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We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…
Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
The harmonizable Piranashvili-type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed.
Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. For bandlimited signals, the distortion due to additive independent Gaussian…
This paper studies the Bayesian regret of a variant of the Thompson-Sampling algorithm for bandit problems. It builds upon the information-theoretic framework of [Russo and Van Roy, 2015] and, more specifically, on the rate-distortion…
This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…