Learning of dynamical systems, or state-space models, is central to many machine learning problems, such as reinforcement learning, sequence modeling, and autonomous systems. Furthermore, state-space models are at the core of recent model developments within the machine learning area, such as Gaussian process state-space models (Frigola et al. 2014a; Mattos et al. 2016; etc.), infinite factorial dynamical models (Gael et al., 2009; Valera et al., 2015), and stochastic recurrent neural networks (Fraccaro et al., 2016, for example). A strategy to learn state-space models, independently suggested by Digalakis et al. (1993) and Ghahramani and Hinton (1996), is the use of the Expectation Maximization (EM, Dempster et al. 1977) method. Even though originally proposed only for maximum likelihood estimation of linear models with Gaussian noise, the strategy can be generalized to the more challenging nonlinear and non-Gaussian cases, as well as the empirical Bayes setting. Many contributions have been made during the last decade, and this paper takes another step along the path towards a more computationally efficient method with a solid theoretical ground for learning of nonlinear dynamical systems.

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the non-spiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a "spectral" nature, and that it is degenerate above. This establishes the maximal region of contiguity between the planted and null models. It is known that this threshold also marks a phase transition for estimating the spike: the latter task is possible above the threshold and impossible below. Therefore, both estimation and detection undergo the same transition in this random matrix model. We also provide further information about the performance of the optimal test. Our proofs are based on Gaussian interpolation methods and a rigorous incarnation of the cavity method, as devised by Guerra and Talagrand in their study of the Sherrington--Kirkpatrick spin-glass model.

Pseudo-marginal Metropolis-Hastings (pmMH) is a versatile algorithm for sampling from target distributions which are not easy to evaluate point-wise. However, pmMH requires good proposal distributions to sample efficiently from the target, which can be problematic to construct in practice. This is especially a problem for high-dimensional targets when the standard random-walk proposal is inefficient. We extend pmMH to allow for constructing the proposal based on information from multiple past iterations. As a consequence, quasi-Newton (qN) methods can be employed to form proposals which utilize gradient information to guide the Markov chain to areas of high probability and to construct approximations of the local curvature to scale step sizes. The proposed method is demonstrated on several problems which indicate that qN proposals can perform better than other common Hessian-based proposals.

The online environment has provided a great opportunity for insurance policyholders to share their complaints with respect to different services. These complaints can reveal valuable information for insurance companies who seek to improve their services; however, analyzing a huge number of online complaints is a complicated task for human and must involve computational methods to create an efficient process. This research proposes a computational approach to characterize the major topics of a large number of online complaints. Our approach is based on using the topic modeling approach to disclose the latent semantic of complaints. The proposed approach deployed on thousands of GEICO negative reviews. Analyzing 1,371 GEICO complaints indicates that there are 30 major complains in four categories: (1) customer service, (2) insurance coverage, paperwork, policy, and reports, (3) legal issues, and (4) costs, estimates, and payments. This research approach can be used in other applications to explore a large number of reviews.

Given independent samples generated from the joint distribution $p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional Independence (CI-Testing), i.e., whether the joint equals the CI distribution $p^{CI}(\mathbf{x},\mathbf{y},\mathbf{z})= p(\mathbf{z}) p(\mathbf{y}|\mathbf{z})p(\mathbf{x}|\mathbf{z})$ or not. We cast this problem under the purview of the proposed, provable meta-algorithm, "Mimic and Classify", which is realized in two-steps: (a) Mimic the CI distribution close enough to recover the support, and (b) Classify to distinguish the joint and the CI distribution. Thus, as long as we have a good generative model and a good classifier, we potentially have a sound CI Tester. With this modular paradigm, CI Testing becomes amiable to be handled by state-of-the-art, both generative and classification methods from the modern advances in Deep Learning, which in general can handle issues related to curse of dimensionality and operation in small sample regime. We show intensive numerical experiments on synthetic and real datasets where new mimic methods such conditional GANs, Regression with Neural Nets, outperform the current best CI Testing performance in the literature. Our theoretical results provide analysis on the estimation of null distribution as well as allow for general measures, i.e., when either some of the random variables are discrete and some are continuous or when one or more of them are discrete-continuous mixtures.

Recently, much progress has been made building systems that can capture static image properties, but natural environments are intrinsically dynamic. For an intelligent agent, perception is responsible not only for capturing features of scene content, but also capturing its \textit{affordances}: how the state of things can change, especially as the result of the agent's actions. We propose an unsupervised method to learn representations of the sensorimotor affordances of an environment. We do so by learning an embedding for stochastic future prediction that is (i) sensitive to scene dynamics and minimally sensitive to static scene content and (ii) compositional in nature, capturing the fact that changes in the environment can be composed to produce a cumulative change. We show that these two properties are sufficient to induce representations that are reusable across visually distinct scenes that share degrees of freedom. We show the applicability of our method to synthetic settings and its potential for understanding more complex, realistic visual settings.

The broad set of deep generative models (DGMs) has achieved remarkable advances. However, it is often difficult to incorporate rich structured domain knowledge with the end-to-end DGMs. Posterior regularization (PR) offers a principled framework to impose structured constraints on probabilistic models, but has limited applicability to the diverse DGMs that can lack a Bayesian formulation or even explicit density evaluation. PR also requires constraints to be fully specified {\it a priori}, which is impractical or suboptimal for complex knowledge with learnable uncertain parts. In this paper, we establish mathematical correspondence between PR and reinforcement learning (RL), and, based on the connection, expand PR to learn constraints as the extrinsic reward in RL. The resulting algorithm is model-agnostic to apply to any DGMs, and is flexible to adapt arbitrary constraints with the model jointly. Experiments on human image generation and templated sentence generation show models with learned knowledge constraints by our algorithm greatly improve over base generative models.

We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed algorithm is adjustable to various levels of communication cost, delays, machines computational power, and functions smoothness. A unique feature is that the stepsizes do not depend on communication delays nor number of machines, which is highly desirable for scalability. We prove that the algorithm converges linearly in the strongly convex case, and provide guarantees of convergence for the non-strongly convex case. The obtained rates are the same as the vanilla proximal gradient algorithm over some introduced epoch sequence that subsumes the delays of the system. We provide numerical results on large-scale machine learning problems to demonstrate the merits of the proposed method.

It surveys the general formulation, terminology, and typical experimental implementations of reinforcement learning and reviews competing solution paradigms. In order to compare the relative merits of various techniques, this survey presents a case study of the Linear Quadratic Regulator (LQR) with unknown dynamics, perhaps the simplest and best studied problem in optimal control. The manuscript describes how merging techniques from learning theory and control can provide non-asymptotic characterizations of LQR performance and shows that these characterizations tend to match experimental behavior. In turn, when revisiting more complex applications, many of the observed phenomena in LQR persist. In particular, theory and experiment demonstrate the role and importance of models and the cost of generality in reinforcement learning algorithms. This survey concludes with a discussion of some of the challenges in designing learning systems that safely and reliably interact with complex and uncertain environments and how tools from reinforcement learning and controls might be combined to approach these challenges.

Semantic labeling is a task of matching unknown data source to labeled data sources. The semantic labels could be properties, classes in knowledge bases or labeled data are manually annotated by domain experts. In this paper, we present EmbNum, a novel approach to match numerical columns from different table data sources. We use a representation network architecture consisting of triplet network and convolutional neural network to learn a mapping function from numerical columns to a transformed space. In this space, the Euclidean distance can be used to measure "semantic similarity" of two columns. Our experiments on City-Data and Open-Data demonstrate that EmbNum achieves considerable improvements in comparison with the state-of-the-art methods on effectiveness and efficiency.