Related papers: Detecting frequency modulation in stochastic time …

Optimal algorithms are developed for robust detection of changes in non-stationary processes. These are processes in which the distribution of the data after change varies with time. The decision-maker does not have access to precise…

We present a spectrogram separation method tailored for mixtures comprising two nonstationary components. By exploiting the unique characteristics of their time-frequency representations, we propose an inverse problem formulation to…

We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those…

Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In…

As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterise and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources,…

We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It is well known that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if…

Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this…

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases.…

A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…

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 study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…

Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…

A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…

Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed…

Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…

Current fluctuations play an important role in non-equilibrium statistical mechanics, and are a key object of interest in both theoretical studies and in practical applications. So far, most of the studies were devoted to the fluctuations…

Spectrograms visualize the frequency components of a given signal which may be an audio signal or even a time-series signal. Audio signals have higher sampling rate and high variability of frequency with time. Spectrograms can capture such…

Non-stationarity of the rate or variance of events is a well-known problem in the description and analysis of time series of events, such as neuronal spike trains. A multiple filter test (MFT) for rate homogeneity has been proposed earlier…