# Browsing by Subject "Feature selection"

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Item Open Access Distributed Feature Selection in Large n and Large p Regression Problems(2016) Wang, XiangyuFitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

Item Open Access Sparse Value Function Approximation for Reinforcement Learning(2013) Painter-Wakefield, Christopher RobertA key component of many reinforcement learning (RL) algorithms is the approximation of the value function. The design and selection of features for approximation in RL is crucial, and an ongoing area of research. One approach to the problem of feature selection is to apply sparsity-inducing techniques in learning the value function approximation; such sparse methods tend to select relevant features and ignore irrelevant features, thus automating the feature selection process. This dissertation describes three contributions in the area of sparse value function approximation for reinforcement learning.

One method for obtaining sparse linear approximations is the inclusion in the objective function of a penalty on the sum of the absolute values of the approximation weights. This L

_{1}regularization approach was first applied to temporal difference learning in the LARS-inspired, batch learning algorithm LARS-TD. In our first contribution, we define an iterative update equation which has as its fixed point the L_{1}regularized linear fixed point of LARS-TD. The iterative update gives rise naturally to an online stochastic approximation algorithm. We prove convergence of the online algorithm and show that the L_{1}regularized linear fixed point is an equilibrium fixed point of the algorithm. We demonstrate the ability of the algorithm to converge to the fixed point, yielding a sparse solution with modestly better performance than unregularized linear temporal difference learning.Our second contribution extends LARS-TD to integrate policy optimization with sparse value learning. We extend the L

_{1}regularized linear fixed point to include a maximum over policies, defining a new, "greedy" fixed point. The greedy fixed point adds a new invariant to the set which LARS-TD maintains as it traverses its homotopy path, giving rise to a new algorithm integrating sparse value learning and optimization. The new algorithm is demonstrated to be similar in performance with policy iteration using LARS-TD.Finally, we consider another approach to sparse learning, that of using a simple algorithm that greedily adds new features. Such algorithms have many of the good properties of the L

_{1}regularization methods, while also being extremely efficient and, in some cases, allowing theoretical guarantees on recovery of the true form of a sparse target function from sampled data. We consider variants of orthogonal matching pursuit (OMP) applied to RL. The resulting algorithms are analyzed and compared experimentally with existing L_{1}regularized approaches. We demonstrate that perhaps the most natural scenario in which one might hope to achieve sparse recovery fails; however, one variant provides promising theoretical guarantees under certain assumptions on the feature dictionary while another variant empirically outperforms prior methods both in approximation accuracy and efficiency on several benchmark problems.Item Open Access Supervised MELD for Multi-domain Mixed Membership Analyses(2017) Shao, WeiWhen variables used in a mixed membership analysis can be classied into conceptu-

ally distinct domains, interpretation of results is facilitated by using domain-specic

models with a small number of imposed pure-type proles and yielding a set of Grade-

of-Membership scores for each domain. We present Supervised Moment Estimation

of Latent Dirichlet Models (supervised MELD) algorithms for mixed membership

models to be used and tested in this context. We challenge the methodology with

data sets collected over time to study malaria risk on the Brazilian Amazon frontier.

By further ignoring spatial specicity and utilizing a binary outcome variable (at

least one person in a household infected with malaria during the past year), we nd

supervised MELD capable of extracting surprisingly nuanced risk patterns.