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Study of high-dimensional data
In statistical theory, the field of high-dimensional statistics studies data whose dimension is larger (relative to the number of datapoints) than typically
High-dimensional_statistics
American statistician
high-dimensional statistics including M-estimators, robust statistics, differential privacy, and the applications of non-convex optimisation in high-dimensional
Po-Ling_Loh
Property of a mathematical space
mechanics is an infinite-dimensional function space. The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur
Dimension
British-Swedish mathematical statistician
statistician known for her research on wavelets, graphons, and high-dimensional statistics and for her columns on algorithmic bias. She is a professor of
Sofia_Olhede
Process of reducing the number of random variables under consideration
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the
Dimensionality_reduction
artificial intelligence, machine learning, statistics and data science. He has worked on high-dimensional statistics, foundations of deep neural network, message
Adel_Javanmard
German computer scientist
approximation algorithms, hardness of approximation, sum of squares, and high-dimensional statistics. He is an associate professor of computer science at ETH Zurich
David_Steurer
Statistician
chair of the Department of Statistics at the University of California, Berkeley. His work spans high-dimensional statistics, nonparametric estimation,
Ryan_Tibshirani
Estimator for quality of a statistical model
doi:10.1214/ss/1177010133. Giraud, C. (2015), Introduction to High-Dimensional Statistics, CRC Press. Hurvich, C. M.; Tsai, C.-L. (1989), "Regression and
Akaike_information_criterion
Serbian-American statistician
professor of statistics and data science at Cornell University. Her research interests include causal inference, high-dimensional statistics, and robust
Jelena_Bradic
Austrian mathematician (born 1980)
contributions to various areas of mathematical statistics; including non-parametric and high-dimensional statistics, empirical process theory, and Bayesian inference
Richard_Nickl
Type of probability distribution
{3/c}}\|A\|K^{2}} . Platykurtic distribution Wainwright MJ. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge: Cambridge University
Sub-Gaussian_distribution
In probability, a theory
johndcook.com. 2018-06-02. Retrieved 2023-12-20. Wainwright MJ. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge: Cambridge University
Mills_ratio
Dutch statistician
process theory, statistical learning theory, and nonparametric and high-dimensional statistics. She is the daughter of psychologist John P. van de Geer. She
Sara_van_de_Geer
Wang, studies dimension reduction, functional data analysis, and aging Lan Wang, Chinese-American expert on high-dimensional statistics and quantile regression
List_of_women_in_statistics
Statistician (born 1973)
Institute of Mathematical Statistics in 2014 "for his fundamental research in statistical machine learning and high-dimensional statistics". In addition to numerous
Martin Wainwright (statistician)
Martin_Wainwright_(statistician)
Criterion for model selection
ISBN 978-1-032-48868-4. Giraud, C. (2015). Introduction to high-dimensional statistics. Chapman & Hall/CRC. ISBN 9781482237948. Priestley, M.B. (1981)
Bayesian information criterion
Bayesian_information_criterion
Researcher and Professor of computing
in 2016. She specialised in large-scale machine learning and high-dimensional statistics. Anandkumar was a principal scientist at Amazon Web Services
Anima_Anandkumar
Russian and American mathematical statistician
Nair Collegiate Professor of Statistics at the University of Michigan, and is known for her work in high-dimensional statistics, including covariance estimation
Elizaveta_Levina
British statistician
Cambridge. His main research interests are in nonparametric and high-dimensional statistics. Particular topics include shape-constrained density estimation
Richard_Samworth
Branch of mathematics
geometric analysis or high-dimensional geometry, is a field of mathematics that investigates the geometric properties of finite-dimensional objects, such as
Asymptotic_geometry
Romanian-American statistician
in machine learning, the theory of empirical processes, and high-dimensional statistics. She is a professor at Cornell University. Bunea earned Bachelor's
Florentina_Bunea
Discrete probability distribution
Hypotheses for example. The distribution is particularly useful in high-dimensional statistics. The Rademacher distribution can be used to show that normally
Rademacher_distribution
Regression algorithm
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron
Least-angle_regression
American statistician
statistician whose research focuses on high-dimensional statistics, quantile regression, and the application of statistics to personalized medicine and the
