(Georgia Institute of Technology, 2017-03-15)
Vempala, Santosh S.
Computational perspectives on scientific phenomena have often proven to be remarkably insightful.
Rapid advances in computational neuroscience, and the resulting plethora of data and models
highlight the lack of an overarching theory for how the brain accomplishes perception and cognition
(the mind). Taking the view that the answer must surely have a computational component, we present
a few approachable questions for computer scientists, along with some recent work (with Christos
Papadimitriou, Samantha Petti and Wolfgang Maass) on mechanisms for the formation of memories,
the creation of associations between memories and the benefits of such associations.
(Georgia Institute of Technology, 2010-09-17)
Vempala, Santosh S.
Principal Component Analysis is the most widely used technique for high-dimensional or large data. For typical applications (nearest neighbor, clustering, learning), it is not hard to build examples on which PCA "fails." Yet, it is popular and successful across a variety of data-rich areas. In this talk, we focus on two algorithmic problems where the performance of PCA is provably near-optimal, and no other method is known to have similar guarantees. The problems we consider are (a) the classical statistical problem of unraveling a sample from a mixture of k unknown Gaussians and (b) the classic learning theory problem of learning an intersection of k halfspaces. During the talk, we will encounter recent extensions of PCA that are noise-resistant, affine-invariant and nonviolent.
(Georgia Institute of Technology, 2007)
Kanade, Varun; Vempala, Santosh S.
We present the wireless manifold, a 2-dimensional surface in 3-dimensional space with the property that geodesic
distances accurately capture wireless signal strengths.
A compact representation of the manifold can be reconstructed from a sparse set of signal measurements.
The manifold distance suggests a simple routing algorithm that avoids obstacles, naturally handles mobile
nodes without explicitly maintaining the connectivity
graph and is more efficient compared to using Euclidean
distance as measured by success rate, routing load and
failure tolerance. Placing sensors to cover the manifold
is more effective than covering the underlying physical
space.