Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restricts the space of possible solutions and leads to over-confident uncertainty estimates. We introduce a fully Bayesian approach, inferring a full posterior over structures, which more reliably captures the uncertainty of the model.

Over the years, ensemble methods have become a staple of machine learning. Similarly, generalized linear models (GLMs) have become very popular for a wide variety of statistical inference tasks. The former have been shown to enhance out- of-sample predictive power and the latter possess easy interpretability. Recently, ensembles of GLMs have been proposed as a possibility. On the downside, this approach loses the interpretability that GLMs possess. We show that minimum description length (MDL)-motivated compression of the inferred ensembles can be used to recover interpretability without much, if any, downside to performance and illustrate on a number of standard classification data sets.

In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an efficient algorithm to approximate the population risk minimizer in generalized linear problems such as binary classification with surrogate losses and generalized linear regression models. We focus on large-scale problems, where the iterative minimization of the empirical risk is computationally intractable, i.e., the number of observations $n$ is much larger than the dimension of the parameter $p$, i.e. $n \gg p \gg 1$. We show that under random sub-Gaussian design, the true minimizer of the population risk is approximately proportional to the corresponding ordinary least squares (OLS) estimator. Using this relation, we design an algorithm that achieves the same accuracy as the empirical risk minimizer through iterations that attain up to a cubic convergence rate, and that are cheaper than any batch optimization algorithm by at least a factor of $\mathcal{O}(p)$. We provide theoretical guarantees for our algorithm, and analyze the convergence behavior in terms of data dimensions. Finally, we demonstrate the performance of our algorithm on well-known classification and regression problems, through extensive numerical studies on large-scale datasets, and show that it achieves the highest performance compared to several other widely used and specialized optimization algorithms.

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In certain situations the full-matrix variant of AdaGrad is expected to attain better performance, however in high dimensions it is computationally impractical. We present Ada-LR and RadaGrad two computationally efficient approximations to full-matrix AdaGrad based on randomized dimensionality reduction. They are able to capture dependencies between features and achieve similar performance to full-matrix AdaGrad but at a much smaller computational cost. We show that the regret of Ada-LR is close to the regret of full-matrix AdaGrad which can have an up-to exponentially smaller dependence on the dimension than the diagonal variant. Empirically, we show that Ada-LR and RadaGrad perform similarly to full-matrix AdaGrad. On the task of training convolutional neural networks as well as recurrent neural networks, RadaGrad achieves faster convergence than diagonal AdaGrad.

Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on second-class sampling. This work fills this gap by proposing a natural methodology to extend standard splitting criteria to the one-class setting, structurally generalizing RFs to one-class classification. An extensive benchmark of seven state-of-the-art anomaly detection algorithms is also presented. This empirically demonstrates the relevance of our approach.

Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, a class of methods that extends the idea of word embeddings to other types of high-dimensional data. As examples, we studied neural data with real-valued observations, count data from a market basket analysis, and ratings data from a movie recommendation system. The main idea is to model each observation conditioned on a set of other observations. This set is called the context, and the way the context is defined is a modeling choice that depends on the problem. In language the context is the surrounding words; in neuroscience the context is close-by neurons; in market basket data the context is other items in the shopping cart. Each type of embedding model defines the context, the exponential family of conditional distributions, and how the latent embedding vectors are shared across data. We infer the embeddings with a scalable algorithm based on stochastic gradient descent. On all three applications - neural activity of zebrafish, users' shopping behavior, and movie ratings - we found exponential family embedding models to be more effective than other types of dimension reduction. They better reconstruct held-out data and find interesting qualitative structure.

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, it is relatively insufficient to empower the discriminative ability of DGMs on making accurate predictions. This paper presents max-margin deep generative models (mmDGMs) and a class-conditional variant (mmDCGMs), which explore the strongly discriminative principle of max-margin learning to improve the predictive performance of DGMs in both supervised and semi-supervised learning, while retaining the generative capability. In semi-supervised learning, we use the predictions of a max-margin classifier as the missing labels instead of performing full posterior inference for efficiency; we also introduce additional max-margin and label-balance regularization terms of unlabeled data for effectiveness. We develop an efficient doubly stochastic subgradient algorithm for the piecewise linear objectives in different settings. Empirical results on various datasets demonstrate that: (1) max-margin learning can significantly improve the prediction performance of DGMs and meanwhile retain the generative ability; (2) in supervised learning, mmDGMs are competitive to the best fully discriminative networks when employing convolutional neural networks as the generative and recognition models; and (3) in semi-supervised learning, mmDCGMs can perform efficient inference and achieve state-of-the-art classification results on several benchmarks.

A growing body of recent research is shedding new light on the role of nonconvex optimization for tackling large scale problems in machine learning, signal processing, and convex programming. This work is developing techniques that help to explain the surprising effectiveness of relatively simple first-order algorithms for certain nonconvex optimizations. When applied to problems that can be formulated as semidefinite programs, these techniques can often be viewed as part of a framework proposed by Burer and Monteiro [4]. The Burer-Monteiro technique is based on factoring the semidefinite variable, and applying classical optimization techniques to the resulting nonconvex objective over the factor. While worst-case complexity considerations imply that such an approach cannot succeed in general, a series of recent papers [11, 40, 35, 13, 1] has shown the strategy to be remarkably effective for a number of problems of practical interest, with analytical convergence guarantees and strong empirical performance. In this paper, we enlarge the collection of problems to which the Burer-Monteiro technique can be successfully applied, by analyzing the convergence properties of gradient descent applied to the problem of rectangular matrix completion from incomplete measurements.

Data science is fast becoming a critical skill for developers and managers across industries, and it looks like a lot of fun as well. But it's pretty complicated - there are a lot of engineering and analytical options to navigate, and it's hard to know if you're doing it right or where the bear traps lie. In this series we explore ways in to making sense of data science - understanding where it's needed and where it's not, and how to make it an asset for you, from people who've been there and done it. This InfoQ article is part of the series "Getting A Handle On Data Science" . You can subscribe to receive notifications via RSS. A lot of Machine Learning (ML) projects consist of fitting a (normally very complicated) function to a dataset with the objective of calculating a number like 1 or 0 (is it spam or not?) for classification problems or a set of numbers (e.g., weekly sales of a product) for regression ones.

Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus (LC) approach which allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops. Furthermore, we also design an efficient rejection-free MCMC scheme for approximating the full series. The main novelty underlying our design is in utilizing the concept of cycle basis, which provides an efficient decomposition of the generalized loops. In essence, the proposed MCMC schemes run on transformed GM built upon the non-trivial BP solution, and our experiments show that this synthesis of BP and MCMC outperforms both direct MCMC and bare BP schemes.