680 research outputs found
Tractability of interpretability via selection of group-sparse models
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. A promise of these models is to lead to “interpretable” signals for which we identify its constituent groups, however we show that, in general, claims of correctly identifying the groups with convex relaxations would lead to polynomial time solution algorithms for an NP-hard problem. Instead, leveraging a graph-based understanding of group models, we describe group structures which enable correct model identification in polynomial time via dynamic programming. We also show that group structures that lead to totally unimodular constraints have tractable relaxations. Finally, we highlight the non-convexity of the Pareto frontier of group-sparse approximations and what it means for tractability
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
Interpretable Subgroup Discovery in Treatment Effect Estimation with Application to Opioid Prescribing Guidelines
The dearth of prescribing guidelines for physicians is one key driver of the
current opioid epidemic in the United States. In this work, we analyze medical
and pharmaceutical claims data to draw insights on characteristics of patients
who are more prone to adverse outcomes after an initial synthetic opioid
prescription. Toward this end, we propose a generative model that allows
discovery from observational data of subgroups that demonstrate an enhanced or
diminished causal effect due to treatment. Our approach models these
sub-populations as a mixture distribution, using sparsity to enhance
interpretability, while jointly learning nonlinear predictors of the potential
outcomes to better adjust for confounding. The approach leads to
human-interpretable insights on discovered subgroups, improving the practical
utility for decision suppor
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