Journal of Machine Learning Research最新文献

Multilayer networks are a useful way to capture and model multiple, binary or weighted relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the development of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set through comparison with a fixed degree random graph model. Multilayer Extraction directly handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure can capture overlapping communities, as well as background vertex-layer pairs that do not belong to any community. We establish consistency of the vertex-layer set optimizer of our proposed multilayer score under the multilayer stochastic block model. We investigate the performance of Multilayer Extraction on three applications and a test bed of simulations. Our theoretical and numerical evaluations suggest that Multilayer Extraction is an effective exploratory tool for analyzing complex multilayer networks. Publicly available code is available at https://github.com/jdwilson4/MultilayerExtraction.

SnapVX is a high-performance solver for convex optimization problems defined on networks. For problems of this form, SnapVX provides a fast and scalable solution with guaranteed global convergence. It combines the capabilities of two open source software packages: Snap.py and CVXPY. Snap.py is a large scale graph processing library, and CVXPY provides a general modeling framework for small-scale subproblems. SnapVX offers a customizable yet easy-to-use Python interface with "out-of-the-box" functionality. Based on the Alternating Direction Method of Multipliers (ADMM), it is able to efficiently store, analyze, parallelize, and solve large optimization problems from a variety of different applications. Documentation, examples, and more can be found on the SnapVX website at http://snap.stanford.edu/snapvx.

Predicting breast cancer risk has long been a goal of medical research in the pursuit of precision medicine. The goal of this study is to develop novel penalized methods to improve breast cancer risk prediction by leveraging structure information in electronic health records. We conducted a retrospective case-control study, garnering 49 mammography descriptors and 77 high-frequency/low-penetrance single-nucleotide polymorphisms (SNPs) from an existing personalized medicine data repository. Structured mammography reports and breast imaging features have long been part of a standard electronic health record (EHR), and genetic markers likely will be in the near future. Lasso and its variants are widely used approaches to integrated learning and feature selection, and our methodological contribution is to incorporate the dependence structure among the features into these approaches. More specifically, we propose a new methodology by combining group penalty and [Formula: see text] (1 ≤ p ≤ 2) fusion penalty to improve breast cancer risk prediction, taking into account structure information in mammography descriptors and SNPs. We demonstrate that our method provides benefits that are both statistically significant and potentially significant to people's lives.

We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set.

It is known that for a certain class of single index models (SIMs) [Formula: see text], support recovery is impossible when X ~ 𝒩(0, 𝕀 _p×p ) and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design X comes from an i.i.d. Gaussian distribution. In the present paper we analyze algorithms based on covariance screening and least squares with L₁ penalization (i.e. LASSO) and demonstrate that they can also enjoy optimal (up to a scalar) rescaled sample size in terms of support recovery, albeit under slightly different assumptions on f and ε compared to the SIR based algorithms. Furthermore, we show more generally, that LASSO succeeds in recovering the signed support of β₀ if X ~ 𝒩 (0, Σ), and the covariance Σ satisfies the irrepresentable condition. Our work extends existing results on the support recovery of LASSO for the linear model, to a more general class of SIMs.