Sparse Principal Component Analysis (SPCA) is a remarkably useful tool for practitioners who had been relying on ad-hoc thresholding methods. Our analysis aims at providing a a framework to test whether the data at hand indeed contains a sparse principal component. More precisely we propose an optimal test procedure to …
The large-scale gathering and storage of personal data is raising new questions about the regulation of privacy. On the technology side, there has been a flurry of recent work on new models for privacy risk and protection. One such model is differential privacy, which quantifies the risk to an individual’s …
In many real-world classification problems, the labels of training examples are randomly corrupted. That is, the set of training examples for each class is contaminated by examples of the other class. Existing approaches to this problem assume that the two classes are separable, that the label noise is independent of …
Many inferential tasks, such as analyzing the functional connectivity of the brain via coactivation patterns or capturing the changing correlations amongst a set of assets for portfolio optimization, rely on modeling a covariance matrix whose elements evolve as a function of time. A number of multivariate heteroscedastic time series models …
Sheida’s talk: In this research we analyzed effective and functional connectivity in a population of five subjects with spina bifida hydrocephalus (SBH) and five healthy control subjects using resting state magnetoencephalography (MEG) recordings. Three types of connectivity are used to describe the brain. Anatomical connectivity refers to physical connections between …
We will discuss a line of recent work on methods for statistical inference in high dimensions. In many real-world applications, samples are not collected cleanly and may be observed subject to systematic corruptions such as missing data and additive noise. We describe how Lasso-based linear regression may be corrected to …
Matt’s talk: Title: Sequential Testing in High Dimensions Sequential methods make use of information as it becomes available, creating an interactive connection between a sampling procedure and information gathered by that procedure. In this talk we explore sequential methods applied to sparse recovery problems, motivated by applications in both communications …
*** Hongbo’s talk: Title: Using a New Nonconvex Singular Value Regularizer in Multivariate Linear Regression. We introduce the weighted singlar value penalization, which uses a nonconvex nonseparable regularizer. We show that in spite of the nonconvexity, one optimization problem with this regularizer is efficiently solvable. Applied to Multivariate Linear Regression, …
***Bryan: Both cognitive constraints and limited amounts of data restrict the complexity of inferential models. Sparse coding is an elegant way to address these restrictions, extracting correlated subparts from data in a way that can be efficient, predictive, and adaptive. We present a sparse coding method for use on binary …
*** Pari’s talk: Title: Group Symmetry and Covariance Regularization Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the notion of a symmetric model via group invariance. We propose projection …