Interpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional functions (commonly referred to as components), is one of the most popular tools for interpretable AI, and recently, various neural networks have been developed for estimating each component in the functional ANOVA model. However, such neural networks are highly unstable when estimating each component since the components themselves are not uniquely defined. That is, there are multiple functional ANOVA decompositions for a given function. In this paper, we propose a novel neural network which guarantees a unique functional ANOVA decomposition and thus is able to estimate each component stably. We call our proposed neural network ANOVA Tensor Product Neural Network (ANOVA-TPNN) since it is motivated by the tensor product basis expansion. Theoretically, we prove that ANOVA-TPNN can approximate any smooth function well. Empirically, we show that ANOVA-TPNN provide much more stable estimation of each component and thus much more stable interpretation when training data and initial values of the model parameters vary than existing neural networks do. Our source code is released at https://github.com/ParkSeokhun/ANOVA-TPNN

Bayesian approaches for training deep neural networks (BNNs) have received significant interest and have been effectively utilized in a wide range of applications. Several studies have examined the properties of posterior concentrations in BNNs. However, most of these studies focus solely on BNN models with sparse or heavy-tailed priors. Surprisingly, there are currently no theoretical results for BNNs using Gaussian priors, which are the most commonly used in practice. The lack of theory arises from the absence of approximation results of Deep Neural Networks (DNNs) that are non-sparse and have bounded parameters. In this paper, we present a new approximation theory for non-sparse DNNs with bounded parameters. Additionally, based on the approximation theory, we show that BNNs with non-sparse general priors can achieve near-minimax optimal posterior concentration rates around the true model.

AI fairness, also known as algorithmic fairness, aims to ensure that algorithms operate without bias or discrimination towards any individual or group. Among various AI algorithms, the Fair Representation Learning (FRL) approach has gained significant interest in recent years. However, existing FRL algorithms have a limitation: they are primarily designed for categorical sensitive attributes and thus cannot be applied to continuous sensitive attributes, such as age or income. In this paper, we propose an FRL algorithm for continuous sensitive attributes. First, we introduce a measure called the Expectation of Integral Probability Metrics (EIPM) to assess the fairness level of representation space for continuous sensitive attributes. We demonstrate that if the distribution of the representation has a low EIPM value, then any prediction head constructed on the top of the representation become fair, regardless of the selection of the prediction head. Furthermore, EIPM possesses a distinguished advantage in that it can be accurately estimated using our proposed estimator with finite samples. Based on these properties, we propose a new FRL algorithm called Fair Representation using EIPM with MMD (FREM). Experimental evidences show that FREM outperforms other baseline methods.

Adversarial robustness is a research area that has recently received a lot of attention in the quest for trustworthy artificial intelligence. However, recent works on adversarial robustness have focused on supervised learning where it is assumed that labeled data is plentiful. In this paper, we investigate semi-supervised adversarial training where labeled data is scarce. We derive two upper bounds for the robust risk and propose a regularization term for unlabeled data motivated by these two upper bounds. Then, we develop a semi-supervised adversarial training algorithm that combines the proposed regularization term with knowledge distillation using a semi-supervised teacher (i.e., a teacher model trained using a semi-supervised learning algorithm). Our experiments show that our proposed algorithm achieves state-of-the-art performance with significant margins compared to existing algorithms. In particular, compared to supervised learning algorithms, performance of our proposed algorithm is not much worse even when the amount of labeled data is very small. For example, our algorithm with only 8% labeled data is comparable to supervised adversarial training algorithms that use all labeled data, both in terms of standard and robust accuracies on CIFAR-10.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better uncertainty quantification. For the success of BNN, search an appropriate architecture of the neural networks is an important task, and various algorithms to find good sparse neural networks have been proposed. In this paper, we propose a new node-sparse BNN model which has good theoretical properties and is computationally feasible. We prove that the posterior concentration rate to the true model is near minimax optimal and adaptive to the smoothness of the true model. In particular the adaptiveness is the first of its kind for node-sparse BNNs. In addition, we develop a novel MCMC algorithm which makes the Bayesian inference of the node-sparse BNN model feasible in practice.

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we propose a new adversarial training algorithm that is theoretically well motivated and empirically superior to other existing algorithms. A novel feature of the proposed algorithm is to apply more regularization to data vulnerable to adversarial attacks than other existing regularization algorithms do. Theoretically, we show that our algorithm can be understood as an algorithm of minimizing a newly derived upper bound of the robust risk. Numerical experiments illustrate that our proposed algorithm improves the generalization (accuracy on examples) and robustness (accuracy on adversarial attacks) simultaneously to achieve the state-of-the-art performance.

As they have a vital effect on social decision-making, AI algorithms should be not only accurate but also fair. Among various algorithms for fairness AI, learning fair representation (LFR), whose goal is to find a fair representation with respect to sensitive variables such as gender and race, has received much attention. For LFR, the adversarial training scheme is popularly employed as is done in the generative adversarial network type algorithms. The choice of a discriminator, however, is done heuristically without justification. In this paper, we propose a new adversarial training scheme for LFR, where the integral probability metric (IPM) with a specific parametric family of discriminators is used. The most notable result of the proposed LFR algorithm is its theoretical guarantee about the fairness of the final prediction model, which has not been considered yet. That is, we derive theoretical relations between the fairness of representation and the fairness of the prediction model built on the top of the representation (i.e., using the representation as the input). Moreover, by numerical experiments, we show that our proposed LFR algorithm is computationally lighter and more stable, and the final prediction model is competitive or superior to other LFR algorithms using more complex discriminators.