[Ml-stat-talks] IDeAS Seminars today AND tomorrow at 3PM - 214 Fine Hall

Amit Singer amits at math.Princeton.EDU
Tue Apr 24 10:12:36 EDT 2012


Date:  Tuesday: 4/24/12

Place:  214 Fine Hall

Time:   3:00 pm

Speaker: Ronen Talmon, Yale University

Title: Differential Stochastic Sensing: Intrinsic Modeling of Random Time
Series with Applications to Nonlinear Tracking 

Abstract: Many natural and artificial high-dimensional data sets are
controlled by few lower-dimensional factors or drivers. As a result, the
data is often highly structured and does not fill uniformly the
high-dimensional space. In this talk, we present a "differential stochastic
sensing" framework for inferring the independent controlling factors (or
drivers) of high-dimensional time series. This approach provides intrinsic
global modeling for noisy observations based on anisotropic diffusion and
local dynamical models. The idea is to implicitly solve local differential
equations based on local density estimates in a global graph-based mechanism
that inverts the observation function and reveals the underlying structure.
Moreover, it implicitly recovers the dynamical model of the data. Hence, it
provides a foundation for sequential processing that is applied to nonlinear
tracking problems. We revisit classical Bayesian filtering methods and
discuss their relationship to the proposed approach. In addition, we show
that the proposed intrinsic modeling is invariant under different
observation schemes and is noise resilient. Hence, it may be applied to a
wide variety of applications. In this talk, we demonstrate applications to
the processing of financial and neuroscience time series, and biological and
medical imaging. 

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Date: Wednesday,  April 25, 2012

Time: 3:00 pm

Room: 214 Fine Hall

Speaker: Sewoong Oh, Massachusetts Institute of Technology

Title: Message-passing algorithms for approximate singular vector
computation 

Abstract: Low-rank matrix approximation is important in many applications
for capturing the important aspects of data naturally described in a matrix
form. In particular, we are interested in solving an inference problem using
the leading singular vectors of a data matrix, which come from crowdsourcing
platforms like Mechanical Turk. Crowdsourcing systems, in which numerous
tasks are electronically distributed to numerous "information
piece-workers", have emerged as an effective paradigm for human-powered
solving of large scale problems. Because these low-paid workers can be
unreliable, we need to devise schemes to infer the correct answers to these
crowdsourcing tasks from possibly incorrect responses from the workers. In
this talk, to solve this inference problem, we introduce a new
message-passing algorithm and prove that this algorithm is asymptotically
optimal through comparison to an oracle that knows the reliability of every
worker. This algorithm is inspired by the power iteration method for
computing the leading singular vectors, and there is an interesting relation
between the fixed point of the message-passing algorithm and the leading
singular vector. The extrinsic nature of message-passing allows us prove
sharp asymptotic bounds on the performance using density evolution. However,
tracking the densities of real-valued messages is an a priori difficult
task. We establish that the messages are sub-Gaussian using recursion, and
compute an upper bound on the parameters in a closed form. 

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