We present a new class of models for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive a method for fitting the models that is effective even when the number of covariates is larger than the sample size. A statistical analysis of the properties of SpAM is given together with empirical results on synthetic and real data, showing that SpAM can be effective in fitting sparse nonparametric models in high dimensional data.

We study boosting in the filtering setting, where the booster draws examples from an oracle instead of using a fixed training set and so may train efficiently on very large datasets. Our algorithm, which is based on a logistic regression technique proposed by Collins, Schapire, & Singer, requires fewer assumptions to achieve bounds equivalent to or better than previous work. Moreover, we give the first proof that the algorithm of Collins et al. is a strong PAC learner, albeit within the filtering setting. Our proofs demonstrate the algorithm's strong theoretical properties for both classification and conditional probability estimation, and we validate these results through extensive experiments. Empirically, our algorithm proves more robust to noise and overfitting than batch boosters in conditional probability estimation and proves competitive in classification.

Rosetta is one of the leading algorithms for protein structure prediction today. It is a Monte Carlo energy minimization method requiring many random restarts to find structures with low energy. In this paper we present a resampling technique for structure prediction of small alpha/beta proteins using Rosetta. From an initial round of Rosetta sampling, we learn properties of the energy landscape that guide a subsequent round of sampling toward lower-energy structures. Rather than attempt to fit the full energy landscape, we use feature selection methods--both L1-regularized linear regression and decision trees--to identify structural features that give rise to low energy. We then enrich these structural features in the second sampling round. Results are presented across a benchmark set of nine small alpha/beta proteins demonstrating that our methods seldom impair, and frequently improve, Rosetta's performance.

We present a new class of models for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive a method for fitting the models that is effective even when the number of covariates is larger than the sample size. A statistical analysis of the properties of SpAM is given together with empirical results on synthetic and real data, showing that SpAM can be effective in fitting sparse nonparametric models in high dimensional data.

Hierarchical penalization is a generic framework for incorporating prior information in the fitting of statistical models, when the explicative variables are organized in a hierarchical structure. The penalizer is a convex functional that performs soft selection at the group level, and shrinks variables within each group. This favors solutions with few leading terms in the final combination. The framework, originally derived for taking prior knowledge into account, is shown to be useful in linear regression, when several parameters are used to model the influence of one feature, or in kernel regression, for learning multiple kernels. Keywords - Optimization: constrained and convex optimization.

Rosetta is one of the leading algorithms for protein structure prediction today. It is a Monte Carlo energy minimization method requiring many random restarts to find structures with low energy. In this paper we present a resampling technique for structure prediction of small alpha/beta proteins using Rosetta. From an initial roundof Rosetta sampling, we learn properties of the energy landscape that guide a subsequent round of sampling toward lower-energy structures. Rather than attempt to fit the full energy landscape, we use feature selection methods--both L1-regularized linear regression and decision trees--to identify structural features that give rise to low energy. We then enrich these structural features in the second sampling round. Results are presented across a benchmark set of nine small alpha/beta proteinsdemonstrating that our methods seldom impair, and frequently improve, Rosetta's performance.

We present a new class of models for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive amethod for fitting the models that is effective even when the number of covariates is larger than the sample size. A statistical analysis of the properties of SpAM is given together with empirical results on synthetic and real data, showing thatSpAM can be effective in fitting sparse nonparametric models in high dimensional data.

Semi-supervised methods use unlabeled data in addition to labeled data to construct predictors.While existing semi-supervised methods have shown some promising empirical performance, their development has been based largely based on heuristics. In this paper we study semi-supervised learning from the viewpoint of minimax theory. Our first result shows that some common methods based on regularization using graph Laplacians do not lead to faster minimax rates of convergence. Thus,the estimators that use the unlabeled data do not have smaller risk than the estimators that use only labeled data. We then develop several new approaches that provably lead to improved performance. The statistical tools of minimax analysis are thus used to offer some new perspective on the problem of semi-supervised learning.

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive a maximum-likelihood procedure for parameter estimation, which relies on variational approximations to handle intractable posterior expectations. Prediction problems motivate this research: we use the fitted model to predict response values for new documents. We test sLDA on two real-world problems: movie ratings predicted from reviews, and web page popularity predicted from text descriptions. We illustrate the benefits of sLDA versus modern regularized regression, as well as versus an unsupervised LDA analysis followed by a separate regression.

We study boosting in the filtering setting, where the booster draws examples from an oracle instead of using a fixed training set and so may train efficiently on very large datasets. Our algorithm, which is based on a logistic regression technique proposed by Collins, Schapire, & Singer, requires fewer assumptions to achieve bounds equivalent to or better than previous work. Moreover, we give the first proof that the algorithm of Collins et al. is a strong PAC learner, albeit within the filtering setting. Our proofs demonstrate the algorithm's strong theoretical properties forboth classification and conditional probability estimation, and we validate these results through extensive experiments. Empirically, our algorithm proves more robust to noise and overfitting than batch boosters in conditional probability estimation and proves competitive in classification.