Many tasks in text and speech processing and computational biology require estimating functions mapping strings to real numbers. A broad class of such functions can be defined by weighted automata. Spectral methods based on the singular value decomposition of a Hankel matrix have been recently proposed for learning a probability distribution represented by a weighted automaton from a training sample drawn according to this same target distribution. In this paper, we show how spectral methods can be extended to the problem of learning a general weighted automaton from a sample generated by an arbitrary distribution. The main obstruction to this approach is that, in general, some entries of the Hankel matrix may be missing. We present a solution to this problem based on solving a constrained matrix completion problem. Combining these two ingredients, matrix completion and spectral method, a whole new family of algorithms for learning general weighted automata is obtained.

We investigate a curious relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. Based on our population-level results, we show how the graphical Lasso may be used to recover the edge structure of certain classes of discrete graphical models, and present simulations to verify our theoretical results.

A common challenge for Bayesian models of perception is the fact that the two fundamental Bayesian components, the prior distribution and the likelihood function, are formally unconstrained. Here we argue that a neural system that emulates Bayesian inference is naturally constrained by the way it represents sensory information in populations of neurons. More specifically, we show that an efficient coding principle creates a direct link between prior and likelihood based on the underlying stimulus distribution. The resulting Bayesian estimates can show biases away from the peaks of the prior distribution, a behavior seemingly at odds with the traditional view of Bayesian estimation, yet one that has been reported in human perception. We demonstrate that our framework correctly accounts for the repulsive biases previously reported for the perception of visual orientation, and show that the predicted tuning characteristics of the model neurons match the reported orientation tuning properties of neurons in primary visual cortex. Our results suggest that efficient coding is a promising hypothesis in constraining Bayesian models of perceptual inference.

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

The ability to predict action content from neural signals in real time before the action occurs has been long sought in the neuroscientific study of decision-making, agency and volition. Online real-time (ORT) prediction is important for understanding the relation between neural correlates of decision-making and conscious, voluntary action as well as for brain-machine interfaces. Here, epilepsy patients, implanted with intracranial depth microelectrodes or subdural grid electrodes for clinical purposes, participated in a "matching-pennies" game against an opponent. In each trial, subjects were given a 5 s countdown, after which they had to raise their left or right hand immediately as the "go" signal appeared on a computer screen. They won a fixed amount of money if they raised a different hand than their opponent and lost that amount otherwise.

R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently. We derive a generalization of Newton-type methods to handle such convex but nonsmooth objective functions. We prove such methods are globally convergent and achieve superlinear rates of convergence in the vicinity of an optimal solution. We also demonstrate the performance of these methods using problems of relevance in machine learning and statistics.

We advocate the use of a new distribution family--the transelliptical--for robust inference of high dimensional graphical models. The transelliptical family is an extension of the nonparanormal family proposed by Liu et al. (2009). Just as the nonparanormal extends the normal by transforming the variables using univariate functions, the transelliptical extends the elliptical family in the same way. We propose a nonparametric rank-based regularization estimator which achieves the parametric rates of convergence for both graph recovery and parameter estimation. Such a result suggests that the extra robustness and flexibility obtained by the semiparametric transelliptical modeling incurs almost no efficiency loss. We also discuss the relationship between this work with the transelliptical component analysis proposed by Han and Liu (2012).

Recent advances in 3D sensing technologies make it possible to easily record color and depth images which together can improve object recognition. Most current methods rely on very well-designed features for this new 3D modality. We introduce a model based on a combination of convolutional and recursive neural networks (CNN and RNN) for learning features and classifying RGB-D images. The CNN layer learns low-level translationally invariant features which are then given as inputs to multiple, fixed-tree RNNs in order to compose higher order features. RNNs can be seen as combining convolution and pooling into one efficient, hierarchical operation. Our main result is that even RNNs with random weights compose powerful features. Our model obtains state of the art performance on a standard RGB-D object dataset while being more accurate and faster during training and testing than comparable architectures such as two-layer CNNs.

In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick-Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB-CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution.

A gaze concurrence is a point in 3D where the gaze directions of two or more people intersect. It is a strong indicator of social saliency because the attention of the participating group is focused on that point. In scenes occupied by large groups of people, multiple concurrences may occur and transition over time. In this paper, we present a method to construct a 3D social saliency field and locate multiple gaze concurrences that occur in a social scene from videos taken by head-mounted cameras. We model the gaze as a cone-shaped distribution emanating from the center of the eyes, capturing the variation of eye-in-head motion. We calibrate the parameters of this distribution by exploiting the fixed relationship between the primary gaze ray and the head-mounted camera pose. The resulting gaze model enables us to build a social saliency field in 3D. We estimate the number and 3D locations of the gaze concurrences via provably convergent modeseeking in the social saliency field. Our algorithm is applied to reconstruct multiple gaze concurrences in several real world scenes and evaluated quantitatively against motion-captured ground truth.