Bernoulli, ISSN 1350-7265, 05/2015, Volume 21, Issue 2, pp. 1231 - 1237

Let epsilon(1) . . . . . epsilon(n) be independent identically distributed Rademacher random variables, that is P{epsilon(i) = +/- 1) = 1/2. Let S-n =a(1)epsilon(1) + . . . +a(n)epsilon(n). where a = (a(1) . . . . . a(n...

Tail comparison | Self-normalized sums | Weighted Rademachers | Random sign | Optimal constants | Student's statistic | Gaussian | Large deviations | Symmetric | Bounds for tail probabilities | large deviations | optimal constants | bounds for tail probabilities | STATISTICS & PROBABILITY | symmetric | random sign | self-normalized sums | tail comparison | weighted Rademachers | Mathematics - Probability | Student’s statistic

Tail comparison | Self-normalized sums | Weighted Rademachers | Random sign | Optimal constants | Student's statistic | Gaussian | Large deviations | Symmetric | Bounds for tail probabilities | large deviations | optimal constants | bounds for tail probabilities | STATISTICS & PROBABILITY | symmetric | random sign | self-normalized sums | tail comparison | weighted Rademachers | Mathematics - Probability | Student’s statistic

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 11/2019, Volume 37, Issue 6, pp. 1092 - 1106

In this correspondence, complete convergence theorems are established for weighted row sums from arrays of random elements taking values in real separable Rademacher type Banach spaces as well as real...

array of Banach space valued random elements | Secondary 60B11 | rowwise independent | Primary 60F15 | Complete convergence | weighted row sums | martingale type p Banach space | Rademacher type p Banach space | martingale differences | Theorems | Banach spaces | Random variables | Arrays | Banach space | Martingales | Sums | Convergence

array of Banach space valued random elements | Secondary 60B11 | rowwise independent | Primary 60F15 | Complete convergence | weighted row sums | martingale type p Banach space | Rademacher type p Banach space | martingale differences | Theorems | Banach spaces | Random variables | Arrays | Banach space | Martingales | Sums | Convergence

Journal Article

3.
Full Text
Multiple source domain adaptation: A sharper bound using weighted Rademacher complexity

2015 Conference on Technologies and Applications of Artificial Intelligence (TAAI), 11/2015, pp. 546 - 553

.... In this paper, we introduce a novelty complexity (weighted Rademacher complexity) to restrict the complexity of a hypothesis class in multiple source domain adaptation...

multiple source domain adaptation | weighted combination | Rademacher complexity | learning bound | Learning | Training | Conferences | Benchmarking | Artificial intelligence | Expert systems | Complexity | Adaptation

multiple source domain adaptation | weighted combination | Rademacher complexity | learning bound | Learning | Training | Conferences | Benchmarking | Artificial intelligence | Expert systems | Complexity | Adaptation

Conference Proceeding

Stochastic Analysis and Applications, ISSN 0736-2994, 01/2003, Volume 21, Issue 5, pp. 1169 - 1187

...} is an array of mean 0 random elements in a separable real Rademacher type p (1 ≤ p ≤ 2) Banach space, and {k n , n ≥ 1} and {T n , n ≥ 1} are sequences of positive integers and positive integer-valued random variables, respectively...

Separable real Rademacher type p Banach space | Mean convergence | Array of rowwise independent random elements | Random indices | Random weights | Weighted sums | Separable real rademacher type p Banach space | random indices | NORMED LINEAR-SPACES | MATHEMATICS, APPLIED | LARGE NUMBERS | UNIFORM INTEGRABILITY | STATISTICS & PROBABILITY | ARRAYS | weighted sums | random weights | WEAK LAW | separable real Rademacher type p Banach space | array of rowwise independent random elements | mean convergence

Separable real Rademacher type p Banach space | Mean convergence | Array of rowwise independent random elements | Random indices | Random weights | Weighted sums | Separable real rademacher type p Banach space | random indices | NORMED LINEAR-SPACES | MATHEMATICS, APPLIED | LARGE NUMBERS | UNIFORM INTEGRABILITY | STATISTICS & PROBABILITY | ARRAYS | weighted sums | random weights | WEAK LAW | separable real Rademacher type p Banach space | array of rowwise independent random elements | mean convergence

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 03/2018, Volume 716, pp. 89 - 106

.... We present new data-dependent generalization guarantees for learning weighted automata expressed in terms of the Rademacher complexity of these classes...

