相关论文: A packing lemma for VCN${}_k$-dimension and learni…

Estimating the relative importance of each sample in a training set has important practical and theoretical value, such as in importance sampling or curriculum learning. This kind of focus on individual samples invokes the concept of…

The logical analysis of data, LAD, is a technique that yields two-class classifiers based on Boolean functions having disjunctive normal form (DNF) representation. Although LAD algorithms employ optimization techniques, the resulting binary…

We propose a quadratic penalty method for continual learning of neural networks that contain batch normalization (BN) layers. The Hessian of a loss function represents the curvature of the quadratic penalty function, and a…

Research on the generalization ability of deep neural networks (DNNs) has recently attracted a great deal of attention. However, due to their complex architectures and large numbers of parameters, measuring the generalization ability of…

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form $h = g \circ p$ where $p : \mathbb{R}^d \rightarrow…

This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of…

We study two related quantities which generalize the concept of upper Banach density of a set to two measurable subsets of the plane. The first of them allows us to generalize a classic result on sufficiently large distances realized in a…

In recent years the framework of learning from label proportions (LLP) has been gaining importance in machine learning. In this setting, the training examples are aggregated into subsets or bags and only the average label per bag is…

Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…

Graph neural networks have demonstrated excellent applicability to a wide range of domains, including social networks, biological systems, recommendation systems, and wireless communications. Yet a principled theoretical understanding of…

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes…

In this paper, we provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different target distribution. On the one hand,…

A caveat to many applications of the current Deep Learning approach is the need for large-scale data. One improvement suggested by Kolmogorov Complexity results is to apply the minimum description length principle with computationally…

Abstract We present PAC-Bayesian bounds for the generalisation error of the K-nearest-neighbour classifier (K-NN). This is achieved by casting the K-NN classifier into a kernel space framework in the limit of vanishing kernel bandwidth. We…

Graph neural networks (GNNs) have achieved remarkable success in processing graph-structured data across various applications. A critical aspect of real-world graphs is their dynamic nature, where new nodes are continually added and…

This is a set of lecture notes for an introductory course (advanced undergaduates or the 1st graduate course) on foundations of supervised machine learning (in Portuguese). The topics include: the geometry of the Hamming cube, concentration…

We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local…

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…

Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…

Conventional deep learning models embed data in Euclidean space $\mathbb{R}^d$, a poor fit for strictly hierarchical objects such as taxa, word senses, or file systems. We introduce van der Put Neural Networks (v-PuNNs), the first…