Related papers: Iterative Gaussianization: from ICA to Random Rota…

In this paper we elaborate an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. Although RBIG has been successfully applied to many tasks, it is limited to medium dimensionality data…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

We develop an iterative (greedy) deep learning (DL) algorithm which is able to transform an arbitrary probability distribution function (PDF) into the target PDF. The model is based on iterative Optimal Transport of a series of 1D slices,…

We introduce a new approximate multiresolution analysis (MRA) using a single Gaussian as the scaling function, which we call Gaussian MRA (GMRA). As an initial application, we employ this new tool to accurately and efficiently compute the…

It is known that circularly symmetric Gaussian signals are the optimal input signals for the partial decode-and-forward (PDF) coding scheme in the Gaussian multiple-input multiple-output (MIMO) relay channel, but there is currently no…

This paper proposes a deep recurrent Rotation Averaging Graph Optimizer (RAGO) for Multiple Rotation Averaging (MRA). Conventional optimization-based methods usually fail to produce accurate results due to corrupted and noisy relative…

Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for…

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…

PDF files are primarily intended for human reading rather than automated processing. In addition, the heterogeneous content of PDFs, such as text, tables, and images, poses significant challenges for parsing and information extraction. To…

Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…

We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem…

We consider the problem of computing a Gaussian approximation to the posterior distribution of a parameter given a large number N of observations and a Gaussian prior, when the dimension of the parameter d is also large. To address this…

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

This paper presents an advancement in Question-Answering (QA) systems using a Retrieval Augmented Generation (RAG) framework to enhance information extraction from PDF files. Recognizing the richness and diversity of data within…

Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting…

This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to…

Retrieval-Augmented Generation (RAG) has emerged as a promising technique to enhance the quality and relevance of responses generated by large language models. While recent advancements have mainly focused on improving RAG for text-based…

Handling geometric transformations, particularly rotations, remains a challenge in deep learning for computer vision. Standard neural networks lack inherent rotation invariance and typically rely on data augmentation or architectural…