Lan_Wang_(statistician)
Measure of complexity of real-valued functions
169–* doi:10.1007/978-3-540-28650-9_8 Wainwright, Martin (2019). High-dimensional statistics : a non-asymptotic viewpoint. Cambridge, United Kingdom. pp. Exercise
Rademacher_complexity
American biostatistician
Mathematical Statistics at the University of Washington. Her research investigates the use of machine learning to understand high-dimensional data. Witten
Daniela_Witten
Type of light-tailed probability distribution
Vershynin, University of California, Irvine, June 9, 2020 High-Dimensional Statistics: A Non-Asymptotic Viewpoint, Martin J. Wainwright, Cambridge University
Subexponential distribution (light-tailed)
Subexponential_distribution_(light-tailed)
Chinese-American statistician
nonparametric statistics, semiparametric statistics, big data analytics, high-dimensional data, and official statistics. She is a professor of statistics at George
Lily_Wang
Mathematical model of ferromagnetism in statistical mechanics
Ising. The one-dimensional Ising model was solved by Ising (1925) alone in his 1924 thesis; it has no phase transition. The two-dimensional square-lattice
Ising_model
Professor of biostatistics
statistics and machine learning, emphasizing both theoretical development and methodological innovation. His work covers: High-dimensional statistics
Yang_Feng_(statistician)
Integral inequality
(link) Wainwright, Martin J. (2019). "Concentration of Measure". High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge University Press. pp. 72–76
Prékopa–Leindler_inequality
American mathematician and statistician
professor of statistics at Harvard University from 1991 to 1994. From 1994 to 2004, he was Assistant, Associate, and full Professor of Statistics (promoted
Jun_S._Liu
model Hierarchical linear modeling High-dimensional statistics Higher-order factor analysis Higher-order statistics Hirschman uncertainty Histogram Historiometry
List_of_statistics_articles
Mathematical result
embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded
Johnson–Lindenstrauss_lemma
Matrix-valued random variable
sample covariance matrices—which is of particular interest in high-dimensional statistics. Random matrix theory also saw applications in neural networks
Random_matrix
American statistician
Mathematical Statistics (IMS) gave her their Tweedie New Researcher Award "for groundbreaking contributions in high-dimensional statistics, including the
Rina_Foygel_Barber
Statistic used in model selection
|journal= ignored (help) Giraud, C. (2015), Introduction to high-dimensional statistics, Chapman & Hall/CRC, ISBN 9781482237948 Daniel, C.; Wood, F.
Mallows's_Cp
Monte Carlo algorithm
for sampling from multi-dimensional distributions, especially when the number of dimensions is high. For single-dimensional distributions, there are
Metropolis–Hastings_algorithm
French mathematical statistician
models, latent variables, high-dimensional structured data, the relation between statistics and coding theory, and the statistics of sequence data over finite
Élisabeth_Gassiat
Branch of statistics mathematics
probability, etc. Intrinsically, functional data are infinite dimensional. The high intrinsic dimensionality of these data brings challenges for theory as well as
Functional_data_analysis
Statistician
frequentist Statistics in the areas of variable selection, factor models, non-parametric Bayes, tree-based and deep-learning methods, high-dimensional inference
Veronika_Ročková
Statistical distribution for dependence between random variables
1]^{d}\rightarrow [0,1]} is a d-dimensional copula if C is a joint cumulative distribution function of a d-dimensional random vector on the unit cube [
Copula_(statistics)
Method in statistics
statistical method for dimensionality reduction (the transformation of data from a high-dimensional space into a low-dimensional space). SM can be used
Semantic_mapping_(statistics)
Statistical method
{\displaystyle \alpha } as n goes to infinity. This result is related to high-dimensional statistics and is proven by Fan, Hall & Yao (2007). Specifically, if we
Šidák_correction_for_t-test
inner-product space. MVU creates a mapping from the high dimensional input vectors to some low dimensional Euclidean vector space in the following steps: A
Semidefinite_embedding
Polish statistician
Fellow of the Institute of Mathematical Statistics in 2024, "for innovative contributions to high-dimensional statistics with a focus on multiple testing and
Małgorzata_Bogdan
American statistician
development of effective methods for the construction of low-dimensional representations for high-dimensional data problems (multiscale geometric analysis), development
David_Donoho
Posits ability to interpolate within latent manifolds
that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space.
