Related papers: Checking the Statistical Assumptions Underlying th…
Finding a basis/coordinate system that can efficiently represent an input data stream by viewing them as realizations of a stochastic process is of tremendous importance in many fields including data compression and computational…
A broad and widely used class of stationary, linear, additive time series models can have statistical properties which many authors have asserted imply that the underlying process must be non-linear, non-stationary, multiplicative, or…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…
In the image processing pipeline of almost every digital camera there is a part dedicated to computational color constancy i.e. to removing the influence of illumination on the colors of the image scene. Some of the best known illumination…
We study the verification problem of stochastic systems under signal temporal logic (STL) specifications. We propose a novel approach that enables the verification of the probabilistic satisfaction of STL specifications for nonlinear…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Spatio-temporal receptive fields (STRF) of visual neurons are often estimated using spike-triggered averaging of binary pseudo-random stimulus sequences. The spike train of a visual neuron is recorded simultaneously with the stimulus…
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…
Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…
Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…
In this paper we describe a detailed analysis of the photometric uncertainties present within the Sloan Digital Sky Survey (SDSS) imaging survey based on repeat observations of approximately 200 square degrees of the sky. We show that, for…
Particle tracking velocimetry (PTV) is widely used to measure time-resolved, three-dimensional velocity and pressure fields in fluid dynamics research. Inaccurate localization and tracking of particles is a key source of error in PTV,…
Spatiotemporal (ST) data collected by sensors can be represented as multi-variate time series, which is a sequence of data points listed in an order of time. Despite the vast amount of useful information, the ST data usually suffer from the…
We study the problem of traffic forecasting, aiming to predict the inflow and outflow of a region in the subsequent time slot. The problem is complex due to the intricate spatial and temporal interdependence among regions. Prior works study…
In industrial settings, surface defects on steel can significantly compromise its service life and elevate potential safety risks. Traditional defect detection methods predominantly rely on manual inspection, which suffers from low…
Reachability analysis has been a prominent way to provide safety guarantees for neurally controlled autonomous systems, but its direct application to neural perception components is infeasible due to imperfect or intractable perception…
Statistical inference in observational science typically relies on a fundamental assumption: as sample size increases and uncertainties decrease, the inferred results should converge to the true physical quantities. This assumption…
When observing spatial data, what standard errors should we report? With the finite population framework, we identify three channels of spatial correlation: sampling scheme, assignment design, and model specification. The Eicker-Huber-White…