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We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…

Understanding recrystallization boundary migration mechanisms is crucial for materials design. However, the lack of comprehensive mobility data for high-angle grain boundaries in typical polycrystalline samples has impeded gaining insights…

We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The…

Even though a train/test split of the dataset randomly performed is a common practice, could not always be the best approach for estimating performance generalization under some scenarios. The fact is that the usual machine learning…

This paper introduces an approach to multi-stream quickest change detection and fault isolation for unnormalized and score-based statistical models. Traditional optimal algorithms in the quickest change detection literature require explicit…

Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the…

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…

We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…

Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…

Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…

A new segmentation fusion method is proposed that ensembles the output of several segmentation algorithms applied on a remotely sensed image. The candidate segmentation sets are processed to achieve a consensus segmentation using a…

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…

Automated f ault detection and monitoring in engineering are critical but frequently difficult owing to the necessity for collecting and labeling large amounts of defective samples . We present an unsupervised method that uses the high end…

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses…

Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…

We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…

We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…

We introduce novel variants of momentum by incorporating the variance of the stochastic loss function. The variance characterizes the confidence or uncertainty of the local features of the averaged loss surface across the i.i.d. subsets of…