Related papers: The Interpolating Information Criterion for Overpa…
The model selection procedure is usually a single-criterion decision making in which we select the model that maximizes a specific metric in a specific set, such as the Validation set performance. We claim this is very naive and can perform…
The first investigation is made of designs for screening experiments where the response variable is approximated by a generalised linear model. A Bayesian information capacity criterion is defined for the selection of designs that are…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
The impressive performance exhibited by modern machine learning models hinges on the ability to train such models on a very large amounts of labeled data. However, since access to large volumes of labeled data is often limited or expensive,…
We investigate a new structure for machine learning classifiers applied to problems in high-energy physics by expanding the inputs to include not only measured features but also physics parameters. The physics parameters represent a…
The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with…
Information criteria have had a profound impact on modern ecological science. They allow researchers to estimate which probabilistic approximating models are closest to the generating process. Unfortunately, information criterion comparison…
In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional…
Consider the setting where there are B>1 candidate statistical models, and one is interested in model selection. Two common approaches to solve this problem are to select a single model or to combine the candidate models through model…
In many parameter estimation problems, the exact model is unknown and is assumed to belong to a set of candidate models. In such cases, a predetermined data-based selection rule selects a parametric model from a set of candidates before the…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine…
Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses new…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…
The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing…