In this paper, we consider the problem of preserving privacy in the online
learning setting. We study the problem in the online convex programming (OCP)
framework---a popular online learning setting with several interesting
theoretical and practical implications---while using differential privacy as
the formal privacy measure.
In this paper, we consider the problem of compressed sensing where the goal
is to recover almost all the sparse vectors using a small number of fixed
linear measurements. For this problem, we propose a novel partial
hard-thresholding operator that leads to a general family of iterative
algorithms. While one extreme of the family yields well known hard thresholding
algorithms like ITI (Iterative Thresholding with Inversion) and HTP (Hard
Thresholding Pursuit), the other end of the spectrum leads to a novel algorithm
that we call Orthogonal Matching Pursuit with Replacement (OMPR).
Metric and kernel learning are important in several machine learning
applications. However, most existing metric learning algorithms are limited to
learning metrics over low-dimensional data, while existing kernel learning
algorithms are often limited to the transductive setting and do not generalize
to new data points. In this paper, we study metric learning as a problem of
learning a linear transformation of the input data.
Minimizing the rank of a matrix subject to affine constraints is a
fundamental problem with many important applications in machine learning and
statistics.
Self assembly is a process by which supramolecular species form spontaneously
from their components. This process is ubiquitous throughout the life chemistry
and is central to biological information processing. It has been predicted that
in future self assembly will become an important engineering discipline by
combining the fields of bio molecular computation, nano technology and
medicine. However error control is a key challenge in realizing the potential
of self assembly.