相关论文: Assessing Prediction Error at Interpolation and Ex…

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…

Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test…

It has been shown that AIC-type criteria are asymptotically efficient selectors of the tuning parameter in non-concave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is…

Richardson extrapolation is a classical technique from numerical analysis that can improve the approximation error of an estimation method by combining linearly several estimates obtained from different values of one of its hyperparameters,…

The Akaike information criterion (AIC) is a model selection criterion widely used in practical applications. The AIC is an estimator of the log-likelihood expected value, and measures the discrepancy between the true model and the estimated…

A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…

We study the estimation of average effects in nonlinear panel data models with fixed effects when the time dimension $T$ is only moderately large. Our approach, called approximate operator inversion (AOI), offers a new perspective on bias…

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: used covariance function differs from…

Prototype models are an important method for explainable artificial intelligence (XAI) and interpretable machine learning. In this paper, we perform an in-depth analysis of a set of prominent prototype models including ProtoPNet, ProtoPool…

For a class of parametric modal regression models with measurement error, a simulation extrapolation estimation procedure is proposed in this paper for estimating the modal regression coefficients. Large sample properties of the proposed…

Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper,…

A local surrogate for an AI-model correcting a simpler 'base' model is introduced representing an analytical method to yield explanations of AI-predictions. The approach is studied here in the context of the base model being linear…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the…

We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated…

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…

In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point:…

The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…

Estimating conditional means using only the marginal means available from aggregate data is commonly known as the ecological inference problem (EI). We provide a reassessment of EI, including a new formalization of identification conditions…