Changing How Changes Change (Next Week at the Statistics Seminar)
Attention conservation notice: Only of interest if you (1)
care about covariance matrices and (2) will be in Pittsburgh on
Since so much of multivariate statistics depends on patterns of correlation
among variables, it is a bit awkward to have to admit that in lots of practical
contexts, correlations matrices are just not very stable, and can change quite
people pay a lot to rediscover this.) It turns out that there are more
constructive responses to this situation than throwing up one's hands and
saying "that sucks", and on Monday a friend of the department and general
brilliant-type-person will be kind enough to tell us about them:
- Emily Fox, "Bayesian
Covariance Regression and Autoregression"
- Abstract: Many inferential tasks, such as analyzing the functional
connectivity of the brain via coactivation patterns or capturing the changing
correlations amongst a set of assets for portfolio optimization, rely on
modeling a covariance matrix whose elements evolve as a function of time. A
number of multivariate heteroscedastic time series models have been proposed
within the econometrics literature, but are typically limited by lack of clear
margins, computational intractability, and curse of dimensionality. In this
talk, we first introduce and explore a new class of time series models for
covariance matrices based on a constructive definition exploiting inverse
Wishart distribution theory. The construction yields a stationary, first-order
autoregressive (AR) process on the cone of positive semi-definite matrices.
- We then turn our focus to more general predictor spaces and scaling to
high-dimensional datasets. Here, the predictor space could represent not only
time, but also space or other factors. Our proposed Bayesian nonparametric
covariance regression framework harnesses a latent factor model representation.
In particular, the predictor-dependent factor loadings are characterized as a
sparse combination of a collection of unknown dictionary functions (e.g.,
Gaussian process random functions). The induced predictor-dependent covariance
is then a regularized quadratic function of these dictionary elements. Our
proposed framework leads to a highly-flexible, but computationally tractable
formulation with simple conjugate posterior updates that can readily handle
missing data. Theoretical properties are discussed and the methods are
illustrated through an application to the Google Flu Trends data and the task
of word classification based on single-trial MEG data.
- Time and place: 4--5 pm on Monday, 30 January 2012, in Scaife Hall 125
As always, the talk is free and open to the public.
Enigmas of Chance
Posted at January 27, 2012 14:25 | permanent link