Generalization bounds | Weighted automata | Learning theory | Rademacher complexity | COMPUTER SCIENCE, THEORY & METHODS | Robots

Generalization bounds | Weighted automata | Learning theory | Rademacher complexity | COMPUTER SCIENCE, THEORY & METHODS | Robots

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 7/1997, Volume 10, Issue 3, pp. 605 - 623

...} in a real separable Rademacher type p (1≤p≤2) Banach space, and a sequence of positive integer-valued random variables {T n, n≥1...

random indices | weighted sums | Probability Theory and Stochastic Processes | Mathematics | weak law of large numbers | Statistics, general | Rademacher type p Banach space | array of rowwise independent random elements | Array of rowwise independent random elements | Random indices | Weak law of large numbers | Weighted sums | LARGE NUMBERS | VALUED RANDOM-VARIABLES | STATISTICS & PROBABILITY | SUMS

random indices | weighted sums | Probability Theory and Stochastic Processes | Mathematics | weak law of large numbers | Statistics, general | Rademacher type p Banach space | array of rowwise independent random elements | Array of rowwise independent random elements | Random indices | Weak law of large numbers | Weighted sums | LARGE NUMBERS | VALUED RANDOM-VARIABLES | STATISTICS & PROBABILITY | SUMS

Journal Article

Electronic journal of statistics, ISSN 1935-7524, 2009, Volume 3, pp. 557 - 624

In this paper, a new family of resampling-based penalization procedures for model selection is defined in a general framework. It generalizes several methods,...

Adaptivity | Penalization | Model selection | Histogram selection | Non-parametric regression | Regressogram | Resampling | Heteroscedastic data | Non-parametric statistics | Exchangeable weighted bootstrap | non-parametric regression | ERROR RATE | RISK MINIMIZATION | NEGATIVE MOMENTS | model selection | STATISTICS & PROBABILITY | PREDICTION RULE | LOCAL RADEMACHER COMPLEXITIES | resampling | adaptivity | histogram selection | BOOTSTRAP | regressogram | exchangeable weighted bootstrap | CROSS-VALIDATION | penalization | heteroscedastic data | CONVERGENCE | PENALTIES | GAUSSIAN REGRESSION | Statistics | Statistics Theory | Mathematics

Adaptivity | Penalization | Model selection | Histogram selection | Non-parametric regression | Regressogram | Resampling | Heteroscedastic data | Non-parametric statistics | Exchangeable weighted bootstrap | non-parametric regression | ERROR RATE | RISK MINIMIZATION | NEGATIVE MOMENTS | model selection | STATISTICS & PROBABILITY | PREDICTION RULE | LOCAL RADEMACHER COMPLEXITIES | resampling | adaptivity | histogram selection | BOOTSTRAP | regressogram | exchangeable weighted bootstrap | CROSS-VALIDATION | penalization | heteroscedastic data | CONVERGENCE | PENALTIES | GAUSSIAN REGRESSION | Statistics | Statistics Theory | Mathematics

Journal Article

8.
Full Text
A weak law for normed weighted sums of random elements in rademacher type p banach spaces

Journal of Multivariate Analysis, ISSN 0047-259X, 1991, Volume 37, Issue 2, pp. 259 - 268

For weighted sums Σ j = 1 n a j V j of independent random elements { V n , n ≥ 1} in real separable, Rademacher type p...

real separable Rademacher type p Banach space | convergence in probability | weak law of large numbers | independent random elements | normed weighted sums | stochastically dominated random elements | LARGE NUMBERS | REAL SEPARABLE RADEMACHER TYPE-P BANACH SPACE | NORMED WEIGHTED SUMS | STABILITY | VALUED RANDOM-VARIABLES | CONVERGENCE IN PROBABILITY | STATISTICS & PROBABILITY | WEAK LAW OF LARGE NUMBERS | INDEPENDENT RANDOM ELEMENTS | STOCHASTICALLY DOMINATED RANDOM ELEMENTS | real separable Rademacher type p Banach space independent random elements normed weighted sums weak law of large numbers convergence in probability stochastically dominated random elements

real separable Rademacher type p Banach space | convergence in probability | weak law of large numbers | independent random elements | normed weighted sums | stochastically dominated random elements | LARGE NUMBERS | REAL SEPARABLE RADEMACHER TYPE-P BANACH SPACE | NORMED WEIGHTED SUMS | STABILITY | VALUED RANDOM-VARIABLES | CONVERGENCE IN PROBABILITY | STATISTICS & PROBABILITY | WEAK LAW OF LARGE NUMBERS | INDEPENDENT RANDOM ELEMENTS | STOCHASTICALLY DOMINATED RANDOM ELEMENTS | real separable Rademacher type p Banach space independent random elements normed weighted sums weak law of large numbers convergence in probability stochastically dominated random elements

Journal Article

Sankhyā: The Indian Journal of Statistics (2003-2007), ISSN 0972-7671, 5/2007, Volume 69, Issue 2, pp. 330 - 343

...} in a real separable Rademacher type p Banach space for some p ∈ [1, 2], and a sequence of positive integer-valued random variables {Tn, n ≥ 1...

Integers | Mathematical theorems | Law of large numbers | Expected values | Separable spaces | Positive laws | Random variables | Banach space | Limit Laws and Convergence | Perceptron convergence procedure | Array of rowwise independent random elements | Random indices | Rademacher type p Banach space | Weak law of large numbers | Weighted sums

Integers | Mathematical theorems | Law of large numbers | Expected values | Separable spaces | Positive laws | Random variables | Banach space | Limit Laws and Convergence | Perceptron convergence procedure | Array of rowwise independent random elements | Random indices | Rademacher type p Banach space | Weak law of large numbers | Weighted sums

Journal Article

Lithuanian Mathematical Journal, ISSN 0363-1672, 10/2014, Volume 54, Issue 4, pp. 403 - 408

Let ε, ε1, ε2, . . . be independent identically distributed Rademacher random variables, P{ε = ± 1} = 1/2. Denote S = ∑ i = 1 ∞ a i ε i , where a1, a2, . . . is a (weight...

Ordinary Differential Equations | bounds for tail probabilities | weighted sums of Rademacher random variables | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Actuarial Sciences | Number Theory | random signs | MATHEMATICS | INEQUALITIES | QUADRATIC OPTIMIZATION | BOUNDS | PRODUCT | SUMS

Ordinary Differential Equations | bounds for tail probabilities | weighted sums of Rademacher random variables | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Actuarial Sciences | Number Theory | random signs | MATHEMATICS | INEQUALITIES | QUADRATIC OPTIMIZATION | BOUNDS | PRODUCT | SUMS

Journal Article

ACTA MATHEMATICA SINICA-ENGLISH SERIES, ISSN 1439-8516, 04/2012, Volume 28, Issue 4, pp. 857 - 868

The paper investigates L (p) convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition that the Banach space is of Rademacher type p, 1 < p < 2...

WEIGHTED SUMS | MATHEMATICS | MATHEMATICS, APPLIED | L-r convergence | LARGE NUMBERS | Rademacher type p | WEAK LAW | UNIFORM INTEGRABILITY | THEOREMS | random element | Marcinkiewicz-Zygmund strong law of large number | P BANACH-SPACES

WEIGHTED SUMS | MATHEMATICS | MATHEMATICS, APPLIED | L-r convergence | LARGE NUMBERS | Rademacher type p | WEAK LAW | UNIFORM INTEGRABILITY | THEOREMS | random element | Marcinkiewicz-Zygmund strong law of large number | P BANACH-SPACES

Journal Article

12.
Full Text
Strong laws of large numbers for weighted sums of random elements in normed linear spaces

International journal of mathematics and mathematical sciences, ISSN 1687-0425, 1989, Volume 12, Issue 3, pp. 507 - 529

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 01/2004, Volume 22, Issue 4, pp. 1111 - 1120

.... No geometric conditions on are required for this result. Moreover, when is of Rademacher type p (1 < p ≤ 2...

Slowly varying function | Secondary 60B11 | Real separable Banach space | Almost sure convergence | Independent and identically distributed random elements | Normed weighted sums | Primary 60B12 | Rademacher type p Banach space | Convergence in probability | real separable Banach space | MATHEMATICS, APPLIED | independent and identically distributed random elements | LARGE NUMBERS | LAW | almost sure convergence | slowly varying function | convergence in probability | STATISTICS & PROBABILITY | normed weighted sums | RANDOM-VARIABLES

Slowly varying function | Secondary 60B11 | Real separable Banach space | Almost sure convergence | Independent and identically distributed random elements | Normed weighted sums | Primary 60B12 | Rademacher type p Banach space | Convergence in probability | real separable Banach space | MATHEMATICS, APPLIED | independent and identically distributed random elements | LARGE NUMBERS | LAW | almost sure convergence | slowly varying function | convergence in probability | STATISTICS & PROBABILITY | normed weighted sums | RANDOM-VARIABLES

Journal Article

Nonlinearity, ISSN 0951-7715, 10/2017, Volume 30, Issue 11, pp. 4029 - 4061

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function...

Keller-Segel model | traveling wave solutions | absolute instabilities | logarithmic chemosensitivity | spectral stability | weighted essential spectrum | absolute spectrum | SYSTEM | MATHEMATICS, APPLIED | STABILITY | PHYSICS, MATHEMATICAL | SPIKE | CHEMOTACTIC BACTERIA | DYNAMICS | travelling wave solutions | SPECTRA | BANDS | Mathematics - Dynamical Systems

Keller-Segel model | traveling wave solutions | absolute instabilities | logarithmic chemosensitivity | spectral stability | weighted essential spectrum | absolute spectrum | SYSTEM | MATHEMATICS, APPLIED | STABILITY | PHYSICS, MATHEMATICAL | SPIKE | CHEMOTACTIC BACTERIA | DYNAMICS | travelling wave solutions | SPECTRA | BANDS | Mathematics - Dynamical Systems

Journal Article

NeuroImage (Orlando, Fla.), ISSN 1053-8119, 2013, Volume 80, pp. 426 - 444

The human brain is a complex, interconnected network par excellence. Accurate and informative mapping of this human connectome has become a central goal of...

DIFFUSION-WEIGHTED MRI | FUNCTIONAL BRAIN NETWORKS | CORTICAL NETWORKS | NEUROSCIENCES | NEUROIMAGING | HUMAN CEREBRAL-CORTEX | SMALL-WORLD NETWORKS | LOCAL CONNECTIVITY | DYNAMIC CONNECTIVITY | ANATOMICAL NETWORKS | GLOBAL SIGNAL | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | EFFECTIVE CONNECTIVITY | Algorithms | Brain - anatomy & histology | Nerve Net - anatomy & histology | Humans | Connectome - methods | Models, Neurological | Brain - physiology | Nerve Net - physiology | Models, Anatomic | Neurosciences | Analysis | Brain research | Graph theory | Combinatorics | Graph representations | Estimates

DIFFUSION-WEIGHTED MRI | FUNCTIONAL BRAIN NETWORKS | CORTICAL NETWORKS | NEUROSCIENCES | NEUROIMAGING | HUMAN CEREBRAL-CORTEX | SMALL-WORLD NETWORKS | LOCAL CONNECTIVITY | DYNAMIC CONNECTIVITY | ANATOMICAL NETWORKS | GLOBAL SIGNAL | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | EFFECTIVE CONNECTIVITY | Algorithms | Brain - anatomy & histology | Nerve Net - anatomy & histology | Humans | Connectome - methods | Models, Neurological | Brain - physiology | Nerve Net - physiology | Models, Anatomic | Neurosciences | Analysis | Brain research | Graph theory | Combinatorics | Graph representations | Estimates

Journal Article

16.
Full Text
Reliable identification of the auditory thalamus using multi-modal structural analyses

NeuroImage (Orlando, Fla.), ISSN 1053-8119, 2006, Volume 30, Issue 4, pp. 1112 - 1120

The medial geniculate body (MGB) of the thalamus is a key component of the auditory system. It is involved in relaying and transforming auditory information to...

