Related papers: A Review of Methods for Estimating Algorithmic Com…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…
Efforts to promote equitable public policy with algorithms appear to be fundamentally constrained by the "impossibility of fairness" (an incompatibility between mathematical definitions of fairness). This technical limitation raises a…
We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in…
Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…
The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural…
When modelling competing risks survival data, several techniques have been proposed in both the statistical and machine learning literature. State-of-the-art methods have extended classical approaches with more flexible assumptions that can…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Software systems are expansive, exhibiting behaviors characteristic of complex systems, such as self-organization and emergence. These systems, highlighted by advancements in Large Language Models (LLMs) and other AI applications developed…
Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a…
We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and…
This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…
Artificial Intelligence (AI) algorithms are increasingly providing decision making and operational support across multiple domains. AI includes a wide library of algorithms for different problems. One important notion for the adoption of AI…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
Much of machine learning research focuses on predictive accuracy: given a task, create a machine learning model (or algorithm) that maximizes accuracy. In many settings, however, the final prediction or decision of a system is under the…
The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods. Most of the mathematical results related to the convergence are not found in most of the…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…