Related papers: Generalization Bounds for Quantum Learning via R\'…
We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated,…
Sandwiched (quantum) $\alpha$-R\'enyi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and M\"uller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications…
The generalization bound is a crucial theoretical tool for assessing the generalizability of learning methods and there exist vast literatures on generalizability of normal learning, adversarial learning, and data poisoning. Unlike other…
We derive upper bounds on the generalization error of learning algorithms based on their \emph{algorithmic transport cost}: the expected Wasserstein distance between the output hypothesis and the output hypothesis conditioned on an input…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a…
We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern…
In this paper, we present generalization bounds for the unsupervised risk in the Deep Contrastive Representation Learning framework, which employs deep neural networks as representation functions. We approach this problem from two angles.…
Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…
The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine…
Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…
A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…
Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error.…
In this paper, we present the Bennett-type generalization bounds of the learning process for i.i.d. samples, and then show that the generalization bounds have a faster rate of convergence than the traditional results. In particular, we…
This PhD thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning. We introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are…
We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$…
We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation…
In this work, we show that the sample complexity required in quantum learning theory within a general parametric framework, is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower…
Traditional supervised learning aims to train a classifier in the closed-set world, where training and test samples share the same label space. In this paper, we target a more challenging and realistic setting: open-set learning (OSL),…
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…