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Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…
We propose a framework which generalizes "decision making with structured observations" by allowing robust (i.e. multivalued) models. In this framework, each model associates each decision with a convex set of probability distributions over…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
We apply the generalized sphere-packing bound to two classes of subblock-constrained codes. A la Fazeli et al. (2015), we made use of automorphism to significantly reduce the number of variables in the associated linear programming problem.…
Research on generalization bounds for deep networks seeks to give ways to predict test error using just the training dataset and the network parameters. While generalization bounds can give many insights about architecture design, training…
The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental…
Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless %asynchronous multiple access channels with two senders, via the method of subtypes, a refinement of the method of…
Confidence bounds are an essential tool for rigorously quantifying the uncertainty of predictions. They are a core component in many sequential learning and decision-making algorithms, with tighter confidence bounds giving rise to…
We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is…
The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also…
Classification is a fundamental task in supervised learning, while achieving valid misclassification rate control remains challenging due to possibly the limited predictive capability of the classifiers or the intrinsic complexity of the…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
Autoencoders are widely used for unsupervised learning and as a regularization scheme in semi-supervised learning. However, theoretical understanding of their generalization properties and of the manner in which they can assist supervised…
We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…
A problem of bounding the generalization error of a classifier f in H, where H is a "base" class of functions (classifiers), is considered. This problem frequently occurs in computer learning, where efficient algorithms of combining simple…
Generalization error bounds are critical to understanding the performance of machine learning models. In this work, we propose a new information-theoretic based generalization error upper bound applicable to supervised learning scenarios.…
This work addresses the classic machine learning problem of online prediction with expert advice. A new potential-based framework for the fixed horizon version of this problem has been recently developed using verification arguments from…
Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…