We study how to automatically select and adapt multiple abstractions or representations of the world to support model-based reinforcement learning. We address the challenges of transfer learning in heterogeneous environments with varying tasks. We present an efficient, online framework that, through a sequence of tasks, learns a set of relevant representations to be used in future tasks. Without pre-defined mapping strategies, we introduce a general approach to support transfer learning across different state spaces. We demonstrate the potential impact of our system through improved jumpstart and faster convergence to near optimum policy in two benchmark domains.

Despite the variety of robust regression methods that have been developed, current regression formulations are either NP-hard, or allow unbounded response to even a single leverage point. We present a general formulation for robust regression --Variational M-estimation--that unifies a number of robust regression methods while allowing a tractable approximation strategy. We develop an estimator that requires only polynomial-time, while achieving certain robustness and consistency guarantees. An experimental evaluation demonstrates the effectiveness of the new estimation approach compared to standard methods.

We present a method for approximate inference for a broad class of non-conjugate probabilistic models. In particular, for the family of generalized linear model target densities we describe a rich class of variational approximating densities which can be best fit to the target by minimizing the Kullback-Leibler divergence. Our approach is based on using the Fourier representation which we show results in efficient and scalable inference.

Multiple-output regression models require estimating multiple functions, one for each output. To improve parameter estimation in such models, methods based on structural regularization of the model parameters are usually needed. In this paper, we present a multiple-output regression model that leverages the covariance structure of the functions (i.e., how the multiple functions are related with each other) as well as the conditional covariance structure of the outputs. This is in contrast with existing methods that usually take into account only one of these structures. More importantly, unlike most of the other existing methods, none of these structures need be known a priori in our model, and are learned from the data. Several previously proposed structural regularization based multiple-output regression models turn out to be special cases of our model. Moreover, in addition to being a rich model for multiple-output regression, our model can also be used in estimating the graphical model structure of a set of variables (multivariate outputs) conditioned on another set of variables (inputs). Experimental results on both synthetic and real datasets demonstrate the effectiveness of our method.

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that have low rank. Backfitting algorithms are derived and justified using a nonparametric form of the nuclear norm subdifferential. Oracle inequalities on excess risk are derived that exhibit the scaling behavior of the procedure in the high dimensional setting. The methods are illustrated on gene expression data.

We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multiclass classification problems. We propose a model that is generic enough to handle any supervised learning task and also subsumes the model previously proposed for classification. We give a ''goodness'' criterion for similarity functions w.r.t. a given supervised learning task and then adapt a well-known landmarking technique to provide efficient algorithms for supervised learning using ''good'' similarity functions. We demonstrate the effectiveness of our model on three important supervised learning problems: a) real-valued regression, b) ordinal regression and c) ranking where we show that our method guarantees bounded generalization error. Furthermore, for the case of real-valued regression, we give a natural goodness definition that, when used in conjunction with a recent result in sparse vector recovery, guarantees a sparse predictor with bounded generalization error. Finally, we report results of our learning algorithms on regression and ordinal regression tasks using non-PSD similarity functions and demonstrate the effectiveness of our algorithms, especially that of the sparse landmark selection algorithm that achieves significantly higher accuracies than the baseline methods while offering reduced computational costs.

The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. In this paper, we propose a GP Regression model with a latent variable that serves as an additional unobserved covariate for the regression. This model (which we call GPLC) allows for heteroscedasticity since it allows the function to have a changing partial derivative with respect to this unobserved covariate. With a suitable covariance function, our GPLC model can handle (a) Gaussian residuals with input-dependent variance, or (b) non-Gaussian residuals with input-dependent variance, or (c) Gaussian residuals with constant variance. We compare our model, using synthetic datasets, with a model proposed by Goldberg, Williams and Bishop (1998), which we refer to as GPLV, which only deals with case (a), as well as a standard GP model which can handle only case (c). Markov Chain Monte Carlo methods are developed for both modelsl. Experiments show that when the data is heteroscedastic, both GPLC and GPLV give better results (smaller mean squared error and negative log-probability density) than standard GP regression. In addition, when the residual are Gaussian, our GPLC model is generally nearly as good as GPLV, while when the residuals are non-Gaussian, our GPLC model is better than GPLV.

Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fixed design and measure the distance between functions by the mean squared error at the design points. While procedures based on exponential weights are known to solve the problem of model selection aggregation in expectation, they are, surprisingly, sub-optimal in deviation. We propose a new formulation called Q-aggregation that addresses this limitation; namely, its solution leads to sharp oracle inequalities that are optimal in a minimax sense. Moreover, based on the new formulation, we design greedy Q-aggregation procedures that produce sparse aggregation models achieving the optimal rate. The convergence and performance of these greedy procedures are illustrated and compared with other standard methods on simulated examples.

This paper is about searching the combinatorial space of contingency tables during the inner loop of a nonlinear statistical optimization. Examples of this operation in various data analytic communities include searching for nonlinear combinations of attributes that contribute significantly to a regression (Statistics), searching for items to include in a decision list (machine learning) and association rule hunting (Data Mining). This paper investigates a new, efficient approach to this class of problems, called RADSEARCH (Real-valued All-Dimensions-tree Search). RADSEARCH finds the global optimum, and this gives us the opportunity to empirically evaluate the question: apart from algorithmic elegance what does this attention to optimality buy us? We compare RADSEARCH with other recent successful search algorithms such as CN2, PRIM, APriori, OPUS and DenseMiner. Finally, we introduce RADREG, a new regression algorithm for learning real-valued outputs based on RADSEARCHing for high-order interactions.