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Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
In many biological systems, the network of interactions between the elements can only be inferred from experimental measurements. In neuroscience, non-invasive imaging tools are extensively used to derive either structural or functional…
Measuring the predictability and complexity of time series using entropy is essential tool de-signing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the…
We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in…
Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include,…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method of Chang et al. (2023) for which the convergence rates of the associated estimators may…
By introducing the generalized uncertainty principle, we calculate the entropy of the bulk scalar field on the Randall-Sundrum brane background without any cutoff. We obtain the entropy of the massive scalar field proportional to the…
Analytically continuing the von Neumann entropy from R\'enyi entropies is a challenging task in quantum field theory. While the $n$-th R\'enyi entropy can be computed using the replica method in the path integral representation of quantum…
The matrix pencil method (MPM) is a well-known technique for estimating the parameters of exponentially damped sinusoids in noise by solving a generalized eigenvalue problem. However, in several cases, this is an ill-conditioned problem…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
In this paper, we present a technically simple method to establish upper bounds on the expected injective norm of real and complex random tensors. Our approach is somewhat analogous to the moment method in random matrix theory, and is based…
This paper is concerned with non-parametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random…
Maximum entropy methods provide a principled path connecting measurements of neural activity directly to statistical physics models, and this approach has been successful for populations of $N\sim 100$ neurons. As $N$ increases in new…
The high-dimensional parameter space of deep neural networks -- the neuromanifold -- is endowed with a unique metric tensor defined by the Fisher information. Reliable and scalable computation of this metric tensor is valuable for theorists…
arXiv:1205.2953 defines an entropy for a gaussian scalar field $\phi$ in an arbitrary region of either a causal set or a continuous spacetime, given only the correlator $\langle\phi(x)\phi(y)\rangle$ within the region. As a first…