Related papers: Statistical Learnability of Generalized Additive M…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
Machine learning technologies have been used in a wide range of practical systems. In practical situations, it is natural to expect the input-output pairs of a machine learning model to satisfy some requirements. However, it is difficult to…
A time series is a sequence of observations taken sequentially in time. The autoregressive integrated moving average is a class of the model more used for times series data. However, this class of model has two critical limitations. It fits…
In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…
Sharpness-Aware Minimization (SAM) is a recent training method that relies on worst-case weight perturbations which significantly improves generalization in various settings. We argue that the existing justifications for the success of SAM…
Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear…
Programming by demonstration has recently gained much attention due to its user-friendly and natural way to transfer human skills to robots. In order to facilitate the learning of multiple demonstrations and meanwhile generalize to new…
This paper studies generalization error bounds for Transformer models. Based on the offset Rademacher complexity, we derive sharper generalization bounds for different Transformer architectures, including single-layer single-head,…
Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where…
In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…
Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space $\H$ that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis…
Cognitive diagnosis models (CDMs) are restricted latent class models widely used to measure attributes of interest in diagnostic assessments across education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs…
Uncertainty quantification in deep learning is crucial for safe and reliable decision-making in downstream tasks. Existing methods quantify uncertainty at the last layer or other approximations of the network which may miss some sources of…
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…
The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep…
The generalization gap of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature.…
A classical result in approximation theory states that for any continuous function \( \varphi: \mathbb{R} \to \mathbb{R} \), the set \( \operatorname{span}\{\varphi \circ g : g \in \operatorname{Aff}(\mathbb{R})\} \) is dense in \(…
The generalized gamma convolutions class of distributions appeared in Thorin's work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the…