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Register a new userRobust Classification Under $ell_0$ Attack for the Gaussian Mixture Model
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It is well-known that machine learning models are vulnerable to small but cleverly-designed adversarial perturbations that can cause misclassification. While there has been major progress in designing attacks and defenses for various adversarial settings, many fundamental and theoretical problems are yet to be resolved. In this paper, we consider classification in the presence of $ell_0$-bounded adversarial perturbations, a.k.a. sparse attacks. This setting is significantly different from other $ell_p$-adversarial settings, with $pgeq 1$, as the $ell_0$-ball is non-convex and highly non-smooth. Under the assumption that data is distributed according to the Gaussian mixture model, our goal is to characterize the optimal robust classifier and the corresponding robust classification error as well as a variety of trade-offs between robustness, accuracy, and the adversarys budget. To this end, we develop a novel classification algorithm called FilTrun that has two main modules: Filtration and Truncation. The key idea of our method is to first filter out the non-robust coordinates of the input and then apply a carefully-designed truncated inner product for classification. By analyzing the performance of FilTrun, we derive an upper bound on the optimal robust classification error. We also find a lower bound by designing a specific adversarial strategy that enables us to derive the corresponding robust classifier and its achieved error. For the case that the covariance matrix of the Gaussian mixtures is diagonal, we show that as the inputs dimension gets large, the upper and lower bounds converge; i.e. we characterize the asymptotically-optimal robust classifier. Throughout, we discuss several examples that illustrate interesting behaviors such as the existence of a phase transition for adversarys budget determining whether the effect of adversarial perturbation can be fully neutralized.
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Investigation of machine learning algorithms robust to changes between the training and test distributions is an active area of research. In this paper we explore a special type of dataset shift which we call class-dependent domain shift. It is characterized by the following features: the input data causally depends on the label, the shift in the data is fully explained by a known variable, the variable which controls the shift can depend on the label, there is no shift in the label distribution. We define a simple optimization problem with an information theoretic constraint and attempt to solve it with neural networks. Experiments on a toy dataset demonstrate the proposed method is able to learn robust classifiers which generalize well to unseen domains.
This paper proposes a dual-supervised uncertainty inference (DS-UI) framework for improving Bayesian estimation-based uncertainty inference (UI) in deep neural network (DNN)-based image recognition. In the DS-UI, we combine the classifier of a DNN, i.e., the last fully-connected (FC) layer, with a mixture of Gaussian mixture models (MoGMM) to obtain an MoGMM-FC layer. Unlike existing UI methods for DNNs, which only calculate the means or modes of the DNN outputs distributions, the proposed MoGMM-FC layer acts as a probabilistic interpreter for the features that are inputs of the classifier to directly calculate the probability density of them for the DS-UI. In addition, we propose a dual-supervised stochastic gradient-based variational Bayes (DS-SGVB) algorithm for the MoGMM-FC layer optimization. Unlike conventional SGVB and optimization algorithms in other UI methods, the DS-SGVB not only models the samples in the specific class for each Gaussian mixture model (GMM) in the MoGMM, but also considers the negative samples from other classes for the GMM to reduce the intra-class distances and enlarge the inter-class margins simultaneously for enhancing the learning ability of the MoGMM-FC layer in the DS-UI. Experimental results show the DS-UI outperforms the state-of-the-art UI methods in misclassification detection. We further evaluate the DS-UI in open-set out-of-domain/-distribution detection and find statistically significant improvements. Visualizations of the feature spaces demonstrate the superiority of the DS-UI.
We study the problem of robust learning under clean-label data-poisoning attacks, where the attacker injects (an arbitrary set of) correctly-labeled examples to the training set to fool the algorithm into making mistakes on specific test instances at test time. The learning goal is to minimize the attackable rate (the probability mass of attackable test instances), which is more difficult than optimal PAC learning. As we show, any robust algorithm with diminishing attackable rate can achieve the optimal dependence on $epsilon$ in its PAC sample complexity, i.e., $O(1/epsilon)$. On the other hand, the attackable rate might be large even for some optimal PAC learners, e.g., SVM for linear classifiers. Furthermore, we show that the class of linear hypotheses is not robustly learnable when the data distribution has zero margin and is robustly learnable in the case of positive margin but requires sample complexity exponential in the dimension. For a general hypothesis class with bounded VC dimension, if the attacker is limited to add at most $t>0$ poison examples, the optimal robust learning sample complexity grows almost linearly with $t$.
Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This strategy, however, is ineffective when there are outlier data samples whose latent representations are meaningless, yet contaminating the estimation of key major clusters in the latent space. This exact problem arises in the context of resting-state fMRI (rs-fMRI) analysis, where clustering major functional connectivity patterns is often hindered by heavy noise of rs-fMRI and many minor clusters (rare connectivity patterns) of no interest to analysis. In this paper we propose a novel generative process, in which we use a Gaussian-mixture to model a few major clusters in the data, and use a non-informative uniform distribution to capture the remaining data. We embed this truncated Gaussian-Mixture model in a Variational AutoEncoder framework to obtain a general joint clustering and outlier detection approach, called tGM-VAE. We demonstrated the applicability of tGM-VAE on the MNIST dataset and further validated it in the context of rs-fMRI connectivity analysis.
Despite of the pervasive existence of multi-label evasion attack, it is an open yet essential problem to characterize the origin of the adversarial vulnerability of a multi-label learning system and assess its attackability. In this study, we focus on non-targeted evasion attack against multi-label classifiers. The goal of the threat is to cause miss-classification with respect to as many labels as possible, with the same input perturbation. Our work gains in-depth understanding about the multi-label adversarial attack by first characterizing the transferability of the attack based on the functional properties of the multi-label classifier. We unveil how the transferability level of the attack determines the attackability of the classifier via establishing an information-theoretic analysis of the adversarial risk. Furthermore, we propose a transferability-centered attackability assessment, named Soft Attackability Estimator (SAE), to evaluate the intrinsic vulnerability level of the targeted multi-label classifier. This estimator is then integrated as a transferability-tuning regularization term into the multi-label learning paradigm to achieve adversarially robust classification. The experimental study on real-world data echos the theoretical analysis and verify the validity of the transferability-regularized multi-label learning method.
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