The purpose of the New York Workshop on Computer, Earth and Space Sciences is to bring together the New York area's finest Astronomers, Statisticians, Computer Scientists, Space and Earth Scientists to explore potential synergies between their respective fields. The 2011 edition (CESS2011) was a great success, and we would like to thank all of the presenters and participants for attending. This year was also special as it included authors from the upcoming book titled "Advances in Machine Learning and Data Mining for Astronomy". Over two days, the latest advanced techniques used to analyze the vast amounts of information now available for the understanding of our universe and our planet were presented. These proceedings attempt to provide a small window into what the current state of research is in this vast interdisciplinary field and we'd like to thank the speakers who spent the time to contribute to this volume.

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is numerically very challenging. We address this challenge by developing a new adaptive gradient-based method that carefully combines gradient information with an adaptive step-scaling strategy, which results in a scalable, highly competitive method. Our algorithm, like its predecessors, maximizes an $\ell_1$-norm penalized log-likelihood and has the same per iteration arithmetic complexity as the best methods in its class. Our experiments reveal that our approach outperforms state-of-the-art competitors, often significantly so, for large problems.

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution comparison such as outlier detection, transfer learning, and two-sample homogeneity test. However, since density-ratio functions often possess high fluctuation, divergence estimation is still a challenging task in practice. In this paper, we propose to use relative divergences for distribution comparison, which involves approximation of relative density-ratios. Since relative density-ratios are always smoother than corresponding ordinary density-ratios, our proposed method is favorable in terms of the non-parametric convergence speed. Furthermore, we show that the proposed divergence estimator has asymptotic variance independent of the model complexity under a parametric setup, implying that the proposed estimator hardly overfits even with complex models. Through experiments, we demonstrate the usefulness of the proposed approach.

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization. The active set update rules rely on the ability of the predictive distributions of a Gaussian process classifier to estimate the relative contribution of a datapoint when being either included or removed from the model. This means that we can use it to include points with potentially high impact to the classifier decision process while removing those that are less relevant. We introduce two active set rules based on different criteria, the first one prefers a model with interpretable active set parameters whereas the second puts computational complexity first, thus a model with active set parameters that directly control its complexity. We also provide both theoretical and empirical support for our active set selection strategy being a good approximation of a full Gaussian process classifier. Our extensive experiments show that our approach can compete with state-of-the-art classification techniques with reasonable time complexity. Source code publicly available at http://cogsys.imm.dtu.dk/passgp.

Motivation: Biomarker discovery from high-dimensional data is a crucial problem with enormous applications in biology and medicine. It is also extremely challenging from a statistical viewpoint, but surprisingly few studies have investigated the relative strengths and weaknesses of the plethora of existing feature selection methods. Methods: We compare 32 feature selection methods on 4 public gene expression datasets for breast cancer prognosis, in terms of predictive performance, stability and functional interpretability of the signatures they produce. Results: We observe that the feature selection method has a significant influence on the accuracy, stability and interpretability of signatures. Simple filter methods generally outperform more complex embedded or wrapper methods, and ensemble feature selection has generally no positive effect. Overall a simple Student's t-test seems to provide the best results. Availability: Code and data are publicly available at http://cbio.ensmp.fr/~ahaury/.

To better understand the spatial structure of large panels of economic and financial time series and provide a guideline for constructing semiparametric models, this paper first considers estimating a large spatial covariance matrix of the generalized $m$-dependent and $\beta$-mixing time series (with $J$ variables and $T$ observations) by hard thresholding regularization as long as ${{\log J \, \cx^*(\ct)}}/{T} = \Co(1)$ (the former scheme with some time dependence measure $\cx^*(\ct)$) or $\log J /{T} = \Co(1)$ (the latter scheme with some upper bounded mixing coefficient). We quantify the interplay between the estimators' consistency rate and the time dependence level, discuss an intuitive resampling scheme for threshold selection, and also prove a general cross-validation result justifying this. Given a consistently estimated covariance (correlation) matrix, by utilizing its natural links with graphical models and semiparametrics, after "screening" the (explanatory) variables, we implement a novel forward (and backward) label permutation procedure to cluster the "relevant" variables and construct the corresponding semiparametric model, which is further estimated by the groupwise dimension reduction method with sign constraints. We call this the SCE (screen - cluster - estimate) approach for modeling high dimensional data with complex spatial structure. Finally we apply this method to study the spatial structure of large panels of economic and financial time series and find the proper semiparametric structure for estimating the consumer price index (CPI) to illustrate its superiority over the linear models.

We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Exact computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcription and are thus potentially useful in a number of music applications such as adaptive automatic accompaniment, score typesetting and music information retrieval.

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse undirected graphical model structure via thresholding of each among many $\ell_1$-norm penalized regression functions; we then estimate the covariance matrix and its inverse using the maximum likelihood estimator. We show that under suitable conditions, this approach yields consistent estimation in terms of graphical structure and fast convergence rates with respect to the operator and Frobenius norm for the covariance matrix and its inverse. We also derive an explicit bound for the Kullback Leibler divergence.

This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several approximative methods have been proposed. The expectation propagation (EP) has been found to be a very accurate method in many empirical studies but the convergence of the EP is known to be problematic with models containing non-log-concave site functions such as the Student-t distribution. In this paper we illustrate the situations where the standard EP fails to converge and review different modifications and alternative algorithms for improving the convergence. We demonstrate that convergence problems may occur during the type-II maximum a posteriori (MAP) estimation of the hyperparameters and show that the standard EP may not converge in the MAP values in some difficult cases. We present a robust implementation which relies primarily on parallel EP updates and utilizes a moment-matching-based double-loop algorithm with adaptively selected step size in difficult cases. The predictive performance of the EP is compared to the Laplace, variational Bayes, and Markov chain Monte Carlo approximations.

We develop, analyze, and evaluate a novel, supervised, specific-to-general learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, event-description language called AMA that is sufficiently expressive to represent many events yet sufficiently restrictive to support learning. We then give algorithms, along with lower and upper complexity bounds, for the subsumption and generalization problems for AMA formulas. We present a positive-examples--only specific-to-general learning method based on these algorithms. We also present a polynomial-time--computable ``syntactic'' subsumption test that implies semantic subsumption without being equivalent to it. A generalization algorithm based on syntactic subsumption can be used in place of semantic generalization to improve the asymptotic complexity of the resulting learning algorithm. Finally, we apply this algorithm to the task of learning relational event definitions from video and show that it yields definitions that are competitive with hand-coded ones.