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In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change…

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…

Periodicity is a fundamental characteristic of time series data and has long played a central role in forecasting. Recent deep learning methods strengthen the exploitation of periodicity by treating patches as basic tokens, thereby…

Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…

We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our…

An algorithm for determining stationary periods for time series of random sea waves is proposed in this work. This is a problem in which changes between stationary sea states are usually slow and segmentation procedures based on…

Instance segmentation is the problem of detecting and delineating each distinct object of interest appearing in an image. Current instance segmentation approaches consist of ensembles of modules that are trained independently of each other,…

The present paper develops recursive algorithms to track shifts in the resonance frequency of linear systems in real time. To date, automatic resonance tracking has been limited to non-model-based approaches, which rely solely on the phase…

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based…

System identification refers to estimation of process parameters and is a necessity in control theory. Physical systems usually have varying parameters. For such processes, accurate identification is particularly important. Online…

Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to…

Data segmentation a.k.a. multiple change point analysis has received considerable attention due to its importance in time series analysis and signal processing, with applications in a variety of fields including natural and social sciences,…

Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…

We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to perform Bayesian inference computations, to…