High-dimensional inference problems, where the number of parameters to be estimated greatly exceeds the data sample size, are increasingly prevalent in the era of big data. Despite their high-dimensionality, these problems often contain hidden structures exhibiting some form of sparsity that can be exploited to achieve consistent inference. However, computational efficiency becomes a bottleneck in cases of very large-scale analysis, as current state-of-the-art high-dimensional estimators involving non-differentiable regularization are not readily scalable.
In this talk I introduce a new paradigm of elementary estimators for structurally constrained high-dimensional inference that addresses the scaling issue at the source. These estimators are in many cases available in closed-form, cover wide classes of supervised and unsupervised learning problems, and possess strong statistical guarantees despite their extreme simplicity. To illustrate the principles underlying such closed-form/elementary estimators, I focus on two key classes of high-dimensional estimation problems: linear regression, and sparse covariance estimation where traditional penalized maximum likelihood estimation yields non-convex problems.
Aurélie C. Lozano is a research staff member in the Machine Learning group at the IBM T.J. Watson Research Center. She received a Ph.D. in Electrical Engineering from Princeton University in 2007, where she was a recipient of the Gordon Y.S. Wu Fellowship. Her research interests include machine learning, statistics, convex optimization, and data mining. Her current focus is on methods for solving high-dimensional data problems, their theoretical analysis, and applications to computational biology, environmental sciences, and social media analytics. She was a recipient of the best paper award at the conference on Uncertainty in Artificial Intelligence (UAI) 2013.