Related papers: Fractional Gaussian noise criterion for correlatio…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…
We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate…
In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed…
We introduce a new approach to functional causal modeling from observational data, called Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks to learn a generative model of the joint distribution of the…
Conventionally, covariances do not distinguish between spatial and temporal correlations. The same covariance matrix could equally describe temporal correlations between observations of the same system at two different times or correlations…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may…
We introduce a new analysis method to deal with stationary non-Gaussian noises in gravitational wave detectors in terms of the independent component analysis. First, we consider the simplest case where the detector outputs are linear…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
Penalized Least Squares are widely used in signal and image processing. Yet, it suffers from a major limitation since it requires fine-tuning of the regularization parameters. Under assumptions on the noise probability distribution,…
We describe a general approach to detection of transient gravitational-wave signals in the presence of non-Gaussian background noise. We prove that under quite general conditions, the ratio of the likelihood of observed data to contain a…
We develop and present a generalization of the GN-model - the generalized Gaussian noise (GGN) model - to enabling a fair application of GN-model to predict generation of nonlinear interference when loss parameters relevantly vary with…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a…