相关论文: Statistical Learnability of Generalized Additive M…

Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total…

This paper studies the problem of learning weighted automata from a finite labeled training sample. We consider several general families of weighted automata defined in terms of three different measures: the norm of an automaton's weights,…

Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. However, despite its success, several important questions…

In the field of computer vision, data augmentation is widely used to enrich the feature complexity of training datasets with deep learning techniques. However, regarding the generalization capabilities of models, the difference in…

We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and the Bayesian…

Logistic regression (LR) is widely used in clinical prediction because it is simple to deploy and easy to interpret. Nevertheless, being a linear model, LR has limited expressive capability and often has unsatisfactory performance.…

While interpretability is crucial for machine learning applications in safety-critical domains and for regulatory compliance, existing tabular foundation models like TabPFN lack transparency. Generalized Additive Models (GAMs) provide the…

Interpretability is one of the considerations when applying machine learning to high-stakes fields such as healthcare that involve matters of life safety. Generalized Additive Models (GAMs) enhance interpretability by visualizing shape…

There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…

Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet…

Generalized additive models (GAMs) are favored in many regression and binary classification problems because they are able to fit complex, nonlinear functions while still remaining interpretable. In the first part of this paper, we…

Recurrent Neural Networks (RNNs) have achieved great success in the prediction of sequential data. However, their theoretical studies are still lagging behind because of their complex interconnected structures. In this paper, we establish a…

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…

We address the component-based regularisation of a multivariate Generalised Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory…

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or…

Generalized additive models (GAMs) connecting a set of scalar covariates that map 1-1 to a response are commonly employed in ecology and beyond. However, covariates are often inherently non-scalar, taking multiple values for each…

Let $f$ be a measurable, real function defined in a neighbourhood of infinity. The function $f$ is said to be of generalised regular variation if there exist functions $h \not\equiv 0$ and $g > 0$ such that $f(xt) - f(t) = h(x) g(t) +…

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train. The recently proposed Wasserstein GAN (WGAN) creates principled research directions towards addressing these issues. But we found in practice…