Medial geniculate body | Diffusion-weighted imaging | Lateral geniculate nucleus | Tractography | Proton density | PATHWAYS | SYSTEM | LOCALIZATION | medial geniculate body | HUMAN BRAIN-STEM | lateral geniculate nucleus | NEUROSCIENCES | NEUROIMAGING | tractography | NUCLEI | proton density | diffusion-weighted imaging | CORTEX | HIGH-RESOLUTION | DIFFUSION MRI | SOUND | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | FMRI | Brain Stem - anatomy & histology | Humans | Geniculate Bodies - anatomy & histology | Male | Reference Values | Auditory Cortex - anatomy & histology | Auditory Perception - physiology | Magnetic Resonance Imaging | Dominance, Cerebral - physiology | Image Processing, Computer-Assisted | Diffusion Magnetic Resonance Imaging | Brain Mapping | Adult | Female | Auditory Pathways - anatomy & histology | Thalamic Nuclei - anatomy & histology | Gunboats | Studies | Brain | Nuclear magnetic resonance--NMR | Noise | Scanners | Divisions | Methods | diffusion weighted imaging

Medial geniculate body | Diffusion-weighted imaging | Lateral geniculate nucleus | Tractography | Proton density | PATHWAYS | SYSTEM | LOCALIZATION | medial geniculate body | HUMAN BRAIN-STEM | lateral geniculate nucleus | NEUROSCIENCES | NEUROIMAGING | tractography | NUCLEI | proton density | diffusion-weighted imaging | CORTEX | HIGH-RESOLUTION | DIFFUSION MRI | SOUND | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | FMRI | Brain Stem - anatomy & histology | Humans | Geniculate Bodies - anatomy & histology | Male | Reference Values | Auditory Cortex - anatomy & histology | Auditory Perception - physiology | Magnetic Resonance Imaging | Dominance, Cerebral - physiology | Image Processing, Computer-Assisted | Diffusion Magnetic Resonance Imaging | Brain Mapping | Adult | Female | Auditory Pathways - anatomy & histology | Thalamic Nuclei - anatomy & histology | Gunboats | Studies | Brain | Nuclear magnetic resonance--NMR | Noise | Scanners | Divisions | Methods | diffusion weighted imaging

Journal Article

Brain, ISSN 0006-8950, 07/2004, Volume 127, Issue 7, pp. 1479 - 1487

A traditional method of localizing brain functions has been to identify shared areas of brain damage in individuals who have a particular deficit. The...

Magnetic resonance perfusion imaging | Aphasia | Insula | Apraxia | Acute stroke | WEIGHTED MRI | LANGUAGE | aphasia | LOCALIZATION | magnetic resonance perfusion imaging | insula | NEUROSCIENCES | CLINICAL NEUROLOGY | STROKE | acute stroke | APHEMIA | PENUMBRA | MOTOR RECOVERY | DIFFUSION | PERFUSION | apraxia | Neurological Impairments | Brain | Brain Hemisphere Functions | Diagnostic Tests | Articulation (Speech) | Speech Tests | Speech Language Pathology | Probability | Speech Impairments | Patients | Brain - anatomy & histology | Humans | Cerebral Cortex - pathology | Stroke - complications | Articulation Disorders - complications | Brain - physiology | Neuropsychological Tests | Stroke - pathology | Magnetic Resonance Imaging | Speech - physiology | Articulation Disorders - pathology | Brain - pathology | Frontal Lobe - pathology

