We consider the task of collaborative preference completion: given a pool of items, a pool of users and a partially observed item-user rating matrix, the goal is to recover the personalized ranking of each user over all of the items. Our approach is nonparametric: we assume that each item $i$ and each user $u$ have unobserved features $x_i$ and $y_u$, and that the associated rating is given by $g_u(f(x_i,y_u))$ where $f$ is Lipschitz and $g_u$ is a monotonic transformation that depends on the user. We propose a $k$-nearest neighbors-like algorithm and prove that it is consistent. To the best of our knowledge, this is the first consistency result for the collaborative preference completion problem in a nonparametric setting. Finally, we conduct experiments on the Netflix and Movielens datasets that suggest that our algorithm has some advantages over existing neighborhood-based methods and that its performance is comparable to some state-of-the art matrix factorization methods.

Growing interest in automatic speaker verification (ASV)systems has lead to significant quality improvement of spoofing attackson them. Many research works confirm that despite the low equal er-ror rate (EER) ASV systems are still vulnerable to spoofing attacks. Inthis work we overview different acoustic feature spaces and classifiersto determine reliable and robust countermeasures against spoofing at-tacks. We compared several spoofing detection systems, presented so far,on the development and evaluation datasets of the Automatic SpeakerVerification Spoofing and Countermeasures (ASVspoof) Challenge 2015.Experimental results presented in this paper demonstrate that the useof magnitude and phase information combination provides a substantialinput into the efficiency of the spoofing detection systems. Also wavelet-based features show impressive results in terms of equal error rate. Inour overview we compare spoofing performance for systems based on dif-ferent classifiers. Comparison results demonstrate that the linear SVMclassifier outperforms the conventional GMM approach. However, manyresearchers inspired by the great success of deep neural networks (DNN)approaches in the automatic speech recognition, applied DNN in thespoofing detection task and obtained quite low EER for known and un-known type of spoofing attacks.

We consider parametric exponential families of dimension $K$ on the real line. We study a variant of \textit{boundary crossing probabilities} coming from the multi-armed bandit literature, in the case when the real-valued distributions form an exponential family of dimension $K$. Formally, our result is a concentration inequality that bounds the probability that $\mathcal{B}^\psi(\hat \theta_n,\theta^\star)\geq f(t/n)/n$, where $\theta^\star$ is the parameter of an unknown target distribution, $\hat \theta_n$ is the empirical parameter estimate built from $n$ observations, $\psi$ is the log-partition function of the exponential family and $\mathcal{B}^\psi$ is the corresponding Bregman divergence. From the perspective of stochastic multi-armed bandits, we pay special attention to the case when the boundary function $f$ is logarithmic, as it is enables to analyze the regret of the state-of-the-art \KLUCB\ and \KLUCBp\ strategies, whose analysis was left open in such generality. Indeed, previous results only hold for the case when $K=1$, while we provide results for arbitrary finite dimension $K$, thus considerably extending the existing results. Perhaps surprisingly, we highlight that the proof techniques to achieve these strong results already existed three decades ago in the work of T.L. Lai, and were apparently forgotten in the bandit community. We provide a modern rewriting of these beautiful techniques that we believe are useful beyond the application to stochastic multi-armed bandits.

Many real datasets contain values missing not at random (MNAR). In this scenario, investigators often perform list-wise deletion, or delete samples with any missing values, before applying causal discovery algorithms. List-wise deletion is a sound and general strategy when paired with algorithms such as FCI and RFCI, but the deletion procedure also eliminates otherwise good samples that contain only a few missing values. In this report, we show that we can more efficiently utilize the observed values with test-wise deletion while still maintaining algorithmic soundness. Here, test-wise deletion refers to the process of list-wise deleting samples only among the variables required for each conditional independence (CI) test used in constraint-based searches. Test-wise deletion therefore often saves more samples than list-wise deletion for each CI test, especially when we have a sparse underlying graph. Our theoretical results show that test-wise deletion is sound under the justifiable assumption that none of the missingness mechanisms causally affect each other in the underlying causal graph. We also find that FCI and RFCI with test-wise deletion outperform their list-wise deletion and imputation counterparts on average when MNAR holds in both synthetic and real data.

