相关论文: MDL Convergence Speed for Bernoulli Sequences

This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the…

Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical…

Model-based deep learning (MBDL) is a powerful methodology for designing deep models to solve imaging inverse problems. MBDL networks can be seen as iterative algorithms that estimate the desired image using a physical measurement model and…

We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…

We consider the problem of sequential decision making under uncertainty in which the loss caused by a decision depends on the following binary observation. In competitive on-line learning, the goal is to design decision algorithms that are…

Simulation-based inference techniques are indispensable for parameter estimation of mechanistic and simulable models with intractable likelihoods. While traditional statistical approaches like approximate Bayesian computation and Bayesian…

Constant gain least-mean-squares (LMS) algorithms have a wide range of applications in trajectory tracking problems, but the formal convergence of LMS in mean square is not yet fully established. This work provides an upper bound on the…

This work focuses on classification over time series data. When a time series is generated by non-stationary phenomena, the pattern relating the series with the class to be predicted may evolve over time (concept drift). Consequently,…

We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…

The use of machine learning methods for predictive purposes has increased dramatically over the past two decades, but uncertainty quantification for predictive comparisons remains elusive. This paper addresses this gap by extending the…

Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…

A major bottleneck of standard auto-regressive large language models is that their inference process is inherently sequential, resulting in very long and costly inference times. To circumvent this, practitioners proposed a class of language…

Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for…

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work…

Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using…

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…

The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's…

Consider a regression problem where the learner is given a large collection of $d$-dimensional data points, but can only query a small subset of the real-valued labels. How many queries are needed to obtain a $1+\epsilon$ relative error…

We introduce the first application of the lean methodology to machine learning projects. Similar to lean startups and lean manufacturing, we argue that lean machine learning (LeanML) can drastically slash avoidable wastes in commercial…

It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…