Statistics Seminar Series

Semester Schedule: Statistics - Spring 2012

Seminars are on Mondays
Time:12:00 - 1:30 PM Location: Room 903, 1255 Amsterdam Avenue, Tea and Coffee will be served before the seminar at 11:30 AM, Room 1025

Feb 20

Dean Foster (U Penn)

Title: Linear methods for large data

Using random matrix theory, we now have some very easy to understand and fast to use methods of computing low rank representations of matrices.  I have been using these methods as a hammer to improve several statistical methods.  I'll discuss three of these in this talk.  First, I'll show how these ideas can be used to speed up stepwise regression.  Then I'll turn to using them to contruct new linear features motivated by CCA's.  Finally, I'll use these methods to get a fast way of estimating an HMM.

Feb 27

March 5

*Cancelled

*CANCELLED

David Landriault (University of Waterloo)

March 12

				
Spring Break

				

March 19

				Title: Multi-resolution inference of stochastic models from partially observed data

Stochastic models, diffusion models in particular, are widely used in science, engineering and economics. Inferring the parameter values from data is often complicated by the fact that the underlying stochastic 
processes are only partially observed. Examples include inference of discretely observed diffusion processes, stochastic volatility models, and double stochastic Poisson (Cox) processes. Likelihood based inference 
faces the difficulty that the likelihood is usually not available even numerically. Conventional approach discretizes the stochastic model to approximate the likelihood. In order to have desirable accuracy, one has to use highly dense discretization. However, dense discretization usually imposes unbearable computation burden. In this talk we will introduce the framework of Bayesian multi-resolution inference to address this 
difficulty. By working on different resolution (discretization) levels simultaneously and by letting the resolutions talk to each other, we  
substantially improve not only the computational efficiency, but also the estimation accuracy. We will illustrate the strength of the 
multi-resolution approach by examples.


				

March 26 

Ming Yuan (Georgia Tech)

Title : Adaptive Estimation of Large Covariance Matrices

Abstract :
Estimation of large covariance matrices has drawn considerable recent attention and the theoretical focus so far is mainly on developing a minimax theory over a fixed parameter space. In this talk, I shall discuss adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. The estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding. I shall
also illustrate the use of the technical tools developed in other matrix estimation problems.

Arnaud Doucet (Oxford)


Title: Forward Smoothing in State-Space Models with Application to Maximum Likelihood Parameter Estimation

Abstract: Maximum likelihood parameter estimates in state-space models are generally computed using  a gradient ascent procedure or an Expectation-Maximization (EM) procedure. Both approaches rely on a forward filtering-backward smoothing procedure which is computationally expensive for large data sets. Additionally the memory requirements increase linearly with the number of data as it is necessary to store the filtering distributions computed in the forward pass to carry out the backward pass. For nonlinear non-Gaussian state-space models, particle approximations of these algorithms can be easily derived but they obviously suffer from the same problems. We present a forward only version of the forward-backward procedure which bypasses entirely the backward pass, does not require storing the filtering distributions and allow us to implement online versions of gradient ascent and EM. We propose a non-standard particle implementation of the forward smoothing procedure which is provably numerically stable. This allows us to perform recursive maximum likelihood parameter estimation in nonlinear non-Gaussian state-space models using particle algorithms which do not not suffer from the particle path degeneracy problem.

This is joint work with Pierre Del Moral (INRIA Bordeaux) and Sumeet Singh (Cambridge).

April 9

Vladimir I. Koltchinskii (Georgia Tech)

Complexity Penalties in Low Rank Matrix Estimation

Consider a problem of estimation of a large m × m Hermitian matrix  based on i.i.d. measurements
Yj = tr(Xj) + j , j = 1, . . . , n,
where Xj are random m × m Hermitian matrices and {j} is a zero mean random noise. The goal is to estimate  in the case when it has relativelysmall rank, or it can be well approximated by small rank matrices. There has been an extensive study of this problem in the recent years. Its important instances include matrix completion, where a random sample of entries of 
is observed, and quantum state tomography, where  is a density matrix of
a quantum system and it has to be estimated based on the measurements of n observables X1, . . . ,Xn. We will consider several approaches to such problems
based on a penalized least squares method (and its modifications) with complexity penalties defined in terms of nuclear norm, von Neumann entropy
and other functionals that “promote” small rank solutions and discuss oracle inequalities for the resulting estimators with explicit dependence of the error
terms on the rank and other parameters of the problem. We will also discuss a version of these methods when the target matrix is a “smooth ” low rank kernel defined on a graph.
 