Magnetic resonance perfusion imaging | Aphasia | Insula | Apraxia | Acute stroke | WEIGHTED MRI | LANGUAGE | aphasia | LOCALIZATION | magnetic resonance perfusion imaging | insula | NEUROSCIENCES | CLINICAL NEUROLOGY | STROKE | acute stroke | APHEMIA | PENUMBRA | MOTOR RECOVERY | DIFFUSION | PERFUSION | apraxia | Neurological Impairments | Brain | Brain Hemisphere Functions | Diagnostic Tests | Articulation (Speech) | Speech Tests | Speech Language Pathology | Probability | Speech Impairments | Patients | Brain - anatomy & histology | Humans | Cerebral Cortex - pathology | Stroke - complications | Articulation Disorders - complications | Brain - physiology | Neuropsychological Tests | Stroke - pathology | Magnetic Resonance Imaging | Speech - physiology | Articulation Disorders - pathology | Brain - pathology | Frontal Lobe - pathology

Journal Article

Hydrogeology Journal, ISSN 1431-2174, 2/2016, Volume 24, Issue 1, pp. 141 - 158

The daily groundwater level (GWL) response in the Permo-Triassic Sandstone aquifers in the Eden Valley, England (UK), has been studied using the seasonal trend...

Earth Sciences | Hydrology/Water Resources | Hydrogeology | Geology | Time series analysis | Water Quality/Water Pollution | Geophysics/Geodesy | Groundwater statistics | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | Sandstone | Conceptual models | SYSTEM | MECHANISM | CATCHMENT | WATER RESOURCES | TIME | HYDROGRAPHS | LOCALLY WEIGHTED REGRESSION | SPECTRAL-ANALYSES | GEOSCIENCES, MULTIDISCIPLINARY | NITRATE CONCENTRATIONS | WATER | RECHARGE | Decomposition | Seasons | Groundwater | Statistics | Analysis | Aquifers | Heterogeneity | Valleys | Boreholes | Trends

Earth Sciences | Hydrology/Water Resources | Hydrogeology | Geology | Time series analysis | Water Quality/Water Pollution | Geophysics/Geodesy | Groundwater statistics | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | Sandstone | Conceptual models | SYSTEM | MECHANISM | CATCHMENT | WATER RESOURCES | TIME | HYDROGRAPHS | LOCALLY WEIGHTED REGRESSION | SPECTRAL-ANALYSES | GEOSCIENCES, MULTIDISCIPLINARY | NITRATE CONCENTRATIONS | WATER | RECHARGE | Decomposition | Seasons | Groundwater | Statistics | Analysis | Aquifers | Heterogeneity | Valleys | Boreholes | Trends

Journal Article

Pattern recognition, ISSN 0031-3203, 2016, Volume 58, pp. 49 - 67

Fuzzy clustering for interval-valued data helps us to find natural vague boundaries in such data. The Fuzzy c-Medoids Clustering (FcMdC) method is one of the...

Interval-valued data | Fuzzy c-ordered medoids clustering | Robust clustering | Outlier interval data | Huber׳s M-estimators | Ordered weighted averaging | Hubers M-estimators | REGRESSION | PRINCIPAL COMPONENT ANALYSIS | Huber's M-estimators | EXTENSION | NOISE | ALGORITHMS | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | SYMBOLIC DATA | K-MEANS | Analysis | Algorithms | Operators | Partitioning | Outliers (statistics) | Pattern recognition | Boundaries | Fuzzy | Clustering

Interval-valued data | Fuzzy c-ordered medoids clustering | Robust clustering | Outlier interval data | Huber׳s M-estimators | Ordered weighted averaging | Hubers M-estimators | REGRESSION | PRINCIPAL COMPONENT ANALYSIS | Huber's M-estimators | EXTENSION | NOISE | ALGORITHMS | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | SYMBOLIC DATA | K-MEANS | Analysis | Algorithms | Operators | Partitioning | Outliers (statistics) | Pattern recognition | Boundaries | Fuzzy | Clustering

Journal Article