IEEE Transactions on Information Theory, ISSN 0018-9448, 02/2015, Volume 61, Issue 2, pp. 708 - 714

The classical entropy power inequality is extended to the Rényi entropy. We also discuss the question of the existence of the entropy for sums of independent...

entropy power inequality | Atmospheric measurements | Tin | Particle measurements | Educational institutions | Entropy | Vectors | Random variables | Renyi entropy | CONVERSE | COMPUTER SCIENCE, INFORMATION SYSTEMS | PROOF | YOUNGS-INEQUALITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Random noise theory | Usage | Innovations | Information theory

entropy power inequality | Atmospheric measurements | Tin | Particle measurements | Educational institutions | Entropy | Vectors | Random variables | Renyi entropy | CONVERSE | COMPUTER SCIENCE, INFORMATION SYSTEMS | PROOF | YOUNGS-INEQUALITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Random noise theory | Usage | Innovations | Information theory

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 05/2010, Volume 32, Issue 5, pp. 847 - 860

We introduce kernel entropy component analysis (kernel ECA) as a new method for data transformation and dimensionality reduction. Kernel ECA reveals structure...

Laplace equations | Multidimensional systems | Noise reduction | Spectral data transformation | Entropy | kernel PCA | Statistics | Machine intelligence | pattern denoising | Parzen windowing | Clustering algorithms | Eigenvalues and eigenfunctions | clustering | Kernel | Principal component analysis | Renyi entropy | Kernel PCA | Pattern denoising | Clustering | DIMENSIONALITY REDUCTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | PCA | ENGINEERING, ELECTRICAL & ELECTRONIC | Models, Theoretical | Algorithms | Information Storage and Retrieval - methods | Artificial Intelligence | Computer Simulation | Database Management Systems | Pattern Recognition, Automated - methods | Databases, Factual | Usage | Pattern recognition | Kernel functions | Object recognition (Computers) | Entropy (Information theory) | Analysis | Kernels | Reduction | Intelligence | Eigenvalues | Transformations | Spectra | Pattern analysis | Index Medicus

Laplace equations | Multidimensional systems | Noise reduction | Spectral data transformation | Entropy | kernel PCA | Statistics | Machine intelligence | pattern denoising | Parzen windowing | Clustering algorithms | Eigenvalues and eigenfunctions | clustering | Kernel | Principal component analysis | Renyi entropy | Kernel PCA | Pattern denoising | Clustering | DIMENSIONALITY REDUCTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | PCA | ENGINEERING, ELECTRICAL & ELECTRONIC | Models, Theoretical | Algorithms | Information Storage and Retrieval - methods | Artificial Intelligence | Computer Simulation | Database Management Systems | Pattern Recognition, Automated - methods | Databases, Factual | Usage | Pattern recognition | Kernel functions | Object recognition (Computers) | Entropy (Information theory) | Analysis | Kernels | Reduction | Intelligence | Eigenvalues | Transformations | Spectra | Pattern analysis | Index Medicus

Journal Article

Entropy, ISSN 1099-4300, 03/2016, Volume 18, Issue 3, pp. 84 - 84

The entropies of Shannon, Renyi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a...

Iterated function system | Box-counting dimension | Fractal dimension | Rényi entropy | Generalized fractal dimension | Shannon entropy | Fractal antenna | Kolmogorov entropy | fractal antenna | iterated function system | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | COMPLEXITY | fractal dimension | generalized fractal dimension | box-counting dimension | Renyi entropy | SIERPINSKI | Fractals | Entropy | Entropy (Information) | Fractal analysis | Antennas | Matematisk analys | Computational Mathematics | Mathematics | Mathematical Analysis | Naturvetenskap | Natural Sciences | Beräkningsmatematik | Mathematics/Applied Mathematics | Matematik | matematik/tillämpad matematik

Iterated function system | Box-counting dimension | Fractal dimension | Rényi entropy | Generalized fractal dimension | Shannon entropy | Fractal antenna | Kolmogorov entropy | fractal antenna | iterated function system | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | COMPLEXITY | fractal dimension | generalized fractal dimension | box-counting dimension | Renyi entropy | SIERPINSKI | Fractals | Entropy | Entropy (Information) | Fractal analysis | Antennas | Matematisk analys | Computational Mathematics | Mathematics | Mathematical Analysis | Naturvetenskap | Natural Sciences | Beräkningsmatematik | Mathematics/Applied Mathematics | Matematik | matematik/tillämpad matematik

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 01/2018, Volume 64, Issue 1, pp. 4 - 25

This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Rényi conditional...

