Related papers: Lecture Notes: Temporal Point Processes and the Co…
This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.
Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
Many scientific fields, from medicine to seismology, rely on analyzing sequences of events over time to understand complex systems. Traditionally, machine learning models must be built and trained from scratch for each new dataset, which is…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
We define dynamic treatment regimes and associated potential outcomes for data described by marked point processes (MPPs). These definitions motivate MPP analogues of the commonly used consistency, exchangeability, and positivity conditions…
Several theoretical results concerning event-by-event fluctuations are discussed: (1) a role of the global conservation laws and concept of statistical ensembles; (2) strongly intensive measures are introduced; they give a possibility to…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
Predictive process monitoring is a subfield of process mining that aims to estimate case or event features for running process instances. Such predictions are of significant interest to the process stakeholders. However, state-of-the-art…
We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss of the predictor on the next point conditioned on the set…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external…
This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…
We describe the Clinical TempEval task which is currently in preparation for the SemEval-2015 evaluation exercise. This task involves identifying and describing events, times and the relations between them in clinical text. Six discrete…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to define separately the marginal distribution and the…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
We consider the problem of defining conditional objects (a|b), which would allow one to regard the conditional probability Pr(a|b) as a probability of a well-defined event rather than as a shorthand for Pr(ab)/Pr(b). The next issue is to…
Intermittent demand, where demand occurrences appear sporadically in time, is a common and challenging problem in forecasting. In this paper, we first make the connections between renewal processes, and a collection of current models used…