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This paper investigates the efficiency of the K-fold cross-validation (CV) procedure and a debiased version thereof as a means of estimating the generalization risk of a learning algorithm. We work under the general assumption of uniform…

With flexible modeling software - such as the probabilistic programming language Stan - growing in popularity, quantities of interest (QOIs) calculated post-estimation are increasingly desired and customly implemented, both by statistical…

Inference for prediction errors is critical in time series forecasting pipelines. However, providing statistically meaningful uncertainty intervals for prediction errors remains relatively under-explored. Practitioners often resort to…

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

How many different binary classification problems a single learning algorithm can solve on a fixed data with exactly zero or at most a given number of cross-validation errors? While the number in the former case is known to be limited by…

K-fold cross validation (CV) is a popular method for estimating the true performance of machine learning models, allowing model selection and parameter tuning. However, the very process of CV requires random partitioning of the data and so…

This paper presents a theory of error in cross-validation testing of algorithms for predicting real-valued attributes. The theory justifies the claim that predicting real-valued attributes requires balancing the conflicting demands of…

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable, and predictors are trained in a memoryless fashion. However, these assumptions and constraints are…

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series.…

Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for…

Two key tasks in high-dimensional regularized regression are tuning the regularization strength for accurate predictions and estimating the out-of-sample risk. It is known that the standard approach -- $k$-fold cross-validation -- is…

Machine learning technologies have been used in a wide range of practical systems. In practical situations, it is natural to expect the input-output pairs of a machine learning model to satisfy some requirements. However, it is difficult to…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…

The past few years have witnessed the rapid development in multivariate time series forecasting. The key to accurate forecasting results is capturing the long-term dependency between each time step (cross-time dependency) and modeling the…

Conditional independence testing is an important problem, yet provably hard without assumptions. One of the assumptions that has become popular of late is called "model-X", where we assume we know the joint distribution of the covariates,…

Penalized logistic regression methods are frequently used to investigate the relationship between a binary outcome and a set of explanatory variables. The model performance can be assessed by measures such as the concordance statistic…

Cross-validation (CV) is routinely used across the sciences to select models and tune parameters, and the resulting choices are often interpreted as substantive scientific conclusions (e.g., which variables, mechanisms, or risk factors are…

Automatic Machine Learning (Auto-ML) systems tackle the problem of automating the design of prediction models or pipelines for data science. In this paper, we present Lifelong Bayesian Optimization (LBO), an online, multitask Bayesian…

Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…