Related papers: The Past as a Stochastic Process

The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording, and analyzing the dynamics of different processes,…

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…

A theoretical model is presented which provides a way to simulate, at a very abstract level, power struggles in the social world. In the model, agents can benefit or harm each other, to varying degrees and with differing levels of…

A critically challenging problem facing statisticians is the identification of a suitable framework which consolidates data of various types, from different sources, and across different time frames or scales (many of which can be missing),…

Starting with a collection of traces generated by process executions, process discovery is the task of constructing a simple model that describes the process, where simplicity is often measured in terms of model size. The challenge of…

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…

Recent studies have shown that macroscopic patterns of continuity and change over the course of centuries can be detected through the analysis of time series extracted from massive textual corpora. Similar data-driven approaches have…

Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they…

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

A rational framework is proposed to explain how we accommodate unbounded sensory input within bounded memory. According to this framework, memory is stored as a statistic-like representation that is repeatedly summarized and compressed to…

Patterns embody repeating phenomena, and, as such, they are partly but not fully detachable from their context. 'Design patterns' and 'pattern languages' are established methods for working with patterns. They have been applied in…

Process mining methods often analyze processes in terms of the individual end-to-end process runs. Process behavior, however, may materialize as a general state of many involved process components, which can not be captured by looking at…

A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…

An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…

This two-part paper presents a new approach to predictive analysis for social processes. In Part I, we begin by identifying a class of social processes which are simultaneously important in applications and difficult to predict using…

Process mining leverages event data extracted from IT systems to generate insights into the business processes of organizations. Such insights benefit from explicitly considering the frequency of behavior in business processes, which is…

The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a…

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…