The Markov chain is a convenient tool to represent the dynamics of complex systems such as traffic and social systems, where probabilistic transition takes place between internal states. A Markov chain is characterized by initial-state probabilities and a state-transition probability matrix. In the traditional setting, a major goal is to study properties of a Markov chain when those probabilities are known. This paper tackles an inverse version of the problem: we find those probabilities from partial observations at a limited number of states. The observations include the frequency of visiting a state and the rate of reaching a state from another. Practical examples of this task include traffic monitoring systems in cities, where we need to infer the traffic volume on single link on a road network from a limited number of observation points. We formulate this task as a regularized optimization problem, which is efficiently solved using the notion of natural gradient. Using synthetic and real-world data sets including city traffic monitoring data, we demonstrate the effectiveness of our method.

In this paper we investigate the use of Langevin Monte Carlo methods on the probability simplex and propose a new method, Stochastic gradient Riemannian Langevin dynamics, which is simple to implement and can be applied to large scale data. We apply this method to latent Dirichlet allocation in an online minibatch setting, and demonstrate that it achieves substantial performance improvements over the state of the art online variational Bayesian methods.

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 (i.e.

Logistic-normal topic models can effectively discover correlation structures among latent topics. However, their inference remains a challenge because of the non-conjugacy between the logistic-normal prior and multinomial topic mixing proportions. Existing algorithms either make restricting mean-field assumptions or are not scalable to large-scale applications. This paper presents a partially collapsed Gibbs sampling algorithm that approaches the provably correct distribution by exploring the ideas of data augmentation. To improve time efficiency, we further present a parallel implementation that can deal with large-scale applications and learn the correlation structures of thousands of topics from millions of documents. Extensive empirical results demonstrate the promise.

Stochastic And-Or grammars compactly represent both compositionality and reconfigurability 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.

Structure learning algorithms for graphical models have focused almost exclusively on stable environments in which the underlying generative process does not change; that is, they assume that the generating model is globally stationary. In real-world environments, however, such changes often occur without warning or signal. Real-world data often come from generating models that are only locally stationary. In this paper, we present LoSST, a novel, heuristic structure learning algorithm that tracks changes in graphical model structure or parameters in a dynamic, real-time manner. We show by simulation that the algorithm performs comparably to batch-mode learning when the generating graphical structure is globally stationary, and significantly better when it is only locally stationary.

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.

How do humans perceive the speed of a coherent motion stimulus that contains motion energy in multiple spatiotemporal frequency bands? Here we tested the idea that perceived speed is the result of an integration process that optimally combines speed information across independent spatiotemporal frequency channels. We formalized this hypothesis with a Bayesian observer model that combines the likelihood functions provided by the individual channel responses (cues). We experimentally validated the model with a 2AFC speed discrimination experiment that measured subjects' perceived speed of drifting sinusoidal gratings with different contrasts and spatial frequencies, and of various combinations of these single gratings. We found that the perceived speeds of the combined stimuli are independent of the relative phase of the underlying grating components. The results also show that the discrimination thresholds are smaller for the combined stimuli than for the individual grating components, supporting the cue combination hypothesis. The proposed Bayesian model fits the data well, accounting for the full psychometric functions of both simple and combined stimuli. Fits are improved if we assume that the channel responses are subject to divisive normalization. Our results provide an important step toward a more complete model of visual motion perception that can predict perceived speeds for coherent motion stimuli of arbitrary spatial structure.

With the advent of modern stimulation techniques in neuroscience, the opportunity arises to map neuron to neuron connectivity. In this work, we develop a method for efficiently inferring posterior distributions over synaptic strengths in neural microcircuits. The input to our algorithm is data from experiments in which action potentials from putative presynaptic neurons can be evoked while a subthreshold recording is made from a single postsynaptic neuron. We present a realistic statistical model which accounts for the main sources of variability in this experiment and allows for significant prior information about the connectivity and neuronal cell types to be incorporated if available. Due to the technical challenges and sparsity of these systems, it is important to focus experimental time stimulating the neurons whose synaptic strength is most ambiguous, therefore we also develop an online optimal design algorithm for choosing which neurons to stimulate at each trial.

We introduce a novel variational method that allows to approximately integrate out kernel hyperparameters, such as length-scales, in Gaussian process regression. This approach consists of a novel variant of the variational framework that has been recently developed for the Gaussian process latent variable model which additionally makes use of a standardised representation of the Gaussian process. We consider this technique for learning Mahalanobis distance metrics in a Gaussian process regression setting and provide experimental evaluations and comparisons with existing methods by considering datasets with high-dimensional inputs.