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This paper proposes a locally-optimal generalized likelihood ratio test (LO-GLRT) for detecting targeted attacks on a classifier, where the attacks add a norm-bounded targeted universal adversarial perturbation (UAP) to the classifier’s input. The paper includes both an analysis of the test as well as its empirical evaluation. The analysis provides an expression for the approximate lower bound of the detection probability, and the empirical evaluation shows this approximation to be similar to the actual detection probability. Since the LO-GLRT requires the score function of the input distribution, which is usually unknown in practice, we study the LO-GLRT for a learned surrogate input distribution. Specifically, we use a Gaussian distribution over the input subvectors as the surrogate distribution, for its mathematical tractability and computational efficiency. We evaluate the detector for several popular image classifiers and datasets, and compare the statistical and computational performance with the perturbation rectifying network (PRN) detector, another successful approach for detecting the UAPs. The LO-GLRT outperforms the PRN detector on both counts, with a running time at least 100 times lower than that of the PRN detector. [ABSTRACT FROM AUTHOR]

Let $X_{i}, i~\in V$ form a Markov random field (MRF) represented by an undirected graph $G = (V,E)$ , and $V'$ be a subset of $V$. We determine the smallest graph that can always represent the subfield $X_{i}, i~\in V'$ as an MRF. Based on this result, we obtain a necessary and sufficient condition for a subfield of a Markov tree to be also a Markov tree. When $G$ is a path so that $X_{i}, i~\in V$ form a Markov chain, it is known that the $I$ -Measure is always nonnegative (Kawabata and Yeung in 1992). We prove that Markov chain is essentially the only MRF such that the $I$ -Measure is always nonnegative. By applying our characterization of the smallest graph representation of a subfield of an MRF, we develop a recursive approach for constructing information diagrams for MRFs. Our work is built on the set-theoretic characterization of an MRF (Yeung et al. in 2002). [ABSTRACT FROM AUTHOR]

Shannon’s analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume M_ \mathrm avg^*(n,\epsilon ) of length- n codes subject to an average decoding error probability \epsilon is shown to satisfy the following tight asymptotic lower and upper bounds as n \to \infty : , where C is the Shannon capacity, V_\epsilon is the \epsilon -channel dispersion, or second-order coding rate, Q and \overline A_\epsilon are explicitly identified. This expression holds under mild regularity assumptions on the channel, including nonsingularity. The gap \overline A_\epsilon - \underline A_\epsilon is one nat for weakly symmetric channels in the Cover–Thomas sense, and typically a few nats for other symmetric channels, for the binary symmetric channel, and for the $Z$ channel. The derivation is based on strong large-deviations analysis and refined central limit asymptotics. A random coding scheme that achieves the lower bound is presented. The codewords are drawn from a capacity-achieving input distribution modified by an O(1/\sqrt {n}) correction term. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach to image-set-based face recognition, where each training and testing example is a set of face images captured from varying poses, illuminations, expressions, and resolutions. While a number of image set based face recognition methods have been proposed in recent years, most of them model each face image set as a single linear subspace or as the union of linear subspaces, which may lose some discriminative information for face image set representation. To address this shortcoming, we propose exploiting statistics information as feature representations for face image sets and develop a localized multikernel metric learning algorithm to effectively combine different statistics for recognition. Moreover, we propose a localized multikernel multimetric learning method to jointly learn multiple feature-specific distance metrics in the kernel spaces, one for each statistic feature, to better exploit complementary information for recognition. Our methods achieve state-of-the-art performance on four widely used video face datasets including the Honda, MoBo, YouTube Celebrities, and YouTube Face datasets. [ABSTRACT FROM AUTHOR]

We propose a novel robust hashing algorithm based on signal-to-noise ratio (SNR) maximization to learn compact binary codes, where the SNR metric is used to select a set of projection directions, and one hash bit is extracted from each projection direction. We first motivate this approach under a Gaussian model for the underlying signals, in which case maximizing SNR is equivalent to minimizing the robust hashing error probability. A globally optimal solution can be obtained by solving a generalized eigenvalue problem. We also develop a multibit per projection algorithm to learn longer hash codes when the number of high-SNR projections is limited. The proposed algorithms are tested on both synthetic and real data sets, showing significant performance gains over existing hashing algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate order-preserving sparse coding for classifying structured data whose atomic features possess ordering relationships. Examples include time sequences where individual frame-wise features are temporally ordered, as well as still images (landscape, street view, etc.) where different regions of the image are spatially ordered. Classification of these structured data is often tackled by first decomposing the input data into individual atomic features, then performing sparse coding or other processing for each atomic feature vector independently, and finally aggregating individual responses to classify the input data. However, this heuristic approach ignores the underlying order of the individual atomic features within the input data, and results in suboptimal discriminative capability. In this work, we introduce an order preserving regularizer which aims to preserve the ordering structure of the reconstruction coefficients within the sparse coding framework. An efficient Nesterov-type smooth approximation method is developed for optimization of the new regularization criterion, with theoretically guaranteed error bound. We perform extensive experiments for time series classification on a synthetic dataset, several machine learning benchmarks, and an RGB-D human activity dataset. We also report experiments for scene classification on a benchmark image dataset. The encoded representation is discriminative and robust, and our classifier outperforms state-of-the-art methods on these tasks. [ABSTRACT FROM PUBLISHER]