Andrew B. Nobel

Kevin O'Connor, Kevin McGoff, Andrew B Nobel

We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The resulting optimal joining problem captures differences in the long run average behavior of the processes of interest. We introduce estimators of both optimal joinings and the optimal joining cost, and we establish consistency of the estimators under mild conditions. Furthermore, under stronger mixing assumptions we establish finite-sample error rates for the estimated optimal joining cost that extend the best known results in the iid case. Finally, we extend the consistency and rate analysis to an entropy-penalized version of the optimal joining problem.

Bongsoo Yi, Kevin O'Connor, Kevin McGoff et al.

We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.

Miheer Dewaskar, John Palowitch, Mark He et al.

Datasets in which measurements of two (or more) types are obtained from a common set of samples arise in many scientific applications. A common problem in the exploratory analysis of such data is to identify groups of features of different data types that are strongly associated. A bimodule is a pair (A,B) of feature sets from two data types such that the aggregate cross-correlation between the features in A and those in B is large. A bimodule (A,B) is stable if A coincides with the set of features that have significant aggregate correlation with the features in B, and vice-versa. This paper proposes an iterative-testing based bimodule search procedure (BSP) to identify stable bimodules. Compared to existing methods for detecting cross-correlated features, BSP was the best at recovering true bimodules with sufficient signal, while limiting the false discoveries. In addition, we applied BSP to the problem of expression quantitative trait loci (eQTL) analysis using data from the GTEx consortium. BSP identified several thousand SNP-gene bimodules. While many of the individual SNP-gene pairs appearing in the discovered bimodules were identified by standard eQTL methods, the discovered bimodules revealed genomic subnetworks that appeared to be biologically meaningful and worthy of further scientific investigation.

Jeremy Sabourin, William Valdar, Andrew Nobel

We describe a simple, efficient, permutation based procedure for selecting the penalty parameter in the LASSO. The procedure, which is intended for applications where variable selection is the primary focus, can be applied in a variety of structural settings, including generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of three real data sets in which permutation selection is compared with cross-validation (CV), the Bayesian information criterion (BIC), and a selection method based on recently developed testing procedures for the LASSO.