Error probability | Rényi entropy | Entropy | Chernoff information | random coding | Channel coding | Arimoto-Rényi conditional entropy | Upper bound | Rényi divergence | list decoding | Bayesian minimum probability of error | Bayes methods | M -ary hypothesis testing">M -ary hypothesis testing | Fano’s inequality | Testing | Fano's inequality | List decoding | M-ary hypothesis testing | Random coding | Bayes' theorem | Error-correcting codes | Usage | Entropy (Information theory) | Lower bounds | Codes | Divergence | Upper bounds | Tightness | Bayesian analysis

Error probability | Rényi entropy | Entropy | Chernoff information | random coding | Channel coding | Arimoto-Rényi conditional entropy | Upper bound | Rényi divergence | list decoding | Bayesian minimum probability of error | Bayes methods | M -ary hypothesis testing">

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2019, Volume 65, Issue 3, pp. 1387 - 1396

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive...

Geometry | Additives | Power measurement | Rényi entropy | Optimized production technology | log-concave | Entropy | Random variables | Information theory | Entropy power inequality | CONVERSE | Terms Entropy power inequality | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MONOTONICITY | SUM | BRUNN-MINKOWSKI | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC

Geometry | Additives | Power measurement | Rényi entropy | Optimized production technology | log-concave | Entropy | Random variables | Information theory | Entropy power inequality | CONVERSE | Terms Entropy power inequality | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MONOTONICITY | SUM | BRUNN-MINKOWSKI | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 11/2014, Volume 60, Issue 11, pp. 6801 - 6810

The Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or collision entropy. In...

Uncertainty | Measurement uncertainty | Biomedical measurement | Entropy | Random variables | Joints | Information theory | monotonicity and chain rule | Rényi divergence | Conditial Rényi entropy | quantum Rényi entropy | Conditial Renyi entropy | quantum Renyi entropy | Renyi divergence | BOUNDS | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | PRIVACY AMPLIFICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Maximum entropy method | Divergence | Entropy (Information) | Consistency | Chains | Conditioning

Uncertainty | Measurement uncertainty | Biomedical measurement | Entropy | Random variables | Joints | Information theory | monotonicity and chain rule | Rényi divergence | Conditial Rényi entropy | quantum Rényi entropy | Conditial Renyi entropy | quantum Renyi entropy | Renyi divergence | BOUNDS | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | PRIVACY AMPLIFICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Maximum entropy method | Divergence | Entropy (Information) | Consistency | Chains | Conditioning

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2014, Volume 60, Issue 9, pp. 5065 - 5076

A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed....

Context | Upper bound | Entropy | Source coding | Channel coding | Rate-distortion | Rényi entropy rate | source coding | Rényi entropy | tasks | mismatch | Renyi entropy rate | GUESSWORK | Divergence | CUTOFF RATES | COMPUTER SCIENCE, INFORMATION SYSTEMS | LARGE DEVIATIONS | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC | Error-correcting codes | Evaluation | Usage | Data compression | Entropy (Information theory) | Methods | Electrical engineering

Context | Upper bound | Entropy | Source coding | Channel coding | Rate-distortion | Rényi entropy rate | source coding | Rényi entropy | tasks | mismatch | Renyi entropy rate | GUESSWORK | Divergence | CUTOFF RATES | COMPUTER SCIENCE, INFORMATION SYSTEMS | LARGE DEVIATIONS | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC | Error-correcting codes | Evaluation | Usage | Data compression | Entropy (Information theory) | Methods | Electrical engineering

Journal Article

IEEE Transactions on Biomedical Engineering, ISSN 0018-9294, 11/2017, Volume 64, Issue 11, pp. 2711 - 2718

Objective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new...

