Related papers: Kullback-Leibler and Renormalized Entropy: Applica…
Pattern classification in electroencephalography (EEG) signals is an important problem in biomedical engineering since it enables the detection of brain activity, particularly the early detection of epileptic seizures. In this paper, we…
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…
Epilepsy is one of the most common neurological diseases, characterized by transient and unprovoked events called epileptic seizures. Electroencephalogram (EEG) is an auxiliary method used to perform both the diagnosis and the monitoring of…
This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative…
Epilepsy is a prevalent neurological disorder marked by sudden, brief episodes of excessive neuronal activity caused by abnormal electrical discharges, which may lead to some mental disorders. Most existing deep learning methods for…
Identifying abnormal electroencephalographic activity is crucial in diagnosis and treatment of epilepsy. Recent studies showed that decomposing brain activity into periodic (oscillatory) and aperiodic (trend across all frequencies)…
We consider predictive density estimation under logarithmic score for $d$-dimensional infinitely divisible location models. Taking the formal Bayes predictive density under the Lebesgue prior as a benchmark, we study the Kullback-Leibler…
Scalp electroencephalography (EEG) and intracranial EEG (iEEG) are vital for epilepsy diagnosis and treatment. Their unified analysis offers the potential to harness the complementary strengths of each modality but is challenging due to…
Successful epilepsy surgery depends on localising and resecting cerebral abnormalities and networks that generate seizures. Abnormalities, however, may be widely distributed across multiple discontiguous areas. We propose spatially…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
We study a new ensemble of random correlation matrices related to multivariate Student (or more generally elliptic) random variables. We establish the exact density of states of empirical correlation matrices that generalizes the…
The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $\sigma$-finite measure, and not necessarily a probability measure. Under this…
Timely diagnosis is important for saving the life of epileptic patients. In past few years, a lot of treatments are available for epilepsy. These treatments require use of anti-seizure drugs but are not effective in controlling frequency of…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…
We present a measure for characterizing statistical relationships between two time sequences. In contrast to commonly used measures like cross-correlations, coherence and mutual information, the proposed measure is non-symmetric and…
We show that the moment generating function of the Kullback-Leibler divergence (relative entropy) between the empirical distribution of $n$ independent samples from a distribution $P$ over a finite alphabet of size $k$ (i.e. a multinomial…
We show how recent results of Lieb and Seiringer [math-ph/0412009; Phys. Rev. A 71, 062329 (2005)] can be obtained from repeated use of the monotonicity of relative entropy under partial traces, and explain how to use their approach to…
Using a new regulator, we examine 't Hooft's approach for evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon. We find that this calculation yields…
Inherent fuzzy entropy is an objective measurement of electroencephalography (EEG) complexity, reflecting the robustness of brain systems. In this study, we present a novel application of multi-scale relative inherent fuzzy entropy using…