Related papers: The Relative Information Generating Function-A Qua…
This study aims to quantify and visualize the degradation of fidelity (information degradation) that inevitably accompanies the replication of information within the framework of information thermodynamics and to propose an…
Recently, continual learning has received a lot of attention. One of the significant problems is the occurrence of \emph{concept drift}, which consists of changing probabilistic characteristics of the incoming data. In the case of the…
Entropy-like functionals on operator algebras have been studied since the pioneering work of von Neumann, Umegaki, Lindblad, and Lieb. The most well-known are the von Neumann entropy $trace (\rho\log \rho)$ and a generalization of the…
Latent variable models are crucial in scientific research, where a key variable, such as effort, ability, and belief, is unobserved in the sample but needs to be identified. This paper proposes a novel method for estimating realizations of…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
Recently, varextropy has been introduced as a new dispersion index and a measure of information. In this article, we derive the generating function of extropy and present its infinite series representation. Furthermore, we propose new…
Classical approaches in recommender systems such as collaborative filtering are concentrated mainly on static user preference extraction. This approach works well as an example for music recommendations when a user behavior tends to be…
Effective uncertainty quantification is important for training modern predictive models with limited data, enhancing both accuracy and robustness. While Bayesian methods are effective for this purpose, they can be challenging to scale. When…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry,…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into…
Obtaining an accurate estimate of the underlying covariance matrix from finite sample size data is challenging due to sample size noise. In recent years, sophisticated covariance-cleaning techniques based on random matrix theory have been…
In this work we introduce a family of transformations, named \textit{divergence transformations}, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole…
We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs.…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
The entropy is one of the most applicable uncertainty measures in many statistical and en- gineering problems. In statistical literature, the entropy is used in calculation of the Kullback- Leibler (KL) information which is a powerful mean…
In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches…
We prove characterization theorems for relative entropy (also known as Kullback-Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically…