Many current machine learning
algorithms lack provable guarantees on one or more
of the following metrics: solution
quality, sample complexity, running
time. The
goal of our group is to provide algorithms with such
performance guarantees. This can involve designing
fundamentally new algorithms, or proving such
guarantees for existing algorithms.

We are especially interested in
unsupervised learning, where the algorithm is given
data that is unlabeled/unannotated, and the goal is
to learn structure in the data. Often this involves
hypothesizing the existence of such structure via a
model. Learning corresponds to fitting such a model
to the data.

Areas of interest to us include
language models (including topic models and text
embeddings), matrix and tensor factorization, deep
nets, sparse coding, Generative Adversarial Nets
(GANs), all aspects of Deep Learning, etc.

From the viewpoint of
theoretical CS and traditional algorithm design, the
novelty in this project is the need to make modeling
assumptions ---often *statistical* in
nature---about the structure of data, since solving
the problems on worst-case instances is NP-hard. We
need to go *beyond *worst-case analysis.

From the viewpoint of machine
learning theory, the novelty in this project is the
focus on unsupervised settings (by contrast, many
traditional frameworks in learning theory such as
PAC, SVMs, Online Learning, etc., focus on
supervised settings). Methodologically, learning
theory often proceeds by convexifying the problem,
whereas our group wishes to stay with the nonconvex
formalism. Today there is overwhelming empirical
evidence that nonconvex approaches work at large
scale in machine learning, and it is an important
challenge for theory to explain this.