相关论文: A Structural Approach to Coordinate-Free Statistic…

Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a…

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…

Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…

High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…

This paper considers a multi-environment linear regression model in which data from multiple experimental settings are collected. The joint distribution of the response variable and covariates may vary across different environments, yet the…

In the presence of confounders, the ordinary least squares (OLS) estimator is known to be biased. This problem can be remedied by using the two-stage least squares (TSLS) estimator, based on the availability of valid instrumental variables…

We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with…

The widespread use of maximum Jeffreys'-prior penalized likelihood in binomial-response generalized linear models, and in logistic regression, in particular, are supported by the results of Kosmidis and Firth (2021, Biometrika), who show…

We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensional structure, we prove that implicit score matching is able…

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…

We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution…

Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…

Open-Vocabulary Segmentation (OVS) aims to segment classes that are not present in the training dataset. However, most existing studies assume that the training data is fixed in advance, overlooking more practical scenarios where new…

We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…

In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

In this paper, we introduce an alternative method for applying averaging theory of orders $1$ and $2$ in the plane. This is done by combining Taylor expansions of the displacement map with the integral form of the…

In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…