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In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the…
The Poisson process, especially the nonhomogeneous Poisson process (NHPP), is an essentially important counting process with numerous real-world applications. Up to date, almost all works in the literature have been on the estimation of…
Astronomical surveys of celestial sources produce streams of noisy time series measuring flux versus time ("light curves"). Unlike in many other physical domains, however, large (and source-specific) temporal gaps in data arise naturally…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random,…
Recurrent neural networks (RNNs) have been used extensively and with increasing success to model various types of sequential data. Much of this progress has been achieved through devising recurrent units and architectures with the…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
In the new era of very large telescopes, where data is crucial to expand scientific knowledge, we have witnessed many deep learning applications for the automatic classification of lightcurves. Recurrent neural networks (RNNs) are one of…
Generating diverse samples under hard constraints is a core challenge in many areas. With this work we aim to provide an integrative view and framework to combine methods from the fields of MCMC, constrained optimization, as well as…
We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…
Mining frequent sequential patterns consists in extracting recurrent behaviors, modeled as patterns, in a big sequence dataset. Such patterns inform about which events are frequently observed in sequences, i.e. what does really happen.…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
Sequential sampling occurs when the entire population is not known in advance and data are obtained one at a time or in groups of units. This manuscript proposes a new algorithm to sequentially select a balanced sample. The algorithm…
The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit-distance is an effective…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…