Related papers: Using the Softplus Function to Construct Alternati…

Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with…

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…

Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data,…

Preference-based reward learning is widely used for shaping agent behavior to match a user's preference, yet its sparse binary feedback makes it especially vulnerable to causal confusion. The learned reward often latches onto spurious…

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…

In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent…

Imputing missing potential outcomes using an estimated regression function is a natural idea for estimating causal effects. In the literature, estimators that combine imputation and regression adjustments are believed to be comparable to…

When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…

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.…

Counterfactual explanations improve the actionable interpretability of machine learning models by identifying minimal changes required to achieve a desired outcome. However, existing methods often neglect dependencies among features, which…

We propose a nonparametric method for estimating the conditional quantile function that admits a generalized additive specification with an unknown link function. This model nests single-index, additive, and multiplicative quantile…

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…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…

Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…

Non-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. We introduce an extension of the generalized…

Diffusion models have achieved remarkable results in image generation, and have similarly been used to learn high-performing policies in sequential decision-making tasks. Decision-making diffusion models can be trained on lower-quality…

We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…