Measurement | Estimation | conditional Rényi permutation entropy | Entropy | Electronic mail | permutation entropy | r parameter elimination">r parameter elimination | Sorting | HRV timeseries | Physiology | Bubble entropy | embedding dimension | Heart rate variability | entropy | ELECTROENCEPHALOGRAM | r parameter elimination | ENGINEERING, BIOMEDICAL | conditional Renyi permutation entropy | HEART-RATE-VARIABILITY | COMPLEXITY | HRV time-series | Algorithms | Computer Simulation | Humans | Middle Aged | Heart Failure - physiopathology | Electrocardiography | Heart Rate - physiology | Signal Processing, Computer-Assisted | Adult | Aged | Signal processing | Research | Permutations | Parameter estimation | Bubbles | Decoupling | Stability | Mathematical analysis | Data processing | Embedding | Critical point | Vectors (mathematics) | Sorting algorithms | Index Medicus

Measurement | Estimation | conditional Rényi permutation entropy | Entropy | Electronic mail | permutation entropy | r parameter elimination">

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 12/2016, Volume 62, Issue 12, pp. 6800 - 6815

This paper gives improved Rényi entropy power inequalities (R-EPIs). Consider a sum S n = Σ k=1 n X k of n independent continuous random vectors taking values...

entropy power inequality | Rényi entropy | Rényi entropy power | Random access memory | Probability density function | Entropy | Eigenvalues and eigenfunctions | MIMO | Random variables | Information theory | CONVERSE | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MONOTONICITY | YOUNGS-INEQUALITY | Renyi entropy power | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Random noise theory | Entropy (Information theory) | MIMO communications | Matrix | Optimization

entropy power inequality | Rényi entropy | Rényi entropy power | Random access memory | Probability density function | Entropy | Eigenvalues and eigenfunctions | MIMO | Random variables | Information theory | CONVERSE | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MONOTONICITY | YOUNGS-INEQUALITY | Renyi entropy power | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Random noise theory | Entropy (Information theory) | MIMO communications | Matrix | Optimization

Journal Article

Information Sciences, ISSN 0020-0255, 2009, Volume 179, Issue 14, pp. 2426 - 2433

In this paper, we define the conditional Rényi entropy and show that the so-called chain rule holds for the Rényi entropy. Then, we introduce a relation for...

Shannon entropy | Shannon entropy rate | Stationary process | Rényi entropy rate | Rényi entropy | Quasi-linear mean | Renyi entropy rate | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | CONVERGENCE | SYSTEMS | DIVERGENCE | FUNCTIONALS | Renyi entropy | Markov processes | Analysis

Shannon entropy | Shannon entropy rate | Stationary process | Rényi entropy rate | Rényi entropy | Quasi-linear mean | Renyi entropy rate | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | CONVERGENCE | SYSTEMS | DIVERGENCE | FUNCTIONALS | Renyi entropy | Markov processes | Analysis

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 08/2013, Volume 66, Issue 2, pp. 135 - 146

The is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase...

Fractal geometry | Fractal dimension | Rényi entropy | Shannon entropy | Thermodynamic entropy | Fractal physics | Fractal measure | Kolmogorov entropy | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIMENSION | Renyi entropy | Chaos theory

Fractal geometry | Fractal dimension | Rényi entropy | Shannon entropy | Thermodynamic entropy | Fractal physics | Fractal measure | Kolmogorov entropy | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIMENSION | Renyi entropy | Chaos theory

Journal Article

Wuli Huaxue Xuebao/ Acta Physico - Chimica Sinica, ISSN 1000-6818, 11/2015, Volume 31, Issue 11, pp. 2057 - 2063

Density functional theory dictates that the electron density determines everything in a molecular system's ground state, including its structure and reactivity...

