Related papers: An analysis of penalized interaction models
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
Robots that are trained to perform a task in a fixed environment often fail when facing unexpected changes to the environment due to a lack of exploration. We propose a principled way to adapt the policy for better exploration in changing…
The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…
We propose and study a fully efficient method to estimate associations of an exposure with disease incidence when both, incident cases and prevalent cases, i.e. individuals who were diagnosed with the disease at some prior time point and…
Recent years have witnessed the success of adaptive (or unified) approaches in estimating symmetric properties of discrete distributions, where one first obtains a distribution estimator independent of the target property, and then plugs…
This study introduces a general semiparametric clusterwise index distribution model to analyze how latent clusters affect the covariate-response relationships. By employing sufficient dimension reduction to account for the effects of…
Preference learning is critical for aligning large language models (LLMs) with human values, with the quality of preference datasets playing a crucial role in this process. While existing metrics primarily assess data quality based on…
Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data are proposed. This results in not…
We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…
The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest…
We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of $n$ distributions, given one single sample from each distribution. This paper studies mean estimation for entangled…
Given i.i.d. observations of a random vector $X \in \mathbb{R}^p$, we study the problem of estimating both its covariance matrix $\Sigma^*$, and its inverse covariance or concentration matrix {$\Theta^* = (\Sigma^*)^{-1}$.} We estimate…
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…
Recent advances in language modeling have underscored the role of preference feedback in enhancing model performance. This paper investigates the conditions under which preference feedback improves parameter estimation in classes of…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
Reinforcement learning from human feedback usually models preferences using a reward function that does not distinguish between people. We argue that this is unlikely to be a good design choice in contexts with high potential for…
We investigate large-sample properties of treatment effect estimators under unknown interference in randomized experiments. The inferential target is a generalization of the average treatment effect estimand that marginalizes over potential…
Including pairwise interactions between the predictors of a regression model can produce better predicting models. However, to fit such interaction models on typical data sets in biology and other fields can often require solving enormous…