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The follow the leader (FTL) algorithm, perhaps the simplest of all online learning algorithms, is known to perform well when the loss functions it is used on are convex and positively curved. In this paper we ask whether there are other…

Machine Learning · Computer Science 2017-02-13 Ruitong Huang , Tor Lattimore , András György , Csaba Szepesvári

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…

Machine Learning · Statistics 2020-02-25 Danijel Kivaranovic , Kory D. Johnson , Hannes Leeb

Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the…

Machine Learning · Computer Science 2022-07-12 Anthony Vento , Qingyu Zhao , Robert Paul , Kilian M. Pohl , Ehsan Adeli

To investigate the theoretical foundations of deep learning from the viewpoint of the minimum description length (MDL) principle, we analyse risk bounds of MDL estimators based on two-stage codes for simple two-layers neural networks (NNs)…

Information Theory · Computer Science 2024-11-19 Yoshinari Takeishi , Jun'ichi Takeuchi

Mixture Density Networks (MDNs) can be used to generate probability density functions of model parameters $\boldsymbol{\theta}$ given a set of observables $\mathbf{x}$. In some applications, training data are available only for discrete…

Data Analysis, Statistics and Probability · Physics 2021-08-18 Charles Burton , Spencer Stubbs , Peter Onyisi

In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The…

Dynamical Systems · Mathematics 2022-01-19 Victor Kleptsyn , Mark Pollicott , Polina Vytnova

This paper deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the…

Statistics Theory · Mathematics 2014-10-22 Arlene K. H. Kim

Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results…

Machine Learning · Statistics 2023-12-01 Yujing Liu , Zhixin Liu , Lei Guo

Successful machine learning methods require a trade-off between memorization and generalization. Too much memorization and the model cannot generalize to unobserved examples. Too much over-generalization and we risk under-fitting the data.…

Artificial Intelligence · Computer Science 2023-03-09 Chase Yakaboski , Eugene Santos

Deep neural networks (DNNs) are often prone to learn the spurious correlations between target classes and bias attributes, like gender and race, inherent in a major portion of training data (bias-aligned samples), thus showing unfair…

Computer Vision and Pattern Recognition · Computer Science 2024-10-01 Mei Wang , Weihong Deng , Jiani Hu , Sen Su

Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…

Machine Learning · Computer Science 2026-02-05 Behrooz Tahmasebi , Stefanie Jegelka

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

Methodology · Statistics 2018-01-30 Zhong Guan

In [1] it is shown that recurrent neural networks (RNNs) can learn - in a metric entropy optimal manner - discrete time, linear time-invariant (LTI) systems. This is effected by comparing the number of bits needed to encode the…

Dynamical Systems · Mathematics 2022-11-29 Clemens Hutter , Thomas Allard , Helmut Bölcskei

We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same…

Information Theory · Computer Science 2023-09-29 László Györfi , Tamás Linder , Harro Walk

Neural Temporal Difference (TD) Learning is an approximate temporal difference method for policy evaluation that uses a neural network for function approximation. Analysis of Neural TD Learning has proven to be challenging. In this paper we…

Machine Learning · Computer Science 2023-12-12 Haoxing Tian , Ioannis Ch. Paschalidis , Alex Olshevsky

Lifelong machine learning (LML) is an area of machine learning research concerned with human-like persistent and cumulative nature of learning. LML system's objective is consolidating new information into an existing machine learning model…

Machine Learning · Computer Science 2023-03-01 Sazia Mahfuz

We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After…

Machine Learning · Computer Science 2013-01-30 Katy S. Azoury , Manfred K. Warmuth

The problem of estimation of the distribution parameters on the sample when the part of these parameters are discrete (e.g. integer) is considered. We prove that the rate of convergence of MLE estimates under the natural conditions on the…

Statistics Theory · Mathematics 2014-02-27 E. Ostrovsky , L. Sirota , A. Zeldin

Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…

Machine Learning · Computer Science 2025-10-09 Binchuan Qi , Wei Gong , Li Li

This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's prior M, the latter being an excellent predictor in…

Artificial Intelligence · Computer Science 2007-07-13 Marcus Hutter
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