Density functional reactivity theory | Shannon entropy | Rényi entropy | Tsallis entropy | Onicescu information energy | QUANTITIES | ELECTROPHILICITY | CHEMISTRY, PHYSICAL | HIRSHFELD CHARGE | AROMATIC-SUBSTITUTION REACTIONS | MOLECULES | FRAGMENTS | THERMODYNAMICS | ATOMS | NUCLEOPHILICITY | SYSTEMS | Renyi entropy

Density functional reactivity theory | Shannon entropy | Rényi entropy | Tsallis entropy | Onicescu information energy | QUANTITIES | ELECTROPHILICITY | CHEMISTRY, PHYSICAL | HIRSHFELD CHARGE | AROMATIC-SUBSTITUTION REACTIONS | MOLECULES | FRAGMENTS | THERMODYNAMICS | ATOMS | NUCLEOPHILICITY | SYSTEMS | Renyi entropy

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 02/2005, Volume 51, Issue 2, pp. 473 - 478

The moment-entropy inequality shows that a continuous random variable with given second moment and maximal Shannon entropy must be Gaussian. Stam's inequality...

Information measure | Entropy | Moment | Fisher information | Information theory | Renyi entropy | entropy | COMPUTER SCIENCE, INFORMATION SYSTEMS | information theory | information measure | moment | SOBOLEV | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Theory | Information systems | Gaussian | Random variables | Density | Inequalities

Information measure | Entropy | Moment | Fisher information | Information theory | Renyi entropy | entropy | COMPUTER SCIENCE, INFORMATION SYSTEMS | information theory | information measure | moment | SOBOLEV | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Theory | Information systems | Gaussian | Random variables | Density | Inequalities

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2008, Volume 36, Issue 5, pp. 2153 - 2182

A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in ${\Bbb R}^{m}$ is presented. These estimators are based on the kth...

Density estimation | Gaussian distributions | Shannon entropy | Entropy | Sampling distributions | Statistics | Estimators | Consistent estimators | Estimation methods | Estimation of divergence | Rényi entropy | Tsallis entropy | Entropy estimation | Estimation of statistical distance | Havrda-Charvát entropy | Nearest-neighbor distances | nearest-neighbor distances | estimation of divergence | STATISTICS | STATISTICS & PROBABILITY | NEAREST NEIGHBOR DISTANCES | GRAPHS | DISTRIBUTIONS | estimation of statistical distance | CONSISTENCY | LIMIT-THEOREMS | ENTROPY ESTIMATORS | ASYMPTOTICS | SAMPLE ENTROPY | Havrda-Charvat entropy | FUNCTIONALS | Renyi entropy | Studies | Statistical analysis | Normal distribution | Estimates | Statistics Theory | Mathematics | 94A15 | Havrda–Charvát entropy | 62G20

Density estimation | Gaussian distributions | Shannon entropy | Entropy | Sampling distributions | Statistics | Estimators | Consistent estimators | Estimation methods | Estimation of divergence | Rényi entropy | Tsallis entropy | Entropy estimation | Estimation of statistical distance | Havrda-Charvát entropy | Nearest-neighbor distances | nearest-neighbor distances | estimation of divergence | STATISTICS | STATISTICS & PROBABILITY | NEAREST NEIGHBOR DISTANCES | GRAPHS | DISTRIBUTIONS | estimation of statistical distance | CONSISTENCY | LIMIT-THEOREMS | ENTROPY ESTIMATORS | ASYMPTOTICS | SAMPLE ENTROPY | Havrda-Charvat entropy | FUNCTIONALS | Renyi entropy | Studies | Statistical analysis | Normal distribution | Estimates | Statistics Theory | Mathematics | 94A15 | Havrda–Charvát entropy | 62G20

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 05/2018, Volume 498, pp. 74 - 85

One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity–entropy causality plane. This diagram...

Ordinal patterns probabilities | Rényi entropy | Complexity measures | Time series | STATISTICAL MEASURE | PHYSICS, MULTIDISCIPLINARY | INFORMATION | DIVERGENCE | ORDER PATTERNS | Renyi entropy | CAUSALITY PLANE

Ordinal patterns probabilities | Rényi entropy | Complexity measures | Time series | STATISTICAL MEASURE | PHYSICS, MULTIDISCIPLINARY | INFORMATION | DIVERGENCE | ORDER PATTERNS | Renyi entropy | CAUSALITY PLANE

Journal Article

Signal Processing, ISSN 0165-1684, 12/2016, Volume 129, pp. 17 - 24

This paper presents two TFD optimization schemes, extending an optimization method so far limited to the spectrogram. The first method is focused on the...

