Adversarial Coreset Selection for Efficient Robust Training

Neural networks are vulnerable to adversarial attacks: adding well-crafted, imperceptible perturbations to their input can modify their output. Adversarial training is one of the most effective approaches to training robust models against such attacks. Unfortunately, this method is much slower than vanilla training of neural networks since it needs to construct adversarial examples for the entire training data at every iteration. By leveraging the theory of coreset selection, we show how selecting a small subset of training data provides a principled approach to reducing the time complexity of robust training. To this end, we first provide convergence guarantees for adversarial coreset selection. In particular, we show that the convergence bound is directly related to how well our coresets can approximate the gradient computed over the entire training data. Motivated by our theoretical analysis, we propose using this gradient approximation error as our adversarial coreset selection objective to reduce the training set size effectively. Once built, we run adversarial training over this subset of the training data. Unlike existing methods, our approach can be adapted to a wide variety of training objectives, including TRADES, $\ell_p$-PGD, and Perceptual Adversarial Training. We conduct extensive experiments to demonstrate that our approach speeds up adversarial training by 2-3 times while experiencing a slight degradation in the clean and robust accuracy.Comment: Accepted to the International Journal of Computer Vision (IJCV). Extended version of the ECCV2022 paper: arXiv:2112.00378. arXiv admin note: substantial text overlap with arXiv:2112.0037

Modeling heterogeneous variance–Covariance components in two-level models

Applications of multilevel models to continuous outcomes nearly always assume constant residual variance and constant random effects variances and covar-iances. However, modeling heterogeneity of variance can prove a useful indi-cator of model misspecification and in some educational and behavioral studies, it may even be of direct substantive interest. The purpose of this article is to review, describe, and illustrate a set of recent extensions to two-level models that allow the residual and random effects variance–covariance components to be specified as functions of predictors. These predictors can then be entered with random coefficients to allow the Level-1 heteroscedastic relationships to vary across Level-2 units. We demonstrate by simulation that ignoring Level-2 variability in residual variances leads the Level-1 variance function regres-sion coefficients to be estimated with spurious precision. We discuss software options for fitting these extensions, and we illustrate them by reanalyzing the classic High School and Beyond data and two-level school effects models pre-sented by Raudenbush and Bryk.AQ

Moving shape dynamics: A signal processing perspective

This paper provides a new perspective on human motion analysis, namely regarding human motions in video as general discrete time signals. While this seems an intuitive idea, research on human motion analysis has attracted little attention from the signal processing community. Sophisticated signal processing techniques create important opportunities for new solutions to the problem of human motion analysis. This paper investigates how the deformations of human silhouettes (or shapes) during articulated motion can be used as discriminating features to implicitly capture motion dynamics. In particular, we demonstrate the applicability of two widely used signal transform methods, namely the Discrete Fourier Transform (DFT) and Discrete Wavelet Transform (DWT), for characterization and recognition of human motion sequences. Experimental results show the effectiveness of the proposed method on two stateof-the-art data sets. 1