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Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…

We introduce a framework for online changepoint detection and simultaneous model learning which is applicable to highly parametrized models, such as deep neural networks. It is based on detecting changepoints across time by sequentially…

Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a…

Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…

The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one…

As time series data become increasingly prevalent in domains such as manufacturing, IT, and infrastructure monitoring, anomaly detection must adapt to nonstationary environments where statistical properties shift over time. Traditional…

Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data…

We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time…

A new algorithm for estimating the time-varying frequency of a noiseless sinusoidal signal is considered. It is assumed that the amplitude and frequency of the sinusoidal signal are unknown functions of time, but are solutions of linear…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

We suggest a novel procedure for online change point detection. Our approach expands an idea of maximizing a discrepancy measure between points from pre-change and post-change distributions. This leads to flexible algorithms suitable for…

Time series segmentation aims to identify potential change-points in a sequence of temporally dependent data, so that the original sequence can be partitioned into several homogeneous subsequences. It is useful for modeling and predicting…

This article introduces a novel Bayesian method for asynchronous change-point detection in multivariate time series. This method allows for change-points to occur earlier in some (leading) series followed, after a short delay, by…

Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…

Online detection of instantaneous changes in the generative process of a data sequence generally focuses on retrospective inference of such change points without considering their future occurrences. We extend the Bayesian Online Change…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…