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Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures.
Research & information: general --- Mathematics & science --- Bregman divergence --- f-divergence --- Jensen-Bregman divergence --- Jensen diversity --- Jensen-Shannon divergence --- capacitory discrimination --- Jensen-Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data-processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson-Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker's inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin-Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference --- Bregman divergence --- f-divergence --- Jensen-Bregman divergence --- Jensen diversity --- Jensen-Shannon divergence --- capacitory discrimination --- Jensen-Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data-processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson-Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker's inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin-Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference
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The recent successes of machine learning, especially regarding systems based on deep neural networks, have encouraged further research activities and raised a new set of challenges in understanding and designing complex machine learning algorithms. New applications require learning algorithms to be distributed, have transferable learning results, use computation resources efficiently, convergence quickly on online settings, have performance guarantees, satisfy fairness or privacy constraints, incorporate domain knowledge on model structures, etc. A new wave of developments in statistical learning theory and information theory has set out to address these challenges. This Special Issue, "Machine Learning and Information Theory", aims to collect recent results in this direction reflecting a diverse spectrum of visions and efforts to extend conventional theories and develop analysis tools for these complex machine learning systems.
Technology: general issues --- History of engineering & technology --- supervised classification --- independent and non-identically distributed features --- analytical error probability --- empirical risk --- generalization error --- K-means clustering --- model compression --- population risk --- rate distortion theory --- vector quantization --- overfitting --- information criteria --- entropy --- model-based clustering --- merging mixture components --- component overlap --- interpretability --- time series prediction --- finite state machines --- hidden Markov models --- recurrent neural networks --- reservoir computers --- long short-term memory --- deep neural network --- information theory --- local information geometry --- feature extraction --- spiking neural network --- meta-learning --- information theoretic learning --- minimum error entropy --- artificial general intelligence --- closed-loop transcription --- linear discriminative representation --- rate reduction --- minimax game --- fairness --- HGR maximal correlation --- independence criterion --- separation criterion --- pattern dictionary --- atypicality --- Lempel–Ziv algorithm --- lossless compression --- anomaly detection --- information-theoretic bounds --- distribution and federated learning
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Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures.
Research & information: general --- Mathematics & science --- Bregman divergence --- f-divergence --- Jensen–Bregman divergence --- Jensen diversity --- Jensen–Shannon divergence --- capacitory discrimination --- Jensen–Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data–processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson–Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker’s inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin–Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference --- n/a --- Jensen-Bregman divergence --- Jensen-Shannon divergence --- Jensen-Shannon centroid --- conditional Rényi divergence --- Rényi divergence --- Rényi mutual information --- strong data-processing inequalities --- Rényi entropy --- Carlson-Levin inequality --- Pinsker's inequality --- Augustin-Csiszár mutual information
Choose an application
Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures.
Bregman divergence --- f-divergence --- Jensen–Bregman divergence --- Jensen diversity --- Jensen–Shannon divergence --- capacitory discrimination --- Jensen–Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data–processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson–Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker’s inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin–Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference --- n/a --- Jensen-Bregman divergence --- Jensen-Shannon divergence --- Jensen-Shannon centroid --- conditional Rényi divergence --- Rényi divergence --- Rényi mutual information --- strong data-processing inequalities --- Rényi entropy --- Carlson-Levin inequality --- Pinsker's inequality --- Augustin-Csiszár mutual information
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