Related papers: Relative Sparsity for Medical Decision Problems
In healthcare, there is much interest in estimating policies, or mappings from covariates to treatment decisions. Recently, there is also interest in constraining these estimated policies to the standard of care, which generated the…
An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients.…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…
Estimating the causal effect of a treatment or health policy with observational data can be challenging due to an imbalance of and a lack of overlap between treated and control covariate distributions. In the presence of limited overlap,…
Conventional treatment policies map patient covariates to a single recommended intervention in order to maximize expected clinical outcomes. Although a rich body of causal inference methods has been developed to estimate such policies,…
We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise…
We explore and illustrate the concept of ranked sparsity, a phenomenon that often occurs naturally in modeling applications when an expected disparity exists in the quality of information between different feature sets. Its presence can…
Reward comparisons are vital for evaluating differences in agent behaviors induced by a set of reward functions. Most conventional techniques utilize the input reward functions to learn optimized policies, which are then used to compare…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
We consider the problem of sparse variable selection on high dimension heterogeneous data sets, which has been taking on renewed interest recently due to the growth of biological and medical data sets with complex, non-i.i.d. structures and…
As the COVID-19 pandemic progresses, researchers are reporting findings of randomized trials comparing standard care with care augmented by experimental drugs. The trials have small sample sizes, so estimates of treatment effects are…
Predictive models are often introduced to decision-making tasks under the rationale that they improve performance over an existing decision-making policy. However, it is challenging to compare predictive performance against an existing…
A treatment policy defines when and what treatments are applied to affect some outcome of interest. Data-driven decision-making requires the ability to predict what happens if a policy is changed. Existing methods that predict how the…
Many batch RL health applications first discretize time into fixed intervals. However, this discretization both loses resolution and forces a policy computation at each (potentially fine) interval. In this work, we develop a novel framework…
In this paper, we outline a principled approach to estimate an individualized treatment rule that is appropriate for data from observational studies where, in addition to treatment assignment not being independent of individual…
Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, with each targeting a different treatment. Treatment-specific means are…
The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure~$H$ and a…