How to generate semantically meaningful and structurally sound adversarial examples? We propose to answer this question by restricting the search for adversaries in the true data manifold. To this end, we introduce a stochastic variational inference method to learn the data manifold, in the presence of continuous latent variables with intractable posterior distributions, without requiring an a-priori form for the data underlying distribution. We then propose a manifold perturbation strategy that ensures the cases we perturb remain in the manifold of the original examples and thereby generate the adversaries. We evaluate our approach on a number of image and text datasets. Our results show the effectiveness of our approach in producing coherent, and realistic-looking adversaries that can evade strong defenses known to be resilient to traditional adversarial attacks.

Unsupervised domain adaptation techniques have been successful for a wide range of problems where supervised labels are limited. The task is to classify an unlabeled `target' dataset by leveraging a labeled `source' dataset that comes from a slightly similar distribution. We propose metric-based adversarial discriminative domain adaptation (M-ADDA) which performs two main steps. First, it uses a metric learning approach to train the source model on the source dataset by optimizing the triplet loss function. This results in clusters where embeddings of the same label are close to each other and those with different labels are far from one another. Next, it uses the adversarial approach (as that used in ADDA \cite{2017arXiv170205464T}) to make the extracted features from the source and target datasets indistinguishable. Simultaneously, we optimize a novel loss function that encourages the target dataset's embeddings to form clusters. While ADDA and M-ADDA use similar architectures, we show that M-ADDA performs significantly better on the digits adaptation datasets of MNIST and USPS. This suggests that using metric-learning for domain adaptation can lead to large improvements in classification accuracy for the domain adaptation task. The code is available at \url{https://github.com/IssamLaradji/M-ADDA}.

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionally-conjugate models. We present a new stochastic method for variational inference which exploits the geometry of the variational-parameter space and also yields simple closed-form updates even for non-conjugate models. We also give a convergence-rate analysis of our method and many other previous methods which exploit the geometry of the space. Our analysis generalizes existing convergence results for stochastic mirror-descent on non-convex objectives by using a more general class of divergence functions. Beyond giving a theoretical justification for a variety of recent methods, our experiments show that new algorithms derived in this framework lead to state of the art results on a variety of problems. Further, due to its generality, we expect that our theoretical analysis could also apply to other applications.

We present and analyze several strategies for improving the performance of stochastic variance-reduced gradient (SVRG) methods. We first show that the convergence rate of these methods can be preserved under a decreasing sequence of errors in the control variate, and use this to derive variants of SVRG that use growing-batch strategies to reduce the number of gradient calculations required in the early iterations. We further (i) show how to exploit support vectors to reduce the number of gradient computations in the later iterations, (ii) prove that the commonly-used regularized SVRG iteration is justified and improves the convergence rate, (iii) consider alternate mini-batch selection strategies, and (iv) consider the generalization error of the method.

We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substantially improves practical performance, and analyze the rate of convergence of the SAGA variant under non-uniform sampling. Our experimental results reveal that our method often significantly outperforms existing methods in terms of the training objective, and performs as well or better than optimally-tuned stochastic gradient methods in terms of test error.