A key challenge in designing analog-to-digital converters for cortically implanted prosthesis is to sense and process high-dimensional neural signals recorded by the micro-electrode arrays. In this paper, we describe a novel architecture for analog-to-digital (A/D) conversion that combines Σ conversion with spatial de-correlation within a single module. The architecture called multiple-input multiple-output (MIMO) Σ is based on a min-max gradient descent optimization of a regularized linear cost function that naturally lends to an A/D formulation. Using an online formulation, the architecture can adapt to slow variations in cross-channel correlations, observed due to relative motion of the microelectrodes with respect to the signal sources. Experimental results with real recorded multi-channel neural data demonstrate the effectiveness of the proposed algorithm in alleviating cross-channel redundancy across electrodes and performing data-compression directly at the A/D converter.

Online convex programming has recently emerged as a powerful primitive for designing machine learning algorithms. For example, OCP can be used for learning a linear classifier, dynamically rebalancing a binary search tree, finding the shortest path in a graph with unknown edge lengths, solving a structured classification problem, or finding a good strategy in an extensive-form game. Several researchers have designed no-regret algorithms for OCP. But, compared to algorithms for special cases of OCP such as learning from expert advice, these algorithms are not very numerous or flexible. In learning from expert advice, one tool which has proved particularly valuable is the correspondence between no-regret algorithms and convex potential functions: by reasoning about these potential functions, researchers have designed algorithms with a wide variety of useful guarantees such as good performance when the target hypothesis is sparse. Until now, there has been no such recipe for the more general OCP problem, and therefore no ability to tune OCP algorithms to take advantage of properties of the problem or data. In this paper we derive a new class of no-regret learning algorithms for OCP. These Lagrangian Hedging algorithms are based on a general class of potential functions, and are a direct generalization of known learning rules like weighted majority and external-regret matching. In addition to proving regret bounds, we demonstrate our algorithms learning to play one-card poker.

We propose a new technique for sampling the solutions of combinatorial problems in a near-uniform manner. We focus on problems specified as a Boolean formula, i.e., on SAT instances. Sampling for SAT problems has been shown to have interesting connections with probabilistic reasoning, making practical sampling algorithms for SAT highly desirable. The best current approaches are based on Markov Chain Monte Carlo methods, which have some practical limitations.

By adopting Gaussian process priors a fully Bayesian solution to the problem of integrating possibly heterogeneous data sets within a classification setting is presented. Approximate inference schemes employing Variational & Expectation Propagation based methods are developed and rigorously assessed. We demonstrate our approach to integrating multiple data sets on a large scale protein fold prediction problem where we infer the optimal combinations of covariance functions and achieve state-of-the-art performance without resorting to any ad hoc parameter tuning and classifier combination.

Many computer aided diagnosis (CAD) problems can be best modelled as a multiple-instance learning (MIL) problem with unbalanced data: i.e., the training data typically consists of a few positive bags, and a very large number of negative instances. Existing MIL algorithms are much too computationally expensive for these datasets. We describe CH, a framework for learning a Convex Hull representation of multiple instances that is significantly faster than existing MIL algorithms. Our CH framework applies to any standard hyperplane-based learning algorithm, and for some algorithms, is guaranteed to find the global optimal solution. Experimental studies on two different CAD applications further demonstrate that the proposed algorithm significantly improves diagnostic accuracy when compared to both MIL and traditional classifiers. Although not designed for standard MIL problems (which have both positive and negative bags and relatively balanced datasets), comparisons against other MIL methods on benchmark problems also indicate that the proposed method is competitive with the state-of-the-art.

This paper proposes a new approach to model-based clustering under prior knowledge. The proposed formulation can be interpreted from two different angles: as penalized logistic regression, where the class labels are only indirectly observed (via the probability density of each class); as finite mixture learning under a grouping prior. To estimate the parameters of the proposed model, we derive a (generalized) EM algorithm with a closed-form E-step, in contrast with other recent approaches to semi-supervised probabilistic clustering which require Gibbs sampling or suboptimal shortcuts. We show that our approach is ideally suited for image segmentation: it avoids the combinatorial nature Markov random field priors, and opens the door to more sophisticated spatial priors (e.g., wavelet-based) in a simple and computationally efficient way. Finally, we extend our formulation to work in unsupervised, semi-supervised, or discriminative modes.

We present a novel algorithm called PG-means which is able to learn the number of clusters in a classical Gaussian mixture model. Our method is robust and efficient; it uses statistical hypothesis tests on one-dimensional projections of the data and model to determine if the examples are well represented by the model. In so doing, we are applying a statistical test for the entire model at once, not just on a per-cluster basis. We show that our method works well in difficult cases such as non-Gaussian data, overlapping clusters, eccentric clusters, high dimension, and many true clusters. Further, our new method provides a much more stable estimate of the number of clusters than existing methods.

Applications of our proposed technique include embedding with a natural out-of-sample extension and tasks such as tangent distance estimation, frame rate up-conversion, video compression and motion transfer.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation with various interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

Gaussian data is pervasive and many learning algorithms (e.g., k-means) model their inputs as a single sample drawn from a multivariate Gaussian. However, in many real-life settings, each input object is best described by multiple samples drawn from a multivariate Gaussian. Such data can arise, for example, in a movie review database where each movie is rated by several users, or in time-series domains such as sensor networks. Here, each input can be naturally described by both a mean vector and covariance matrix which parameterize the Gaussian distribution. In this paper, we consider the problem of clustering such input objects, each represented as a multivariate Gaussian. We formulate the problem using an information theoretic approach and draw several interesting theoretical connections to Bregman divergences and also Bregman matrix divergences. We evaluate our method across several domains, including synthetic data, sensor network data, and a statistical debugging application.