Related papers: Higher-order correlation functions and nonlinear r…
We calculated a four-point correlation function G_4(k,r;t) and the corresponding structure factor S_4(k,q;t) for a model glass-forming binary mixture. These functions measure the spatial correlations of the relaxation of different…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…
A compact correlation-function expansion is developed for nth order optical susceptibilities in the frequency domain using the Keldysh-Schwinger loop. By not keeping track of the relative time ordering of bra and ket interactions at the two…
Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several…
We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
Density correlations unambiguously reveal the quantum nature of matter. Here, we study correlations between measurements of density in cold-atom clouds at different times at one position, and also at two separated positions. We take into…
Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data,…
Trap models are intuitively appealing and often solvable models of glassy dynamics. In particular, they have been used to study aging and the resulting out-of-equilibrium fluctuation-dissipation relations between correlations and response…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
The motion of a colloidal probe in a complex fluid, such as a micellar solution, is usually described by the generalized Langevin equation, which is linear. However, recent numerical simulations and experiments have shown that this linear…
While uncertainty estimation is a well-studied topic in deep learning, most such work focuses on marginal uncertainty estimates, i.e. the predictive mean and variance at individual input locations. But it is often more useful to estimate…