Related papers: Ising Model Selection Using $\ell_{1}$-Regularized…
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…
Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The…
In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…
Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…
The Ising model is a celebrated example of a Markov random field, introduced in statistical physics to model ferromagnetism. This is a discrete exponential family with binary outcomes, where the sufficient statistic involves a quadratic…
Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to…
We study the trajectory of iterations and the convergence rates of the Expectation-Maximization (EM) algorithm for two-component Mixed Linear Regression (2MLR). The fundamental goal of MLR is to learn the regression models from unlabeled…
Most of previous machine learning algorithms are proposed based on the i.i.d. hypothesis. However, this ideal assumption is often violated in real applications, where selection bias may arise between training and testing process. Moreover,…
Reinforcement learning (RL) methods have been shown to be capable of learning intelligent behavior in rich domains. However, this has largely been done in simulated domains without adequate focus on the process of building the simulator. In…
Linear regression models are useful statistical tools to analyze data sets in several different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally…
Relational logistic regression (RLR) is a representation of conditional probability in terms of weighted formulae for modelling multi-relational data. In this paper, we develop a learning algorithm for RLR models. Learning an RLR model from…
Choosing models from a well-fitted evolved population that generalizes beyond training data is difficult. We introduce a pragmatic method to estimate model complexity using Hessian rank for post-processing selection. Complexity is…
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important…
Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a…
Identifying small subsets of features that are relevant for prediction and/or classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult,…
Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the $\ell_1$-regularized version to the sparsity constrained models. This paper is carried out…