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This paper revisits classical works of Rauch (1963, et al. 1965) and develops a novel method for maximum likelihood (ML) smoothing estimation from incomplete information/data of stochastic state-space systems. Score function and conditional…

This work focuses on optimizing the hybrid quantum noise model to improve the capacity of Gaussian quantum channels using Machine Learning (ML) generated clusters. The work specifically leverages Gaussian Mixture Model (GMM) and the…

We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of…

Estimating the frequencies of multiple sinusoids in the presence of AWGN and when the data record is short is commonly accomplished by subspace-based methods such as ESPRIT, MUSIC, Min-Norm, etc. These methods do not assume that the data…

Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction…

In this paper, we address the classical problem of maximum-likelihood (ML) detection of data in the presence of random phase noise. We consider a system, where the random phase noise affecting the received signal is first compensated by a…

Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences and modified…

The recent physical realisation of quantum computers with dozens to hundreds of noisy qubits has given birth to an intense search for useful applications of their unique capabilities. One area that has received particular attention is…

In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…

We derive a general ansatz for optimizing pseudo-C_l estimators used to measure CMB anisotropy power spectra, and apply it to the recently-proposed pure pseudo-C_l formalism, to obtain an estimator which achieves near-optimal B-mode power…

We propose and analyze deterministic multilevel approximations for Bayesian inversion of operator equations with uncertain distributed parameters, subject to additive Gaussian measurement data. The algorithms use a multilevel (ML) approach…

We present a multi-level solver for drawing constrained Gaussian realizations or finding the maximum likelihood estimate of the CMB sky, given noisy sky maps with partial sky coverage. The method converges substantially faster than existing…

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in…

Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum…

Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for…

We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum-bispectrum probe and we tackle the…

Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively,…

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…

An improved estimator for the amplitude fnl of local-type non-Gaussianity from the cosmic microwave background (CMB) bispectrum is discussed. The standard estimator is constructed to be optimal in the zero-signal (i.e., Gaussian) limit.…

Peak statistics in weak lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complement to two-point and higher-order statistics to constrain…