Continuous-valued word embeddings learned by neural language models have recently been shown to capture semantic and syntactic information about words very well, setting performance records on several word similarity tasks. The best results are obtained by learning high-dimensional embeddings from very large quantities of data, which makes scalability of the training method a critical factor. We propose a simple and scalable new approach to learning word embeddings based on training log-bilinear models with noise-contrastive estimation. Our approach is simpler, faster, and produces better results than the current state-of-the art method of Mikolov et al. (2013a). We achieve results comparable to the best ones reported, which were obtained on a cluster, using four times less data and more than an order of magnitude less computing time. We also investigate several model types and find that the embeddings learned by the simpler models perform at least as well as those learned by the more complex ones.

Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In this paper, we study the family of GGMs with small feedback vertex sets (FVSs), where an FVS is a set of nodes whose removal breaks all the cycles. Exact inference such as computing the marginal distributions and the partition function has complexity $O(k^{2}n)$ using message-passing algorithms, where k is the size of the FVS, and n is the total number of nodes. We propose efficient structure learning algorithms for two cases: 1) All nodes are observed, which is useful in modeling social or flight networks where the FVS nodes often correspond to a small number of high-degree nodes, or hubs, while the rest of the networks is modeled by a tree. Regardless of the maximum degree, without knowing the full graph structure, we can exactly compute the maximum likelihood estimate in $O(kn^2+n^2\log n)$ if the FVS is known or in polynomial time if the FVS is unknown but has bounded size. 2) The FVS nodes are latent variables, where structure learning is equivalent to decomposing a inverse covariance matrix (exactly or approximately) into the sum of a tree-structured matrix and a low-rank matrix. By incorporating efficient inference into the learning steps, we can obtain a learning algorithm using alternating low-rank correction with complexity $O(kn^{2}+n^{2}\log n)$ per iteration. We also perform experiments using both synthetic data as well as real data of flight delays to demonstrate the modeling capacity with FVSs of various sizes. We show that empirically the family of GGMs of size $O(\log n)$ strikes a good balance between the modeling capacity and the efficiency.

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning in nonlinear nonparametric state-space models. We place a Gaussian process prior over the transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. However, to enable efficient inference, we marginalize over the dynamics of the model and instead infer directly the joint smoothing distribution through the use of specially tailored Particle Markov Chain Monte Carlo samplers. Once an approximation of the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. We make use of sparse Gaussian process models to greatly reduce the computational complexity of the approach.

This paper examines the question: What kinds of distributions can be efficiently represented by Restricted Boltzmann Machines (RBMs)? We characterize the RBM's unnormalized log-likelihood function as a type of neural network (called an RBM network), and through a series of simulation results relate these networks to types that are better understood. We show the surprising result that RBM networks can efficiently compute any function that depends on the number of 1's in the input, such as parity. We also provide the first known example of a particular type of distribution which provably cannot be efficiently represented by an RBM (or equivalently, cannot be efficiently computed by an RBM network), assuming a realistic exponential upper bound on the size of the weights. By formally demonstrating that a relatively simple distribution cannot be represented efficiently by an RBM our results provide a new rigorous justification for the use of potentially more expressive generative models, such as deeper ones.

We present a maximum margin framework that clusters data using latent variables. Using latent representations enables our framework to model unobserved information embedded in the data. We implement our idea by large margin learning, and develop an alternating descent algorithm to effectively solve the resultant non-convex optimization problem. We instantiate our latent maximum margin clustering framework with tag-based video clustering tasks, where each video is represented by a latent tag model describing the presence or absence of video tags. Experimental results obtained on three standard datasets show that the proposed method outperforms non-latent maximum margin clustering as well as conventional clustering approaches.

We consider the sensor selection problem on multivariate Gaussian distributions where only a \emph{subset} of latent variables is of inferential interest. For pairs of vertices connected by a unique path in the graph, we show that there exist decompositions of nonlocal mutual information into local information measures that can be computed efficiently from the output of message passing algorithms. We integrate these decompositions into a computationally efficient greedy selector where the computational expense of quantification can be distributed across nodes in the network. Experimental results demonstrate the comparative efficiency of our algorithms for sensor selection in high-dimensional distributions. We additionally derive an online-computable performance bound based on augmentations of the relevant latent variable set that, when such a valid augmentation exists, is applicable for \emph{any} distribution with nuisances.

Latent variable prediction models, such as multi-layer networks, impose auxiliary latent variables between inputs and outputs to allow automatic inference of implicit features useful for prediction. Unfortunately, such models are difficult to train because inference over latent variables must be performed concurrently with parameter optimization---creating a highly non-convex problem. Instead of proposing another local training method, we develop a convex relaxation of hidden-layer conditional models that admits global training. Our approach extends current convex modeling approaches to handle two nested nonlinearities separated by a non-trivial adaptive latent layer. The resulting methods are able to acquire two-layer models that cannot be represented by any single-layer model over the same features, while improving training quality over local heuristics.

Sampling inference methods are computationally difficult to scale for many models in part because global dependencies can reduce opportunities for parallel computation. Without strict conditional independence structure among variables, standard Gibbs sampling theory requires sample updates to be performed sequentially, even if dependence between most variables is not strong. Empirical work has shown that some models can be sampled effectively by going Hogwild'' and simply running Gibbs updates in parallel with only periodic global communication, but the successes and limitations of such a strategy are not well understood. As a step towards such an understanding, we study the Hogwild Gibbs sampling strategy in the context of Gaussian distributions. We develop a framework which provides convergence conditions and error bounds along with simple proofs and connections to methods in numerical linear algebra. In particular, we show that if the Gaussian precision matrix is generalized diagonally dominant, then any Hogwild Gibbs sampler, with any update schedule or allocation of variables to processors, yields a stable sampling process with the correct sample mean. "

Stochastic And-Or grammars compactly represent both compositionality and re-configurability and have been used to model different types of data such as images and events. We present a unified formalization of stochastic And-Or grammars that is agnostic to the type of the data being modeled, and propose an unsupervised approach to learning the structures as well as the parameters of such grammars. Starting from a trivial initial grammar, our approach iteratively induces compositions and reconfigurations in a unified manner and optimizes the posterior probability of the grammar. In our empirical evaluation, we applied our approach to learning event grammars and image grammars and achieved comparable or better performance than previous approaches.

Markov Decision Processes (MDPs) are extremely useful for modeling and solving sequential decision making problems. Graph-based MDPs provide a compact representation for MDPs with large numbers of random variables. However, the complexity of exactly solving a graph-based MDP usually grows exponentially in the number of variables, which limits their application. We present a new varia-tional framework to describe and solve the planning problem of MDPs, and derive both exact and approximate planning algorithms. In particular, by exploiting the graph structure of graph-based MDPs, we propose a factored variational value iteration algorithm in which the value function is first approximated by the multiplication of local-scope value functions, then solved by minimizing a Kullback-Leibler (KL) divergence. The KL divergence is optimized using the belief propagation algorithm, with complexity exponential in only the cluster size of the graph. Experimental comparison on different models shows that our algorithm outperforms existing approximation algorithms at finding good policies.