Related papers: Relevance Vector Machine with Weakly Informative H…

The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression models such as feature regression and kernel regression and…

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS)…

We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients…

In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying…

Due to its strong interpretability, linear regression is widely used in social science, from which significance test provides the significance level of models or coefficients in the traditional statistical inference. However, linear…

This paper proposes a hybrid basis function construction method (GP-RVM) for Symbolic Regression problem, which combines an extended version of Genetic Programming called Kaizen Programming and Relevance Vector Machine to evolve an optimal…

We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is…

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…

The evaluation and post-training of large language models (LLMs) rely on supervision, but strong supervision for difficult tasks is often unavailable, especially when evaluating frontier models. In such cases, models are demonstrated to…

Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…

Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are…

We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures…

This paper develops a method for estimating parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes the noise variance matrix is known and does not require any iterative process. This study…

This paper considers statistical inference for the explained variance $\beta^{\intercal}\Sigma \beta$ under the high-dimensional linear model $Y=X\beta+\epsilon$ in the semi-supervised setting, where $\beta$ is the regression vector and…

Learning knowledge representation is an increasingly important technology that supports a variety of machine learning related applications. However, the choice of hyperparameters is seldom justified and usually relies on exhaustive search.…

Mechanistic interpretation has greatly contributed to a more detailed understanding of generative language models, enabling significant progress in identifying structures that implement key behaviors through interactions between internal…

Learning-to-rank (LTR) algorithms are ubiquitous and necessary to explore the extensive catalogs of media providers. To avoid the user examining all the results, its preferences are used to provide a subset of relatively small size. The…

In many applications, it is desirable to extract only the relevant aspects of data. A principled way to do this is the information bottleneck (IB) method, where one seeks a code that maximizes information about a 'relevance' variable, Y,…

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be…