (sklearn) library, and a 5-fold cross-validation was performed on the three datasets.

[0130] For the law school dataset, the causal model proposed by Kusner et al. is used as the true causal model, which is used to generate counterfactual data on race, enabling the measurement of the total effect of race. More specifically, the total effect is calculated as follows:

[0131]

[0132] Where R is the race, m is the number of counterfactual samples, is the predicted value of the i-th counterfactual sample. Predictors that exhibit higher counterfactual fairness are expected to show lower total effects. For the Adult dataset and the COMPAS dataset, due to their complexity, it is impossible to construct a true causal model to generate counterfactual data, and thus the total effect cannot be calculated. Some studies have pointed out that under certain conditions, predictors that meet counterfactual fairness also meet demographic fairness (Demographic Parity, DP), that is, each group has the same probability of being classified as a positive outcome. In addition, achieving demographic fairness is a common goal in many studies. Therefore, the demographic fairness difference is used as the evaluation metric for these two datasets. The method for calculating the demographic fairness difference is as follows:

[0133] DP=|P(Y=1|A=a)-P(Y=1|A=a′)|.

[0134] To facilitate computation, for the COMPAS dataset, the sensitive attributes and labels in the training data are binarized before training the downstream classifier.

[0135] result:

[0136] Table 1 Experimental results on the adult dataset and COMPAS dataset.

[0137]

[0138]

[0139] Table 2 Experimental results on the law school dataset

[0140]

[0141] The experimental results on the Adult dataset and COMPAS dataset are shown in Table 1, and the results on the Law School dataset are shown in Table 2.

[0142] For the adult dataset, the method of the present invention significantly reduced the unfairness in the original data by 95.9% on average, and reduced the unfairness in the downstream model by 75.9%. Although DECAF achieved the best results in terms of data and model fairness, it significantly reduced the predictive performance of the downstream model, with the F1 score dropping by 70.1% compared to the model trained on the original data. In contrast, the method of the present invention only observed a 7.2% drop in the F1 score. The method of the present invention outperforms DCGAN and CLAIRE in both fairness and predictive performance. On the COMPAS dataset, the fairness of the method of the present invention is comparable to that of DECAF and DCGAN, but significantly surpasses them in predictive performance, with F1 scores increased by 124.7% and 74.2%, respectively. Compared with CLAIRE, the method of the present invention performs well in both fairness and model performance. For the law school dataset, the method of the present invention reduces TE1 and TE2 by 86.5% and 87.0%, respectively, while increasing the root mean square error (RMSE) by 6.1%, surpassing DCGAN in both fairness and utility. Although DECAF achieves the highest fairness, it also results in a higher RMS error. CLAIRE outperforms our method on this dataset, achieving a better balance between RMS error and total effect; however, CLAIRE requires an extra step in the training of the predictor, which our method does not.

[0143] In order to evaluate the sensitivity of the method of the present invention to various downstream model algorithms, different models were trained on the generated data. For the Law School dataset, multilayer perceptron, ridge regression, support vector machine, and linear regression were used. For the Adult dataset and COMPAS dataset, multilayer perceptron, random forest, support vector machine, and logistic regression were used. The results are shown in Figure 2. Figure 3 shown.

[0144] As mentioned above, the method of the present invention introduces a hyperparameter λ f To balance the trade-off between utility and fairness. f The value of generates the utility-fairness trade-off curve of the method of the present invention, such as Figure 4 shown.

[0145] In the ablation experiment, we focused on evaluating whether IDC is more suitable as a fairness penalty term for training generators than total effect. The loss function of the second stage of the intervention-driven relevance reduction method was modified to replace the fairness constraint with the difference before and after random intervention, as follows:

[0146]

[0147] where a r represents a random value of A. The same two-stage training method was used. The results are shown in Table 3.

[0148] Experimental results show that intervention-driven relevance reduction consistently performs well on a range of datasets, including the Adult dataset with binary sensitive attributes and labels, the COMPAS dataset with discrete non-binary sensitive attributes and labels, and the Law School dataset with continuous labels. This demonstrates the versatility of intervention-driven relevance reduction in adapting to a variety of scenarios.

[0149] The present invention and its embodiments are described above, and such description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it, without departing from the purpose of the invention, they can design a structure and embodiment similar to the technical solution without creativity, which should belong to the protection scope of the present invention.

Claims

1. A counterfactual fair decision-making model based on data generation and intervention-driven association, characterized by: This includes estimating counterfactual fairness of causal models based on intervention-driven correlations, and using intervention-driven correlations to reduce data for generating counterfactual fairness models.

2. The counterfactual fair decision-making model based on data generation and intervention-driven association according to claim 1, characterized in that: The causal model is expressed as in: V is the set of endogenous variables, U is the set of exogenous variables, is a set of functions that determine V; That is V i ←fi(pa(V i ), U i ),in: pa(V i ) represents the parent variable set of Vi, P U represents the distribution of U.

3. The counterfactual fair decision-making model based on data generation and intervention-driven association according to claim 1, characterized in that: The specific representation of the intervention-driven correlation includes: ΔA i =D A (a0, a i ), ΔY i =D Y (y0,y i ),in: A is a variable, Y is the descendant variable of A, and (a, y) represents a sample; (a, y)~P(A, Y). Perform n interventions on A, i.e. do(A=a i ), i=1, 2, ..., n; y i represents the value of Y after the intervention, and the changes of A and Y before and after the intervention are expressed as ΔA and ΔY, respectively; D A and D Y is a function that measures the difference between different values ​​of A and Y, while the correlation between ΔA and ΔY is the intervention-driven correlation; IDC(A,Y)=Crr(ΔA,ΔY), where Crr is a function for evaluating the dependency between ΔA and ΔY; When IDC(A,Y)=0, then Y is counterfactually fair to A.

4. The counterfactual fair decision-making model based on data generation and intervention-driven association according to claim 3, characterized in that: The Crr function includes Pearson correlation coefficient, distance correlation and mutual information.

5. The counterfactual fair decision-making model based on data generation and intervention-driven association according to claim 3, characterized in that: The intervention-driven correlation reduction includes causal discovery training and counterfactual fairness training, wherein the data of the counterfactual fairness model includes using CausalGAN as a causal perception generator, in: G i is a subnetwork, representing a conditional GAN, G i Enter as a vector (pa(V i ), z i ), where pa(V i ) indicates V i The parent node value, z i is the noise part of the conditional GAN; The loss function in the causal-aware generator And the discriminator loss function The definition is as follows: Among them, P G is the distribution of samples generated from G(z), D(·) is the discriminator function; P r represents the observed data distribution, P G Represents the data distribution generated by the generator. represents the distribution of interpolated samples between real data samples and generated samples, λ g is the gradient penalty coefficient.

6. The counterfactual fair decision-making model based on data generation and intervention-driven association according to claim 5, characterized in that: The CausalGAN generates tabular data using the formula: Among them, G I (·) represents the conditional generator used to generate variable I, C I is input to G I The conditional vector of variable I, pa(I) is the parent node set of variable I, Z I is noise and plays the role of an exogenous variable of I.

7. The counterfactual fair decision-making model based on data generation and intervention-driven association according to claim 5, characterized in that: In the counterfactual fairness training, the subnetwork responsible for generating data labels is called G Y During this period, the loss function for: Among them, λ f (0<λ f <1) denotes a hyperparameter used to control the trade-off between fairness and data utility.

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