Dylan Small (Wharton School, UPenn)

Title: Case Definition and Design Sensitivity in Case Control Studies

Abstract:

A case-control study compares cases of some disease or disorder to some group of controls (non-cases), looking backwards in time to contrast the frequency of treatment among cases and controls.  Cases are typically matched to controls on measured pretreatment covariates.  However, in an observational study, there may be unmeasured pretreatment covariates that affect both treatment and outcomes.  A sensitivity analysis asks: What magnitude of bias from unmeasured covariates would need to be present to materially alter the conclusions of a naïve analysis that presumes adjustments for measured covariates suffice to remove all bias?

The first step in designing a case-control study is to define a case of disease and a control.  For example, the disease may have different severities and one needs to choose how severe a person’s disease needs to be for the person to be a case.  We examine the effects of this design decision on the sensitivity of conclusions to unmeasured biases.  We develop an adaptive procedure for choosing the case definition based on the data to make the study as insensitive to unmeasured biases as possible asymptotically.  This is joint work with Jing Cheng, Betz Halloran and Paul Rosenbaum.

				


Chris Wiggins (Columbia University)

"Variational and hierarchical modeling for biological data"

Advances in biological technologies over the past two decades have dramatically increased the abundance of data available to biologists, and thereby changed the relationship between biology and statistics. While this is most famously celebrated in the subfield of genomics (both sequencing and functional genomics), there is increasing need in the subfield of molecular biology, particularly for methods based on generative models motivated by biologists' domain expertise. A natural set of tools is that provided by inference with latent variables. In this talk I'll introduce one application of a variational approach to inference; I then present current work on a closely-related hierarchical modeling approach, based on collaborations with the Gonzalez lab at Columbia, for understanding time-series data in single-molecule biophysics. 

Martin Wainwright (Berkeley)

TITLE: High-dimensional matrix decomposition: Applications and estimators

ABSTRACT: Consider a matrix that can be decomposed as the sum of two
unknown matrices, one of which is approximately low-rank and the other having a complementary form of low-dimensional structure, such as bandedness, sparsity, or column-sparsity.  Given noisy or partial observations, how to recover accurate estimates of the underlying decomposition?

Matrix decompositions of this type arise in many applications, among them robust forms of dimensionality reduction (PCA, canonical correlations etc.), collaborative filtering problems (e.g., Netflix and Amazon), and estimating the structure of Gaussian graphical models.  Various researchers have studied conditions under which simple convex programs, based on the nuclear norm as a rank surrogate, can perform exact recovery based on noiseless observations.  In practical settings, observations are likely to be noise-corrupted, and matrices only approximately low-rank.  We describe a related convex relaxation for noisy observations, and sketch how recovery guarantees can be derived under milder conditions.  These error bounds show that our method is information-theoretically optimal.

Based on joint work with Alekh Agarwal and Sahand Negahban.
Paper: http://arxiv.org/abs/1102.4807
 

Douglas Simpson, Department of Statistics, University of Illinois
at Urbana-Champaign

Title: Statistical Methods for Biomedical Research on Diagnostic
Ultrasound

Abstract:
Diagnostic ultrasound is among the most widely used imaging techniques in
biomedicine. Common uses include prenatal ultrasonic imaging of the fetus, echocardiogram images of the heart, ultrasound imaging of tumors in the breast and prostate.  Current research aims to extend the range of applications and increase the diagnostic power of ultrasonic imaging through quantitative ultrasound technology. Statistical issues and results
associated with these efforts will be presented including image
segmentation, pattern  recognition, tissue characterization and
semiparametric functional data analysis.