The problem of ranking arises ubiquitously in almost every aspect of life, and in particular in Machine Learning/Information Retrieval. A statistical model for ranking predicts how humans rank subsets V of some universe U. In this work we define a statistical model for ranking that satisfies certain desirable properties. The model automatically gives rise to a logistic regression based approach to learning how to rank, for which the score and comparison based approaches are dual views. This offers a new generative approach to ranking which can be used for IR.

In this paper lower and upper bounds for the number of support vectors are derived for support vector machines (SVMs) based on the epsilon-insensitive loss function. It turns out that these bounds are asymptotically tight under mild assumptions on the data generating distribution. Finally, we briefly discuss a trade-off in epsilon between sparsity and accuracy if the SVM is used to estimate the conditional median.

We consider robust least-squares regression with feature-wise disturbance. We show that this formulation leads to tractable convex optimization problems, and we exhibit a particular uncertainty set for which the robust problem is equivalent to $\ell_1$ regularized regression (Lasso). This provides an interpretation of Lasso from a robust optimization perspective. We generalize this robust formulation to consider more general uncertainty sets, which all lead to tractable convex optimization problems. Therefore, we provide a new methodology for designing regression algorithms, which generalize known formulations. The advantage is that robustness to disturbance is a physical property that can be exploited: in addition to obtaining new formulations, we use it directly to show sparsity properties of Lasso, as well as to prove a general consistency result for robust regression problems, including Lasso, from a unified robustness perspective.

We introduces a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After working out an inference scheme which combines slice sampling and dynamic programming we demonstrate how the infinite factorial hidden Markov model can be used for blind source separation.

Using machine learning algorithms to decode intended behavior from neural activity serves a dual purpose. First, these tools can be used to allow patients to interact with their environment through a Brain-Machine Interface (BMI). Second, analysis of the characteristics of such methods can reveal the significance of various features of neural activity, stimuli and responses to the encoding-decoding task. In this study we adapted, implemented and tested a machine learning method, called Kernel Auto-Regressive Moving Average (KARMA), for the task of inferring movements from neural activity in primary motor cortex. Our version of this algorithm is used in an on-line learning setting and is updated when feedback from the last inferred sequence become available. We first used it to track real hand movements executed by a monkey in a standard 3D motor control task. We then applied it in a closed-loop BMI setting to infer intended movement, while arms were restrained, allowing a monkey to perform the task using the BMI alone. KARMA is a recurrent method that learns a nonlinear model of output dynamics. It uses similarity functions (termed kernels) to compare between inputs. These kernels can be structured to incorporate domain knowledge into the method. We compare KARMA to various state-of-the-art methods by evaluating tracking performance and present results from the KARMA based BMI experiments.

In classification problems, Support Vector Machines maximize the margin of separation between two classes. While the paradigm has been successful, the solution obtained by SVMs is dominated by the directions with large data spread and biased to separate the classes by cutting along large spread directions. This article proposes a novel formulation to overcome such sensitivity and maximizes the margin relative to the spread of the data. The proposed formulation can be efficiently solved and experiments on digit datasets show drastic performance improvements over SVMs.

Classical Game Theoretic approaches that make strong rationality assumptions have difficulty modeling observed behaviour in Economic games of human subjects. We investigate the role of finite levels of iterated reasoning and non-selfish utility functions in a Partially Observable Markov Decision Process model that incorporates Game Theoretic notions of interactivity. Our generative model captures a broad class of characteristic behaviours in a multi-round Investment game. We invert the generative process for a recognition model that is used to classify 200 subjects playing an Investor-Trustee game against randomly matched opponents.

We address the challenge of assessing conservation of gene expression in complex, non-homogeneous datasets. Recent studies have demonstrated the success of probabilistic models in studying the evolution of gene expression in simple eukaryotic organisms such as yeast, for which measurements are typically scalar and independent. Models capable of studying expression evolution in much more complex organisms such as vertebrates are particularly important given the medical and scientific interest in species such as human and mouse. We present a statistical model that makes a number of significant extensions to previous models to enable characterization of changes in expression among highly complex organisms. We demonstrate the efficacy of our method on a microarray dataset containing diverse tissues from multiple vertebrate species. We anticipate that the model will be invaluable in the study of gene expression patterns in other diverse organisms as well, such as worms and insects.

Cell assemblies exhibiting episodes of recurrent coherent activity have been observed in several brain regions including the striatum and hippocampus CA3. Here we address the question of how coherent dynamically switching assemblies appear in large networks of biologically realistic spiking neurons interacting deterministically. We show by numerical simulations of large asymmetric inhibitory networks with fixed external excitatory drive that if the network has intermediate to sparse connectivity, the individual cells are in the vicinity of a bifurcation between a quiescent and firing state and the network inhibition varies slowly on the spiking timescale, then cells form assemblies whose members show strong positive correlation, while members of different assemblies show strong negative correlation. We show that cells and assemblies switch between firing and quiescent states with time durations consistent with a power-law. Our results are in good qualitative agreement with the experimental studies. The deterministic dynamical behaviour is related to winner-less competition shown in small closed loop inhibitory networks with heteroclinic cycles connecting saddle-points.

Correlations between spike counts are often used to analyze neural coding. The noise is typically assumed to be Gaussian. Yet, this assumption is often inappropriate, especially for low spike counts. In this study, we present copulas as an alternative approach. With copulas it is possible to use arbitrary marginal distributions such as Poisson or negative binomial that are better suited for modeling noise distributions of spike counts. Furthermore, copulas place a wide range of dependence structures at the disposal and can be used to analyze higher order interactions. We develop a framework to analyze spike count data by means of copulas. Methods for parameter inference based on maximum likelihood estimates and for computation of Shannon entropy are provided. We apply the method to our data recorded from macaque prefrontal cortex. The data analysis leads to three significant findings: (1) copula-based distributions provide better fits than discretized multivariate normal distributions; (2) negative binomial margins fit the data better than Poisson margins; and (3) a dependence model that includes only pairwise interactions overestimates the information entropy by at least 19% compared to the model with higher order interactions.