This empirical study is mainly devoted to comparing four tree-based boosting algorithms: mart, abc-mart, robust logitboost, and abc-logitboost, for multi-class classification on a variety of publicly available datasets. Some of those datasets have been thoroughly tested in prior studies using a broad range of classification algorithms including SVM, neural nets, and deep learning. In terms of the empirical classification errors, our experiment results demonstrate: 1. Abc-mart considerably improves mart. 2. Abc-logitboost considerably improves (robust) logitboost. 3. Robust) logitboost} considerably improves mart on most datasets. 4. Abc-logitboost considerably improves abc-mart on most datasets. 5. These four boosting algorithms (especially abc-logitboost) outperform SVM on many datasets. 6. Compared to the best deep learning methods, these four boosting algorithms (especially abc-logitboost) are competitive.

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.

The problem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

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.

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.

The problem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

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.

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 consider the problem of variable group selection for least squares regression, namely, that of selecting groups of variables for best regression performance, leveraging and adhering to a natural grouping structure within the explanatory variables. We show that this problem can be efficiently addressed by using a certain greedy style algorithm. More precisely, we propose the Group Orthogonal Matching Pursuit algorithm (Group-OMP), which extends the standard OMP procedure (also referred to as ``forward greedy feature selection algorithm for least squares regression) to perform stage-wise group variable selection. We prove that under certain conditions Group-OMP can identify the correct (groups of) variables. We also provide an upperbound on the $l_\infty$ norm of the difference between the estimated regression coefficients and the true coefficients. Experimental results on simulated and real world datasets indicate that Group-OMP compares favorably to Group Lasso, OMP and Lasso, both in terms of variable selection and prediction accuracy.

This paper studies the forward greedy strategy in sparse nonparametric regression. Foradditive models, we propose an algorithm called additive forward regression; forgeneral multivariate models, we propose an algorithm called generalized forward regression. Both algorithms simultaneously conduct estimation and variable selection in nonparametric settings for the high dimensional sparse learning problem. Our main emphasis is empirical: on both simulated and real data, these two simple greedy methods can clearly outperform several state-ofthe-art competitors,including LASSO, a nonparametric version of LASSO called the sparse additive model (SpAM) and a recently proposed adaptive parametric forward-backward algorithm called Foba. We also provide some theoretical justifications ofspecific versions of the additive forward regression.