English
Related papers

Related papers: Probabilistic Error Analysis for Inner Products

200 papers

Solomonoff sequence prediction is a scheme to predict digits of binary strings without knowing the underlying probability distribution. We call a prediction scheme informed when it knows the true probability distribution of the sequence.…

Artificial Intelligence · Computer Science 2007-05-23 Marcus Hutter

We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…

Programming Languages · Computer Science 2022-06-07 Raven Beutner , Luke Ong , Fabian Zaiser

Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some…

Machine Learning · Statistics 2025-12-18 Hugo Lavenant , Giacomo Zanella

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…

Statistics Theory · Mathematics 2021-06-07 Victor Mirasierra , Martina Mammarella , Fabrizio Dabbene , Teodoro Alamo

We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$.

Functional Analysis · Mathematics 2015-06-11 David Alonso-Gutierrez , Markus Passenbrunner , Joscha Prochno

We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen's theorem for correlated probability,…

Information Theory · Computer Science 2010-06-29 Hayato Takahashi

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Optimization and Control · Mathematics 2023-01-13 Emiland Garrabe , Giovanni Russo

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…

Statistics Theory · Mathematics 2024-05-14 Yingru Li

In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…

Statistics Theory · Mathematics 2012-12-06 Xinjia Chen

We revisit the sequential variants of linear regression with the squared loss, classification problems with hinge loss, and logistic regression, all characterized by unbounded losses in the setup where no assumptions are made on the…

Machine Learning · Statistics 2025-09-08 Jian Qian , Alexander Rakhlin , Nikita Zhivotovskiy

Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…

Artificial Intelligence · Computer Science 2013-04-12 Norman C. Dalkey

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…

Statistics Theory · Mathematics 2013-05-06 Victor Chernozhukov , Sokbae Lee , Adam M. Rosen

This paper introduces a new technique for quantifying the approximation error of a broad class of probabilistic inference programs, including ones based on both variational and Monte Carlo approaches. The key idea is to derive a subjective…

Artificial Intelligence · Computer Science 2016-06-02 Marco F Cusumano-Towner , Vikash K Mansinghka

Suppose $\{ X_k \}_{k \in \mathbb{Z}}$ is a sequence of bounded independent random matrices with common dimension $d\times d$ and common expectation $\mathbb{E}[ X_k ]= X$. Under these general assumptions, the normalized random matrix…

Probability · Mathematics 2019-07-15 Amelia Henriksen , Rachel Ward

We analyze the problem of sequential probability assignment for binary outcomes with side information and logarithmic loss, where regret---or, redundancy---is measured with respect to a (possibly infinite) class of experts. We provide upper…

Information Theory · Computer Science 2015-01-30 Alexander Rakhlin , Karthik Sridharan

Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

Logic in Computer Science · Computer Science 2018-06-12 Dimitrios Milios , Guido Sanguinetti , David Schnoerr

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Numerical Analysis · Mathematics 2024-06-12 Sören Bartels , Alex Kaltenbach

In this work, we provide deterministic error bounds for the actual state evolution of nonlinear systems embedded with the linear parametric variable (LPV) formulation and steered by model predictive control (MPC). The main novelty concerns…

Optimization and Control · Mathematics 2023-10-11 Dimitrios S. Karachalios , Maryam Nezami , Georg Schildbach , Hossameldin S. Abbas

This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…

Machine Learning · Computer Science 2024-12-30 Jathin Korrapati , Tanish Baranwal , Rahul Shah