Generative adversarial networks (GAN) approximate a target data distribution by jointly optimizing an objective function through a "two-player game" between a generator and a discriminator. Despite their empirical success, however, two very basic questions on how well they can approximate the target distribution remain unanswered. First, it is not known how restricting the discriminator family affects the approximation quality. Second, while a number of different objective functions have been proposed, we do not understand when convergence to the global minima of the objective function leads to convergence to the target distribution under various notions of distributional convergence. In this paper, we address these questions in a broad and unified setting by defining a notion of adversarial divergences that includes a number of recently proposed objective functions. We show that if the objective function is an adversarial divergence with some additional conditions, then using a restricted discriminator family has a moment-matching effect. Additionally, we show that for objective functions that are strict adversarial divergences, convergence in the objective function implies weak convergence, thus generalizing previous results.

Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to multi-dimensional and dependent non-Gaussian components. Indeed, seminal approaches to NGCA are based on PP and ICA. Recently, a novel NGCA approach called least-squares NGCA (LSNGCA) has been developed, which gives a solution analytically through least-squares estimation of log-density gradients and eigendecomposition. However, since pre-whitening of data is involved in LSNGCA, it performs unreliably when the data covariance matrix is ill-conditioned, which is often the case in high-dimensional data analysis. In this paper, we propose a whitening-free LSNGCA method and experimentally demonstrate its superiority.

Incremental methods for structure learning of pairwise Markov random fields (MRFs), such as grafting, improve scalability to large systems by avoiding inference over the entire feature space in each optimization step. Instead, inference is performed over an incrementally grown active set of features. In this paper, we address the computational bottlenecks that current techniques still suffer by introducing online edge grafting, an incremental, structured method that activates edges as groups of features in a streaming setting. The framework is based on reservoir sampling of edges that satisfy a necessary activation condition, approximating the search for the optimal edge to activate. Online edge grafting performs an informed edge search set reorganization using search history and structure heuristics. Experiments show a significant computational speedup for structure learning and a controllable trade-off between the speed and the quality of learning.

Variational inference is a powerful approach for approximate posterior inference. However, it is sensitive to initialization and can be subject to poor local optima. In this paper, we develop proximity variational inference (PVI). PVI is a new method for optimizing the variational objective that constrains subsequent iterates of the variational parameters to robustify the optimization path. Consequently, PVI is less sensitive to initialization and optimization quirks and finds better local optima. We demonstrate our method on three proximity statistics. We study PVI on a Bernoulli factor model and sigmoid belief network with both real and synthetic data and compare to deterministic annealing (Katahira et al., 2008). We highlight the flexibility of PVI by designing a proximity statistic for Bayesian deep learning models such as the variational autoencoder (Kingma and Welling, 2014; Rezende et al., 2014). Empirically, we show that PVI consistently finds better local optima and gives better predictive performance.

In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running time of previous state-of-the-art private optimization algorithms, for both $\epsilon$-DP and $(\epsilon, \delta)$-DP. For non-convex but smooth objectives, we propose an RRPSGD (Random Round Private Stochastic Gradient Descent) algorithm, which provably converges to a stationary point with privacy guarantee. Besides the expected utility bounds, we also provide guarantees in high probability form. Experiments demonstrate that our algorithm consistently outperforms existing method in both utility and running time.

Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is consistent with CNNs with random weights. We give an exact connection to a particular model of model-based compressive sensing (and its recovery algorithms) and random-weight CNNs. We show empirically that several learned networks are consistent with our mathematical analysis and then demonstrate that with such a simple theoretical framework, we can obtain reasonable re- construction results on real images. We also discuss gaps between our model assumptions and the CNN trained for classification in practical scenarios.