Ajit Paul Singh

Near-optimal sensor placements in Gaussian processes

When monitoring spatial phenomena, which are often modeled as Gaussian Processes (GPs), choosing sensor locations is a fundamental task. A common strategy is to place sensors at the points of highest entropy (variance) in the GP model. We propose a mutual information criteria, and show that it produces better placements. Furthermore, we prove that finding the configuration that maximizes mutual information is NP-complete. To address this issue, we describe a polynomial-time approximation that is within (1 -- 1/e) of the optimum by exploiting the submodularity of our criterion. This algorithm is extended to handle local structure in the GP, yielding significant speedups. We demonstrate the advantages of our approach on two real-world data sets.

A Unified View of Matrix Factorization Models

We present a unified view of matrix factorization that frames the differences among popular methods, such as NMF, Weighted SVD, E-PCA, MMMF, pLSI, pLSI-pHITS, Bregman co-clustering, and many others, in terms of a small number of modeling choices. Many of these approaches can be viewed as minimizing a generalized Bregman divergence, and we show that (i) a straightforward alternating projection algorithm can be applied to almost any model in our unified view; (ii) the Hessian for each projection has special structure that makes a Newton projection feasible, even when there are equality constraints on the factors, which allows for matrix co-clustering; and (iii) alternating projections can be generalized to simultaneously factor a set of matrices that share dimensions. These observations immediately yield new optimization algorithms for the above factorization methods, and suggest novel generalizations of these methods such as incorporating row and column biases, and adding or relaxing clustering constraints.

Learning sparse models for a dynamic Bayesian network classifier of protein secondary structure

BackgroundProtein secondary structure prediction provides insight into protein function and is a valuable preliminary step for predicting the 3D structure of a protein. Dynamic Bayesian networks (DBNs) and support vector machines (SVMs) have been shown to provide state-of-the-art performance in secondary structure prediction. As the size of the protein database grows, it becomes feasible to use a richer model in an effort to capture subtle correlations among the amino acids and the predicted labels. In this context, it is beneficial to derive sparse models that discourage over-fitting and provide biological insight.ResultsIn this paper, we first show that we are able to obtain accurate secondary structure predictions. Our per-residue accuracy on a well established and difficult benchmark (CB513) is 80.3%, which is comparable to the state-of-the-art evaluated on this dataset. We then introduce an algorithm for sparsifying the parameters of a DBN. Using this algorithm, we can automatically remove up to 70-95% of the parameters of a DBN while maintaining the same level of predictive accuracy on the SD576 set. At 90% sparsity, we are able to compute predictions three times faster than a fully dense model evaluated on the SD576 set. We also demonstrate, using simulated data, that the algorithm is able to recover true sparse structures with high accuracy, and using real data, that the sparse model identifies known correlation structure (local and non-local) related to different classes of secondary structure elements.ConclusionsWe present a secondary structure prediction method that employs dynamic Bayesian networks and support vector machines. We also introduce an algorithm for sparsifying the parameters of the dynamic Bayesian network. The sparsification approach yields a significant speed-up in generating predictions, and we demonstrate that the amino acid correlations identified by the algorithm correspond to several known features of protein secondary structure. Datasets and source code used in this study are available at http://noble.gs.washington.edu/proj/pssp.

Abstract task specifications for conversation policies

Task Specifications for Conversation Policies