Related papers: Prediction theory in continuous time

This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…

A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum…

We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…

Process analytics is an umbrella of data-driven techniques which includes making predictions for individual process instances or overall process models. At the instance level, various novel techniques have been recently devised, tackling…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…

In self-driving, predicting future in terms of location and motion of all the agents around the vehicle is a crucial requirement for planning. Recently, a new joint formulation of perception and prediction has emerged by fusing rich sensory…

We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…

Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…

The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

We study certain polyadicly continuous sequences from point of view the probability theory.

Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this work, we study preference-based planning in a stochastic system modeled as a Markov decision…

A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…

Is it a good idea to use the frequency of events in the past, as a guide to their frequency in the future (as we all do anyway)? In this paper the question is attacked from the perspective of universal prediction of individual sequences. It…

The goal of sequential event prediction is to estimate the next event based on a sequence of historical events, with applications to sequential recommendation, user behavior analysis and clinical treatment. In practice, the next-event…

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…

I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…

Neural predictive models have achieved remarkable performance improvements in various natural language processing tasks. However, most neural predictive models suffer from the lack of explainability of predictions, limiting their practical…