Robust Inference and Learning of Multivariate Statistical Models PDF Download

Author: Linbo Liu
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Languages : en
Pages : 0

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Book Description
Model robustness has become increasingly popular in recent decades. We study multiple aspects of robustness (in the setting of time series, image classification and linear regression) in this dissertation work. First three chapters concerns the time series setting. Specifically, Chapter 1 establishes a novel Bernstein-type inequality for high dimensional linear processes. We then apply it to investigate two high dimensional robust estimation problems: (1) time series regression with fat-tailed and correlated covariates and errors, (2) fat-tailed vector autoregression. As a natural requirement of consistency, the dimension can be allowed to increase exponentially with the sample size under very mild moment and dependence conditions. In Chapter 2, we develop Gaussian approximation theory for VAR model to derive the asymptotic distribution of the de-biased estimator and propose a multiplier bootstrap-assisted procedure to obtain critical values under very mild moment conditions on the innovations. Chapter 3 studies the threats of adversarial attack on multivariate probabilistic forecasting models and viable defense mechanisms. Our studies discover a new attack pattern that negatively impact the forecasting of a target time series via making strategic, sparse (imperceptible) modifications to the past observations of a small number of other time series. To mitigate the impact of such attack, we also develop two defense strategies. First, we extend a previously developed randomized smoothing technique in classification to multivariate forecasting scenarios. Second, we develop an adversarial training algorithm that learns to create adversarial examples and at the same time optimizes the forecasting model to improve its robustness against such adversarial simulation. In Chapter 4, we improve the robustness of image classifier by enhancing the randomized smoothing technique and model ensemble. Chapter 5 considers the robust estimation of linear regression coefficients under heavy-tailed noise and covariates using a clipping idea.