Related papers: Information theory, Signal Analysis and Inverse Pr…
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…
Information technology and data science development stimulate transformation in many fields of scientific knowledge. In recent years, a large number of specialized systems for information and knowledge management have been created in…
We focus attention on some particular thermodynamic relations (PTR). Using information theory concepts we show that, for a reversible process, microscopic considerations related to these PTR make the concomitant informational contents of…
Imbalanced-learn is an open-source python toolbox aiming at providing a wide range of methods to cope with the problem of imbalanced dataset frequently encountered in machine learning and pattern recognition. The implemented…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
Supervised, semi-supervised, and unsupervised learning estimate a function given input/output samples. Generalization of the learned function to unseen data can be improved by incorporating side information into learning. Side information…
This arXiv report provides a short introduction to the information-theoretic measure proposed by Chen and Golan in 2016 for analyzing machine- and human-centric processes in data intelligence workflows. This introduction was compiled based…
We introduce NIFTY, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of…
Modern online education has the capacity to provide intelligent educational services by automatically analyzing substantial amounts of student behavioral data. Knowledge Tracing (KT) is one of the fundamental tasks for student behavioral…
Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…
Knowledge Tracing (KT) is a research field that aims to estimate a student's knowledge state through learning interactions-a crucial component of Intelligent Tutoring Systems (ITSs). Despite significant advancements, no current KT models…
Large Language Models (LLMs) have demonstrated remarkable capabilities in various reasoning tasks, yet they often struggle with problems involving missing information, exhibiting issues such as incomplete responses, factual errors, and…
This book is based on notes compiled over the many years I have been teaching the course "Applied Functional Analysis" in the first year of the Master programme at Delft University of Technology, for students with previous exposure to the…
DeepInverse is an open-source PyTorch-based library for solving imaging inverse problems. The library covers all crucial steps in image reconstruction from the efficient implementation of forward operators (e.g., optics, MRI, tomography),…
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…
This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time,…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…