Related papers: Narrow-width approximation limitations
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
Reliable uncertainty quantification is essential in survival prediction, particularly in clinical settings where erroneous decisions carry high risk. Conformal prediction has attracted substantial attention as it offers a model-agnostic…
The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish predictability of…
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
Reliable uncertainty estimation is one of the major challenges for medical classification tasks. While many approaches have been proposed, recently the statistical framework of conformal predictions has gained a lot of attention, due to its…
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is…
Applications from finance to epidemiology and cyber-security require accurate forecasts of dynamic phenomena, which are often only partially observed. We demonstrate that a system's predictability degrades as a function of temporal…
In this work, we present a comprehensive study combining mathematical and computational analysis to explain why a two-layer neural network struggles to handle high frequencies in both approximation and learning, especially when machine…
Fully convolutional U-shaped neural networks have largely been the dominant approach for pixel-wise image segmentation. In this work, we tackle two defects that hinder their deployment in real-world applications: 1) Predictions lack…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
Amortized inference allows latent-variable models trained via variational learning to scale to large datasets. The quality of approximate inference is determined by two factors: a) the capacity of the variational distribution to match the…
Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain…
The article addresses the problem of image sampling with minimal possible sampling rates and reviews the recent advances in sampling theory and methods: modern formulations of the sampling theorems, potentials and limitations of Compressed…
In this article a few of the qualitative spatio-temporal knowledge representation techniques developed by the constraint reasoning community within artificial intelligence are reviewed. The objective is to provide a broad exposure to any…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under…
Extracting parameter constraints from cosmological observations requires accurate determination of the covariance matrix for use in the likelihood function. We show here that uncertainties in the elements of the covariance matrix propagate…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…