Easton Li Xu

Detection of Cooperative Interactions in Logistic Regression Models

An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates is considered. Modeling the structure of the interactions by a graph, our goal is to recover the interaction graph from independently identically distributed (i.i.d.) samples of the covariates and the outcome. When viewed as a feature selection problem, a simple quantity called influence is proposed as a measure of the marginal effects of the interaction terms on the outcome. For the case when the underlying interaction graph is known to be acyclic, it is shown that a simple algorithm that is based on a maximum-weight spanning tree with respect to the plug-in estimates of the influences not only has strong theoretical performance guarantees, but can also outperform generic feature selection algorithms for recovering the interaction graph from i.i.d. samples of the covariates and the outcome. Our results can also be extended to the model that includes both individual effects and pairwise interactions via the help of an auxiliary covariate.

Submodular maximization with multi-knapsack constraints and its applications in scientific literature recommendations

Submodular maximization problems belong to the family of combinatorial optimization problems and enjoy wide applications. In this paper, we focus on the problem of maximizing a monotone submodular function subject to a d-knapsack constraint, for which we propose a streaming algorithm that achieves a (1/1+2D − ε)-approximation of the optimal value, while it only needs one single pass through the dataset without storing all the data in the memory. In our experiments, we extensively evaluate the effectiveness of our proposed algorithm via an application in scientific literature recommendation. It is observed that the proposed streaming algorithm achieves both execution speedup and memory saving by several orders of magnitude, compared with existing approaches.

A Novel Pilot Assignment Scheme in Massive MIMO Networks

In this letter, we propose a novel pilot assignment scheme for the pilot contamination problem in massive multiple-input multiple-output multi-cell networks. Based on the asymptotic signal-to-interference-plus-noise ratio (SINR), the proposed pilot assignment scheme adopts the harmonic SINR utility function to quantify the fairness of all users in the network. Specifically, we formulate the pilot assignment problem as a minimum-weight multi-index assignment problem. For a two-cell network, this problem can be solved by the Hungarian algorithm with a strongly polynomial complexity. For the general multi-cell networks with more than two cells, this problem is in general NP-hard and we propose an efficient algorithm to obtain a suboptimal solution. The numerical experiments show that the proposed algorithms outperform other conventional pilot assignment schemes.

Feature selection with interactions in logistic regression models using multivariate synergies for a GWAS application

BackgroundGenotype-phenotype association has been one of the long-standing problems in bioinformatics. Identifying both the marginal and epistatic effects among genetic markers, such as Single Nucleotide Polymorphisms (SNPs), has been extensively integrated in Genome-Wide Association Studies (GWAS) to help derive “causal” genetic risk factors and their interactions, which play critical roles in life and disease systems. Identifying “synergistic” interactions with respect to the outcome of interest can help accurate phenotypic prediction and understand the underlying mechanism of system behavior. Many statistical measures for estimating synergistic interactions have been proposed in the literature for such a purpose. However, except for empirical performance, there is still no theoretical analysis on the power and limitation of these synergistic interaction measures.ResultsIn this paper, it is shown that the existing information-theoretic multivariate synergy depends on a small subset of the interaction parameters in the model, sometimes on only one interaction parameter. In addition, an adjusted version of multivariate synergy is proposed as a new measure to estimate the interactive effects, with experiments conducted over both simulated data sets and a real-world GWAS data set to show the effectiveness.ConclusionsWe provide rigorous theoretical analysis and empirical evidence on why the information-theoretic multivariate synergy helps with identifying genetic risk factors via synergistic interactions. We further establish the rigorous sample complexity analysis on detecting interactive effects, confirmed by both simulated and real-world data sets.

Rényi entropy rate of hidden Markov processes

In this paper, we focus our attention on the Rényi entropy rate of hidden Markov processes under certain positivity assumptions. The existence of the Rényi entropy rate for such processes is established. Furthermore, we show that, with some extra “fast-forgetting” assumptions, the Rényi entropy rate of the approximating Markov processes exponentially converges to that of the original hidden Markov process, as the Markov order goes to infinity.

Pairwise interaction analysis of logistic regression models

An important problem in the field of bioinformaties is to identify interactive effects among profiled variables for outcome prediction. In this paper, a simple logistic regression model with pairwise interactions among a set of binary covariates is considered. Modeling the structure of the interactions by a graph, our goal is to recover the interaction graph from independently identically distributed (i.i.d.) samples of the covariates and the outcome. When viewed as a feature selection problem, a simple quantity called influence is proposed as a measure of the marginal effects of the interaction terms on the outcome. For the case when the underlying interaction graph is known to be acyclic, it is shown that a simple algorithm that is based on a maximum-weight spanning tree with respect to the plug-in estimates of the influences not only has strong theoretical performance guarantees, but can also significantly outperform generic feature selection algorithms for recovering the interaction graph from i.i.d. samples of the covariates and the outcome.

The minimum number of hubs in networks

In this paper, a hub refers to a non-terminal vertex of degree at least three. We study the minimum number of hubs needed in a network to guarantee certain flow demand constraints imposed between multiple pairs of sources and sinks. We prove that under the constraints, regardless of the size of the network, such minimum number is always upper bounded and we derive tight upper bounds for some special parameters. In particular, for two pairs of sources and sinks, we present a novel path-searching algorithm, the analysis of which is instrumental for the derivations of the tight upper bounds. Our results are of both theoretical and practical interest: in theory, they can be viewed as generalizations of the classical Menger’s theorem to a class of undirected graphs with multiple sources and sinks; in practice, our results, roughly speaking, suggest that for some given flow demand constraints, not “too many” hubs are needed in a network.