Probabilistic topic models are a popular tool for the unsupervised analysis of text, providing both a predictive model of future text and a latent topic representation of the corpus. Practitioners typically assume that the latent space is semantically meaningful. It is used to check models, summarize the corpus, and guide exploration of its contents. However, whether the latent space is interpretable is in need of quantitative evaluation. In this paper, we present new quantitative methods for measuring semantic meaning in inferred topics. We back these measures with large-scale user studies, showing that they capture aspects of the model that are undetected by previous measures of model quality based on held-out likelihood. Surprisingly, topic models which perform better on held-out likelihood may infer less semantically meaningful topics.

We explore a new Bayesian model for probabilistic grammars, a family of distributions over discrete structures that includes hidden Markov models and probabilistic context-free grammars. Our model extends the correlated topic model framework to probabilistic grammars, exploiting the logistic normal distribution as a prior over the grammar parameters. We derive a variational EM algorithm for that model, and then experiment with the task of unsupervised grammar induction for natural language dependency parsing. We show that our model achieves superior results over previous models that use different priors.

We describe a hierarchical, probabilistic model that learns to extract complex motion from movies of the natural environment. The model consists of two hidden layers: the first layer produces a sparse representation of the image that is expressed in terms of local amplitude and phase variables. The second layer learns the higher-order structure among the time-varying phase variables. After training on natural movies, the top layer units discover the structure of phase-shifts within the first layer.

We show how smoother priors can preserve the benefits of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it more useful for prediction problems. Additionally, we show how to calculate the derivative of the MAP estimate efficiently with implicit differentiation. One prior that can be differentiated this way is KL-regularization. We demonstrate its effectiveness on a wide variety of applications, and find that online optimization of the parameters of the KL-regularized model can significantly improve prediction performance.

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.