Browsing by Subject "Fused lasso"
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Item Constrained estimation via the fused lasso and some generalizations(2017-05-08) Madrid Padilla, Oscar Hernan; Scott, James (Statistician); Caramanis, Constantine; Sarkar, Purnamrita; Zhou, MingyuanThis dissertation studies structurally constrained statistical estimators. Two entwined main themes are developed: computationally efficient algorithms, and strong statistical guarantees of estimators across a wide range of frameworks. In the first chapter we discuss a unified view of optimization problems that enforces constrains, such as smoothness, in statistical inference. This in turn helps to incorporate spatial and/or temporal information about data. The second chapter studies the fused lasso, a non-parametric regression estimator commonly used for graph denoising. This has been widely used in applications where the graph structure indicates that neighbor nodes have similar signal values. I prove for the fused lasso on arbitrary graphs, an upper bound on the mean squared error that depends on the total variation of the underlying signal on the graph. Moreover, I provide a surrogate estimator that can be found in linear time and attains the same upper–bound. In the third chapter I present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decomposition, in a manner parallel to the generalized lasso for regression and smoothing problems. I present an efficient coordinate-wise optimization algorithm for PTD, and characterize its convergence properties. The fourth chapter proposes histogram trend filtering, a novel approach for density estimation. This estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. The fifth chapter develops a class of estimators for deconvolution in mixture models based on a simple two-step bin-and-smooth procedure, applied to histogram counts. The method is both statistically and computationally efficient. By exploiting recent advances in convex optimization,we are able to provide a full deconvolution path that shows the estimate for the mixing distribution across a range of plausible degrees of smoothness, at far less cost than a full Bayesian analysis. Finally, the sixth chapter summarizes my contributions and provides possible directions for future work.Item Spatial pricing empirical evaluation of ride-sourcing trips using the graph-fussed lasso for total variation denoising(2018-05) Zuniga Garcia, Natalia; Scott, James (Statistician); Machemehl, Randy B.This study explores the spatial pricing discrimination of ride-sourcing trips using empirical data. We use information from more than 1.1 million rides in Austin, Texas, provided by a non-profit transportation network company from a period where the main companies were out of the city. We base the analysis on operational variables such as the waiting or idle time between trips, reaching time, and trip distance. Also, we estimate three different productivity measures to evaluate the impact of the trip destination on the driver continuation payoff. We propose the application of a total variation denoising method that enhances the spatial data interpretation. The selected methodology, known as the graph-fussed lasso (GFL), uses an l₁-norm penalty term that presents a variety of benefits to the denoising process. Specifically, this approach provides local adaptivity; it can adapt to inhomogeneity in the level of smoothness across the graph. Solving the GFL smoothing problem involves convex-optimization methods, we make use of a fast and flexible algorithm that presents scalability and high computational efficiency. The principal contributions of this research effort include a temporal and spatial evaluation of different ride-sourcing productivity measures in the Austin area, an analysis of ride-sourcing trip pricing and its effect on driver equity, and a description of the principal ride-sourcing travel patterns in the city of Austin. The main results suggest that drivers with rides ending in the central area present favorable spatial differences in productivity when including the revenue of two consecutive trips. However, the time effect was more contrasting. Weekend rides tend to provide better driver productivity measures.