Related papers: How far can stochastic and deterministic views be …
Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…
Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…
We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
We address two central notions of fairness in the literature of planning on nondeterministic fully observable domains. The first, which we call stochastic fairness, is classical, and assumes an environment which operates probabilistically…
We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed:…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
The Levenshtein distance is an important tool for the comparison of symbolic sequences, with many appearances in genome research, linguistics and other areas. For efficient applications, an approximation by a distance of smaller…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which…
When optimizing problems with uncertain parameter values in a linear objective, decision-focused learning enables end-to-end learning of these values. We are interested in a stochastic scheduling problem, in which processing times are…
In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider…
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…
In this contribution we establish a dictionary between terms in two different areas in order to show that many of the topics studied are common ones - just with a different terminology. We further analyze the relations between the…