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We present a methodology for model evaluation and selection where the sampling mechanism violates the i.i.d. assumption. Our methodology involves a formulation of the bias between the standard Cross-Validation (CV) estimator and the mean…

In safety-critical applications data-driven models must not only be accurate but also provide reliable uncertainty estimates. This property, commonly referred to as calibration, is essential for risk-aware decision-making. In regression a…

Forward regression is a crucial methodology for automatically identifying important predictors from a large pool of potential covariates. In contexts with moderate predictor correlation, forward selection techniques can achieve screening…

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty.…

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial…

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…

Sure Independence Screening is a fast procedure for variable selection in ultra-high dimensional regression analysis. Unfortunately, its performance greatly deteriorates with increasing dependence among the predictors. To solve this issue,…

Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…

Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…

Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear…

This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…

Making predictions that are fair with regard to protected group membership (race, gender, age, etc.) has become an important requirement for classification algorithms. Existing techniques derive a fair model from sampled labeled data…

Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods…

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null…

Many regression problems involve not one but several response variables (y's). Often the responses are suspected to share a common underlying structure, in which case it may be advantageous to share information across them; this is known as…

Model diagnostics and forecast evaluation are two sides of the same coin. A common principle is that fitted or predicted distributions ought to be calibrated or reliable, ideally in the sense of auto-calibration, where the outcome is a…

In statistical prediction, classical approaches for model selection and model evaluation based on covariance penalties are still widely used. Most of the literature on this topic is based on what we call the "Fixed-X" assumption, where…

Local variable selection aims to test for the effect of covariates on an outcome within specific regions. We outline a challenge that arises in the presence of non-linear effects and model misspecification. Specifically, for common…

Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening…

For many scientific questions, understanding the underlying mechanism is the goal. To help investigators better understand the underlying mechanism, variable selection is a crucial step that permits the identification of the most associated…