Divergence measures based on the Shannon entropy

1991/01/01 by J. Lin, Jinfeng Lin · 5,122 citations
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Bayesian Modeling and Causal Inference #Binary entropy function #Combinatorics #Computer science #Discrete mathematics #Distance measures #Divergence (linguistics) #Entropy (arrow of time) #Information theory #Kullback–Leibler divergence #Mathematics #Maximum entropy thermodynamics #Multi-Criteria Decision Making #Principle of maximum entropy #Probability distribution #Probability of error #Rényi entropy #Shannon's source coding theorem #Statistical Mechanics and Entropy #Statistics

paper · doi:10.1109/18.61115

published in IEEE Transactions on Information Theory 37(1), 145-151 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1991/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A novel class of information-theoretic divergence measures based on the Shannon entropy is introduced. Unlike the well-known Kullback divergences, the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved. More importantly, their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds. These bounds are crucial in many applications of divergence measures. The measures are also well characterized by the properties of nonnegativity, finiteness, semiboundedness, and boundedness.>

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• Language Scent: Exploring Cross-Language Information Navigation
• On Divergences and Informations in Statistics and Information Theory
• D²iT: Dynamic Diffusion Transformer for Accurate Image Generation
• HalluShift: Measuring Distribution Shifts towards Hallucination Detection in LLMs
• Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models
• Evaluating the Bias in LLMs for Surveying Opinion and Decision Making in Healthcare
• Evaluating the robustness of explainable AI in medical image recognition under natural and adversarial data corruption
• Underlay Radar-Massive MIMO Spectrum Sharing: Modeling Fundamentals and Performance Analysis
• Coding limits on the number of transcription factors. [europepmc]
• Improved coarse-graining of Markov state models via explicit consideration of statistical uncertainty. [europepmc]
• DiffSplice: the genome-wide detection of differential splicing events with RNA-seq. [europepmc]
• High-order social interactions in groups of mice. [europepmc]
• Cortical regulation of cell size by a sizer cdr2p. [europepmc]
• The vaginal microbiota of pregnant women who subsequently have spontaneous preterm labor and delivery and those with a normal delivery at term. [europepmc]
• Characterizing the Google Books Corpus: Strong Limits to Inferences of Socio-Cultural and Linguistic Evolution. [europepmc]
• DiffLogo: a comparative visualization of sequence motifs. [europepmc]
• Fast and accurate single-cell RNA-seq analysis by clustering of transcript-compatibility counts. [europepmc]
• Oxalobacter formigenes-associated host features and microbial community structures examined using the American Gut Project. [europepmc]
• The Inuit gut microbiome is dynamic over time and shaped by traditional foods. [europepmc]
• Strain profiling and epidemiology of bacterial species from metagenomic sequencing. [europepmc]
• Analyzing Immunoglobulin Repertoires. [europepmc]
• Quantifying size and diversity of the human T cell alloresponse. [europepmc]
• Quality and bias of protein disorder predictors. [europepmc]
• Benchmarking of alignment-free sequence comparison methods. [europepmc]
• Characteristics, service use and mortality of clusters of multimorbid patients in England: a population-based study. [europepmc]
• Identifying inhibitors of epithelial-mesenchymal plasticity using a network topology-based approach. [europepmc]
• Association of Mobile Phone Location Data Indications of Travel and Stay-at-Home Mandates With COVID-19 Infection Rates in the US. [europepmc]
• A multiresolution framework to characterize single-cell state landscapes. [europepmc]
• On the Jensen-Shannon Symmetrization of Distances Relying on Abstract Means. [europepmc]
• Randomized SMILES strings improve the quality of molecular generative models. [europepmc]
• Topological signatures in regulatory network enable phenotypic heterogeneity in small cell lung cancer. [europepmc]
• Predicting retrosynthetic pathways using transformer-based models and a hyper-graph exploration strategy. [europepmc]
• Reconciling functional differences in populations of neurons recorded with two-photon imaging and electrophysiology. [europepmc]

Related

• Characterization of Generalized Alpha-Beta Divergence and Associated Entropy Measures
• Formulation and properties of a divergence used to compare probability measures without absolute continuity and its application to uncertainty quantification
• Formulation and properties of a divergence used to compare probability measures without absolute continuity
• Normalized information-based divergences
• Sequences of Inequalities Among New Divergence Measures