Quadratic time–frequency distributions | Rényi entropy | S-method | Optimization | Quadratic time-frequency distributions | REPRESENTATION | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Electric properties | Kernels | Signal processing | Entropy (Information theory) (Information) | Criteria | Spectrograms

Quadratic time–frequency distributions | Rényi entropy | S-method | Optimization | Quadratic time-frequency distributions | REPRESENTATION | Renyi entropy | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Electric properties | Kernels | Signal processing | Entropy (Information theory) (Information) | Criteria | Spectrograms

Journal Article

Physics Letters B, ISSN 0370-2693, 10/2015, Volume 749, Issue C, pp. 383 - 388

In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE) and Rényi entropies for 3d CFTs have a logarithmic...

Entanglement entropy | 3-Dimensional field theory | Renyi entropy | PHYSICS, NUCLEAR | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | High Energy Physics - Theory | Physics

Entanglement entropy | 3-Dimensional field theory | Renyi entropy | PHYSICS, NUCLEAR | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | High Energy Physics - Theory | Physics

Journal Article

Entropy, ISSN 1099-4300, 06/2019, Volume 21, Issue 6

The well-known Holder's inequality has been recently utilized as an essential tool for solving several optimization problems. However, such an essential role...

Rényi-Tsallis entropy | Hölder's inequality | Generalized entropy | Optimization | DISTRIBUTIONS | Renyi-Tsallis entropy | MAXIMUM-ENTROPY | LAW | PHYSICS, MULTIDISCIPLINARY | optimization | Holder's inequality | PRINCIPLE | generalized entropy

Rényi-Tsallis entropy | Hölder's inequality | Generalized entropy | Optimization | DISTRIBUTIONS | Renyi-Tsallis entropy | MAXIMUM-ENTROPY | LAW | PHYSICS, MULTIDISCIPLINARY | optimization | Holder's inequality | PRINCIPLE | generalized entropy

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2016, Volume 62, Issue 3, pp. 1193 - 1205

The supremum of the Rényi entropy rate over the class of discrete-time stationary stochastic processes, whose marginals are supported by some given set and...

Renyi entropy rate | Density measurement | entropy rate | Stochastic processes | maximization | Entropy | Electronic mail | spectrum estimation | Indexes | Upper bound | Probability density function | Burg's Theorem | Renyi entropy | Rényi entropy rate | Rényi entropy | GUESSWORK | INEQUALITY | COMPUTER SCIENCE, INFORMATION SYSTEMS | LARGE DEVIATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Stochastic models | Normal distribution | Information theory | Entropy (Information) | Computation | Mathematical analysis | Mathematical models | Logarithms | Vectors (mathematics)

Renyi entropy rate | Density measurement | entropy rate | Stochastic processes | maximization | Entropy | Electronic mail | spectrum estimation | Indexes | Upper bound | Probability density function | Burg's Theorem | Renyi entropy | Rényi entropy rate | Rényi entropy | GUESSWORK | INEQUALITY | COMPUTER SCIENCE, INFORMATION SYSTEMS | LARGE DEVIATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Stochastic models | Normal distribution | Information theory | Entropy (Information) | Computation | Mathematical analysis | Mathematical models | Logarithms | Vectors (mathematics)

Journal Article

International Journal of Modern Physics D, ISSN 0218-2718, 09/2017, Volume 26, Issue 10, p. 1750105

The Rényi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a function of its order...

Bekenstein bound | quantum particle gases | Rényi entropy | holographic theories | black holes | entropic bounds | mechanical statistics | Quantum gravity | ASTRONOMY & ASTROPHYSICS | Renyi entropy | Particle spin | Order parameters | Entropy

Bekenstein bound | quantum particle gases | Rényi entropy | holographic theories | black holes | entropic bounds | mechanical statistics | Quantum gravity | ASTRONOMY & ASTROPHYSICS | Renyi entropy | Particle spin | Order parameters | Entropy

Journal Article

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