Related papers: Information Theoretic I-MMSE generalize Time-Frequ…
Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as…
In biological systems, information is frequently transferred with Poisson like spike processes (shot noise) modulated in time by information-carrying signals. How then to quantify information transfer for the output for such nonstationary…
This paper presents expression of mutual information that defines the information gain in planning of sensing resources, when the goal is to reduce the forecast uncertainty of some quantities of interest and the system dynamics is described…
We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…
In this paper, we generalize the fundamental relation between the derivative of the mutual information and the minimum mean squared error (MMSE) to multiuser setups. We prove that the derivative of the mutual information with respect to the…
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Green's function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as…
We consider a general stochastic input-output dynamical system with output evolving in time as the solution to a functional coefficients, It\^{o}'s stochastic differential equation, excited by an input process. This general class of…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by…
The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…
This paper gives a replica analysis for the minimum mean square error (MSE) of a massive multiple-input multiple-output (MIMO) system by using Bayesian inference. The Bayes-optimal estimator is adopted to estimate the data symbols and the…
We aim to develop simultaneous inference tools for the mean function of functional data from sparse to dense. First, we derive a unified Gaussian approximation to construct simultaneous confidence bands of mean functions based on the…
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of…
A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve…