Invited Sessions Details

Statistical innovation for network analysis

Presenter: Daniela Witten

When: Thursday, July 14, 2016      Time: 2:00 PM - 4:00 PM

Room: Oak Bay 1-2 (Level 1)

Session Synopsis:

Flexible and Interpretable Regression Using Convex Penalties

We consider the problem of fitting a regression model that is both flexible and interpretable. We propose two procedures for this task: the Fused Lasso Additive Model (FLAM), which is an additive model of piecewise constant fits; and Convex Regression with Interpretable Sharp Partitions (CRISP), which extends FLAM to allow for non-additivity. Both FLAM and CRISP are the solutions to convex optimization problems that can be efficiently solved. We also proposed unbiased estimators for the degrees of freedom of FLAM and CRISP, which allow us to characterize their complexity. This is joint work with Noah Simon and Ashley Petersen.

Statistical innovation for network analysis

Presenter: Jacob Bien

When: Thursday, July 14, 2016      Time: 2:00 PM - 4:00 PM

Room: Oak Bay 1-2 (Level 1)

Session Synopsis:

Graph-Guided Banding for Covariance Estimation

Reliable estimation of the covariance matrix is notoriously difficult in high dimensions. Numerous methods assume that the population covariance (or inverse covariance) matrix is sparse while making no particular structural assumptions on the desired sparsity pattern. A highly-related, yet complementary, literature studies the setting in which the measured variables have a known ordering, in which case a banded (or near-banded) population matrix is assumed. This work focuses on the broad middle ground that lies between the former approach of complete neutrality to the sparsity pattern and the latter highly restrictive assumption of having a known ordering. We develop a class of convex regularizers that is in the spirit of banding and yet attains sparsity structures that can be customized to a wide variety of applications.

Statistical innovation for network analysis

Presenter: Duo Jiang

When: Thursday, July 14, 2016      Time: 2:00 PM - 4:00 PM

Room: Oak Bay 1-2 (Level 1)

Session Synopsis:

Weighted inverse covariance estimation for compositional count data with applications to microbiome data

Network estimation on a set of variables is frequently explored using graphical models, in which the relationship between two variables is modeled via their conditional dependency given the other variables. In recent years, various methods for sparse inverse covariance estimation have been proposed to estimate graphical models in the high-dimensional setting. However, current methods do not address the compositional count data that frequently arise in biological studies due to recent advances in high-throughput sequencing technologies. Such data are hard to analyze because the variables of interest are not directly measured, but are reflected by the observed counts in an error-prone way. Adding to the challenge is the compositional nature of the data: the sum of the counts for each sample is an experimental technicality, which carries no scientific information but can vary drastically across samples. To address these issues, we propose a new approach to inverse covariance estimation, which models the observed data using a multinomial log-normal distribution and accounts for the heterogeneity in the error structure among samples by incorporating sample-specific weights. We will compare our approach to current methods for inverse covariance estimation, such as graphical lasso, through simulation studies. We will also illustrate the use of our method in a microbiome data application to estimate microbial interactions.

Statistical innovation for network analysis

Presenter: Uri Eden

When: Thursday, July 14, 2016      Time: 2:00 PM - 4:00 PM

Room: Oak Bay 1-2 (Level 1)

Session Synopsis:

Estimating network structure from electrophysiological brain recordings

To appreciate how brain areas coordinate to control behavior, it is important to be able to estimate and track the functional relationships that develop and evolve in electrophysiological neural data. In this talk, we discuss the problem of estimating dynamic networks from neural spiking and field data. Compounding the usual challenge of estimating dynamic network structure is the fact that neurons receive, process, and transmit information via discrete sequences of sudden, stereotyped electrical impulses, called spikes. We develop a point process modeling framework and state space estimation algorithms to describe and track the evolution of dynamic representations from neural ensembles. We apply these methods to infer network connectivity in a small neural circuit for which the actual physiological synapses between neurons are known and measure changes in the effective connectivity pattern in response to pharmacological interventions. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.