相关论文: R-Estimates vs. GMM: A Theoretical Case Study of V…

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…

Quantile regression \parencite{Koenker1978} is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which…

This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…

Inferring the input parameters of simulators from observations is a crucial challenge with applications from epidemiology to molecular dynamics. Here we show a simple approach in the regime of sparse data and approximately correct models,…

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…

Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to…

Factorial designs are widely used due to their ability to accommodate multiple factors simultaneously. The factor-based regression with main effects and some interactions is the dominant strategy for downstream data analysis, delivering…

The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…

We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we…

In clinical settings, we often face the challenge of building prediction models based on small observational data sets. For example, such a data set might be from a medical center in a multi-center study. Differences between centers might…

A common goal in statistics and machine learning is estimation of unknowns. Point estimates alone are of little value without an accompanying measure of uncertainty, but traditional uncertainty quantification methods, such as confidence…

Ensemble methods can deliver surprising performance gains but also bring significantly higher computational costs, e.g., can be up to 2048X in large-scale ensemble tasks. However, we found that the majority of computations in ensemble…

Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…

We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard…

Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to…

Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with…

This paper introduces an algorithm to select demonstration examples for in-context learning of a query set. Given a set of $n$ examples, how can we quickly select $k$ out of $n$ to best serve as the conditioning for downstream inference?…

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

Missing values are prevalent across various fields, posing challenges for training and deploying predictive models. In this context, imputation is a common practice, driven by the hope that accurate imputations will enhance predictions.…

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…