Related papers: Unbiased Estimation of Structured Prediction Error

Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…

In this work, we provide a refinement of the selective CLT result of Tian and Taylor (2015), which allows for selective inference in non-parametric settings by adjusting for the asymptotic Gaussian limit for selection. Under some regularity…

Given a collection of observed signals corrupted with Gaussian noise, how can we learn to optimally denoise them? This fundamental problem arises in both empirical Bayes and generative modeling. In empirical Bayes, the predominant approach…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In…

Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…

Conformal prediction (CP) provides model-agnostic uncertainty quantification with guaranteed coverage, but conventional methods often produce overly conservative uncertainty sets, especially in multi-dimensional settings. This limitation…

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

The instability in the selection of models is a major concern with data sets containing a large number of covariates. This paper deals with variable selection methodology in the case of high-dimensional problems where the response variable…

Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a…

We propose a censored quantile regression estimator motivated by unbiased estimating equations. Under the usual conditional independence assumption of the survival time and the censoring time given the covariates, we show that the proposed…

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…

The requirement to generate robust robotic platforms is a critical enabling step to allow such platforms to permeate safety-critical applications (i.e., the localization of autonomous platforms in urban environments). One of the primary…

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…

Cross-validation (CV) is a common method to tune machine learning methods and can be used for model selection in regression as well. Because of the structured nature of small, traditional experimental designs, the literature has warned…

The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…

We propose a distributed method for simultaneous inference for datasets with sample size much larger than the number of covariates, i.e., N >> p, in the generalized linear models framework. When such datasets are too big to be analyzed…

Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few…

Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…