We study dual volume sampling, a method for selecting k columns from an n x m short and wide matrix (n <= k <= m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix. This method was proposed by Avron and Boutsidis (2013), who showed it to be a promising method for column subset selection and its multiple applications. However, its wider adoption has been hampered by the lack of polynomial time sampling algorithms. We remove this hindrance by developing an exact (randomized) polynomial time sampling algorithm as well as its derandomization. Thereafter, we study dual volume sampling via the theory of real stable polynomials and prove that its distribution satisfies the "Strong Rayleigh" property. This result has numerous consequences, including a provably fast-mixing Markov chain sampler that makes dual volume sampling much more attractive to practitioners. This sampler is closely related to classical algorithms for popular experimental design methods that are to date lacking theoretical analysis but are known to empirically work well.

Deep neural networks (DNNs) are powerful nonlinear architectures that are known to be robust to random perturbations of the input. However, these models are vulnerable to adversarial perturbations--small input changes crafted explicitly to fool the model. In this paper, we ask whether a DNN can distinguish adversarial samples from their normal and noisy counterparts. We investigate model confidence on adversarial samples by looking at Bayesian uncertainty estimates, available in dropout neural networks, and by performing density estimation in the subspace of deep features learned by the model. The result is a method for implicit adversarial detection that is oblivious to the attack algorithm. We evaluate this method on a variety of standard datasets including MNIST and CIFAR-10 and show that it generalizes well across different architectures and attacks. Our findings report that 85-93% ROC-AUC can be achieved on a number of standard classification tasks with a negative class that consists of both normal and noisy samples.

We propose a new active learning by query synthesis approach using Generative Adversarial Networks (GAN). Different from regular active learning, the resulting algorithm adaptively synthesizes training instances for querying to increase learning speed. We generate queries according to the uncertainty principle, but our idea can work with other active learning principles. We report results from various numerical experiments to demonstrate the effectiveness the proposed approach. In some settings, the proposed algorithm outperforms traditional pool-based approaches. To the best our knowledge, this is the first active learning work using GAN.

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we call delay, is the number of times it has been updated since its creation. Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly. However, the maximum delay is practically unknown. This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint, and it allows for large unbounded delays. An explicit formula of stepsize that guarantees convergence is given depending on delays' statistics. With $p+1$ identical processors, we empirically measured that delays closely follow the Poisson distribution with parameter $p$, matching our theoretical model, and thus the stepsize can be set accordingly. Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay induced stepsize is too conservative, often slowing down the convergence of the algorithm.

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for known density functions accumulating the likelihood ratio statistics is time optimal under a fixed error rate constraint. This paper considers the problem of learning a binary sequential detector from training samples when density functions are unavailable. We formulate the problem as a constrained likelihood ratio estimation which can be solved efficiently through convex optimization by imposing Reproducing Kernel Hilbert Space (RKHS) structure on the log-likelihood ratio function. In addition, we provide a computationally efficient approximated solution for large scale data set. The proposed algorithm, namely Wald-Kernel, is tested on a synthetic data set and two real world data sets, together with previous approaches for likelihood ratio estimation. Our empirical results show that the classifier trained through the proposed technique achieves smaller average sampling cost than previous approaches proposed in the literature for the same error rate.

Throughout its history, Machine Learning (ML) has coexisted with Statistics uneasily, like an ex-boyfriend accidentally seated with the groom's family at a wedding reception: both uncertain where to lead the conversation, but painfully aware of the potential for awkwardness. This is caused in part by the fact that Machine Learning has adopted many of Statistics' methods, but was never intended to replace statistics, or even to have a statistical basis originally. Nevertheless, Statisticians and ML practitioners have often ended up working together, or working on similar tasks, and wondering what each was about. The question, "What's the difference between Machine Learning and Statistics?" has been asked now for decades. Machine Learning is largely a hybrid field, taking its inspiration and techniques from all manner of sources. It has changed directions throughout its history and often seemed like an enigma to those outside of it.1

Consider a social network where only a few nodes (agents) have meaningful interactions in the sense that the conditional dependency graph over node attribute variables (behaviors) is sparse. A company that can only observe the interactions between its own customers will generally not be able to accurately estimate its customers' dependency subgraph: it is blinded to any external interactions of its customers and this blindness creates false edges in its subgraph. In this paper we address the semiblind scenario where the company has access to a noisy summary of the complementary subgraph connecting external agents, e.g., provided by a consolidator. The proposed framework applies to other applications as well, including field estimation from a network of awake and sleeping sensors and privacy-constrained information sharing over social subnetworks. We propose a penalized likelihood approach in the context of a graph signal obeying a Gaussian graphical models (GGM). We use a convex-concave iterative optimization algorithm to maximize the penalized likelihood.

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, they are limited by the computational complexity and their inability to support end-to-end learning with a task-specific objective. On the other hand, deep neural networks have become the de facto solution for end-to-end inference in several learning paradigms. In this article, we explore the idea of using deep architectures to perform kernel machine optimization, for both computational efficiency and end-to-end inferencing. To this end, we develop the DKMO (Deep Kernel Machine Optimization) framework, that creates an ensemble of dense embeddings using Nystrom kernel approximations and utilizes deep learning to generate task-specific representations through the fusion of the embeddings. Intuitively, the filters of the network are trained to fuse information from an ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel dropout regularization to enable improved training convergence. Finally, we extend this framework to the multiple kernel case, by coupling a global fusion layer with pre-trained deep kernel machines for each of the constituent kernels. Using case studies with limited training data, and lack of explicit feature sources, we demonstrate the effectiveness of our framework over conventional model inferencing techniques.

A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter, and consistency of the estimator is established in the well specified case. In experiments, the new method generally outperforms a competing approach with consistency guarantees, and is competitive with a deep conditional density model on datasets that exhibit abrupt transitions and heteroscedasticity.

We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased toward the training samples. Such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the out-of-sample performance. A classical cross validation strategy is the leave-one-out cross validation (LOOCV) where one sample is left out for validation and training is done on the rest of the samples that are presented to the learner, and this process is repeated on all of the samples. LOOCV is rarely used in practice due to the high computational complexity. In this paper, we first develop a computationally efficient approximate LOOCV (ALOOCV) and provide theoretical guarantees for its performance. Then we use ALOOCV to provide an optimization algorithm for finding the regularizer in the empirical risk minimization framework. In our numerical experiments, we illustrate the accuracy and efficiency of ALOOCV as well as our proposed framework for the optimization of the regularizer.