Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 059

Towards the interpretation of time-varying regularization parameters in streaming penalized regression models

Lenka Zbonakova
Ricardo Pio Monti
Wolfgang Karl Härdle

High-dimensional, streaming datasets are ubiquitous in modern applications.
Examples range from nance and e-commerce to the study of biomedical and
neuroimaging data. As a result, many novel algorithms have been proposed to
address challenges posed by such datasets. In this work, we focus on the use of L1-
regularized linear models in the context of (possibly non-stationary) streaming
data. Recently, it has been noted that the choice of the regularization parameter
is fundamental in such models and several methods have been proposed which
iteratively tune such a parameter in a time-varying manner, thereby allowing
the underlying sparsity of estimated models to vary. Moreover, in many applications,
inference on the regularization parameter may itself be of interest, as
such a parameter is related to the underlying sparsity of the model. However, in
this work, we highlight and provide extensive empirical evidence regarding how
various (often unrelated) statistical properties in the data can lead to changes
in the regularization parameter. In particular, through various synthetic experiments,
we demonstrate that changes in the regularization parameter may be
driven by changes in the true underlying sparsity, signal-to-noise ratio or even
model misspecication. The purpose of this letter is, therefore, to highlight and
catalog various statistical properties which induce changes in the associated regularization
parameter. We conclude by presenting two applications: one relating
to nancial data and another to neuroimaging data, where the aforementioned
discussion is relevant.

Lasso, penalty parameter, stock prices, neuroimaging

JEL Classification:
C13, C15, C63