Abstract:
High-dimensional data is ubiquitous in the modern world, arising in images, movies, biomedical measurements, documents, and many other contexts. The "curse of dimensionality" tells us that learning in such regimes is generally intractable. However, practical problems often exhibit special simplifying structures which, when identified and exploited, can render learning in high dimensions tractable. For example, recent developments in parsimonious representations (sparsity, low rank, etc.) have provided efficient tools relevant to a wide range of applications. This is an exciting beginning, but there is much more to explore. In this talk, I will address two challenges associated with high-dimensional learning.

First, in many applications, the parsimonious structures exist but reveal themselves only after a transformation of the data. Studying the space of such transformations and the associated algorithms for their inference constitute an important class of problems in high-dimensional learning. I will present some of my works in this direction related to image segmentation. I will show how low-rank structures become abundant in images when certain spatial and geometric transformations are considered. The algorithm resulting from this work achieves state-of-the-art performance in natural image segmentation.

Second, important scenarios such as deep learning involve high-dimensional nonconvex optimization. Such optimization is generally intractable. However, I show how some properties in the optimization landscape, such as smoothness and stability, can be exploited to obtain reasonable solutions despite nonconvexity. The theory is derived by combining the notion of convex envelopes with differential equations. This results in algorithms involving high-dimensional convolution with the Gaussian kernel, which has a closed form solution in many practical scenarios. I will show applications of this work in image alignment, image matching, and deep learning. Furthermore, I will discuss how this theory justifies heuristics currently used in deep learning, and suggests new training algorithms that offer a significant speedup.

Biography:
Hossein Mobahi (http://people.csail.mit.edu/hmobahi) is a postdoctoral researcher in the Computer Science and Artificial Intelligence Lab. (CSAIL) at the Massachusetts Institute of Technology (MIT). His research interests include machine learning, computer vision, optimization, and especially the intersection of the three. He obtained his PhD from the University of Illinois at Urbana-Champaign (UIUC) in Dec 2012. His is the recipient of Computational Science & Engineering Fellowship, Cognitive Science & AI Award, and Mavis Memorial Scholarship. His recent works on machine learning and optimization have been covered by the MIT news.

Host:
Dr. Arun Ross