High-dimensional low-rank structure arises in many applications including genomics, signal processing, and social science. In this talk, we discuss some recent results on high-dimensional low-rank matrix recovery, including low-rank matrix recovery via rank-one projections and structured matrix completion. We provide theoretical justifications for the proposed methods and derive lower bounds …
In harmonic analysis we work to understand signals and operators by breaking them up into simpler pieces. We will discuss several problems for which these pieces live on lower dimensional sets whose curvature makes them seem bigger than they are. Surprising connections to some geometric and physical problems will also …
We propose an algorithm for minimizing expected risk F that shares some properties with randomized incremental aggregated gradient methods as well as dynamic sampling methods. Unlike aggregated gradient methods, which are designed to revisit the training set many times, the algorithm proposed here is well suited for problems involving a …
Bacteria and other organisms do not follow the paradigm of vertical inheritance of genetic material. Human beings, for example, inherit their DNA from their parents only (vertical transfer), but bacteria can share DNA between different species (horizontal transfer). Therefore, their evolution cannot be modeled by a tree. To incorporate these …
We develop a new active learning algorithm for the streaming setting satisfying three important properties: 1) It provably works for any classifier representation and classification problem including those with severe noise. 2) It is efficiently implementable with an ERM oracle. 3) It is more aggressive than all previous approaches satisfying …
Network models provide a unifying framework for understanding dependencies among variables in medical, biological, and other sciences. Networks can be used to reveal underlying data structures, infer functional modules, and facilitate experiment design. In practice, however, size, uncertainty and complexity of the underlying associations render these applications challenging. In this …
The recent investment in neurotechnology development has spurred tremendous excitement about the potential to uncover the operating principles of biological neural circuits. However, a storm is brewing. If the neuroengineering community is able to achieve their goals of developing technologies that increase the number of interfaced neurons by orders of …
Quasi-Newton methods are viable alternatives to Newton’s method for solving optimization problems because they do not require computing and solving with the potentially very large Hessian matrix while still maintaining a superlinear convergence rate. Systems of linear equations arising from quasi-Newton methods can be solved efficiently using the compact representation …
Optimizing the k-means objective with Lloyd’s algorithm is a classic strategy to separate a set of datapoint into individual clusters. More recent data in biology and social networks necessitates overlapping clustering. I’ll present a generalization of the k-means objective function that incorporates overlapping partitions as well as outlier detection. A …
The notion of machines that can learn has caught imaginations since the days of the early computer. In recent years, as we face burgeoning amounts of data around us that no human mind can process, machines that can learn to automatically find insights from such vast amounts of data have …