Manifold_hypothesis
Chinese-American statistician
statistician and a professor of statistics at Ohio State University. Her research includes work on high-dimensional Bayesian hierarchical modeling, model
Xinyi_Xu
Technique for dimensionality reduction
statistical method for visualizing high-dimensional data by giving each datapoint a location in a two or three-dimensional map. It is based on Stochastic
T-distributed stochastic neighbor embedding
T-distributed_stochastic_neighbor_embedding
nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates
Local_tangent_space_alignment
Russian American statistician and economist
current research focuses on mathematical statistics and machine learning for causal structural models in high-dimensional environments. He graduated from the
Victor_Chernozhukov
Machine learning algorithm
Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve
Sammon_mapping
Computational statistics technique
to sample a random variable in one dimension, one can perform a uniformly random sampling of the two-dimensional Cartesian graph, and keep the samples
Rejection_sampling
American academic
inference of high-dimensional data, particularly genomic data. Storey was the founding director of the Princeton University Center for Statistics and Machine
John_D._Storey
Chinese biostatistician
biostatistician specializing in biomedical imaging, neuroimaging, and high-dimensional data analysis. She is a professor of biostatistics and bioinformatics
Ying_Guo
estimators have been used extensively for estimating density functions in high-dimensional spaces such as in Positron emission tomography (PET). The first exploitation
Sieve_estimator
Probability distribution
specifically the set of K-dimensional discrete distributions. The technical term for the set of points in the support of a K-dimensional Dirichlet distribution
Dirichlet_distribution
Calculation of complex statistical distributions
used to study probability distributions that are too complex or too high dimensional to study with analytic techniques alone. Various algorithms exist for
Markov_chain_Monte_Carlo
Method for dimension reduction in statistics
exponentially with high-dimensional data (as p grows), reducing the number of dimensions can make the operation computable. Dimensionality reduction aims
Sliced_inverse_regression
Australian statistician
the Journal of Computational and Graphical Statistics, and an expert on the visualization of high-dimensional data. She is Professor of Business Analytics
Dianne_Cook_(statistician)
Model in statistical physics
can be used to predict which terms are most important by dimensional analysis. Dimensional analysis is not completely straightforward, because the scaling
High-dimensional_Ising_model
Chinese statistician
Wharton School since August 1, 2017. Cai's research focuses on high-dimensional statistics, statistical machine learning, large-scale inference, nonparametric
T._Tony_Cai
variables revealing the origins of individuals. Statistics on immigration in France have a political dimension. Political discourse and public action rely
Immigration statistics in France
Immigration_statistics_in_France
Theory of subatomic structure
dimensional objects. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes
String_theory
Ethopian-American biostatistician
is a biostatistician focused on the use of Bayesian statistics for inferences about high-dimensional data from genomics, including biomarker discovery,
Mahlet_Tadesse
Method of data analysis
varying illuminations span a low-dimensional subspace. This is one of the reasons for effectiveness of low-dimensional models for imagery data. In particular
Robust principal component analysis
Robust_principal_component_analysis
Technique to reduce dimensionality of points in Euclidean space
with high probability. In random projection, the original d {\displaystyle d} -dimensional data is projected to a k {\displaystyle k} -dimensional subspace
Random_projection
Country in West Asia
among many, by Mark M. Ayyash (2019). Hermeneutics of Violence: A Four-Dimensional Conception. University of Toronto Press, p. 195 Archived 22 March 2024
Israel
Public (magnet) secondary school in Boynton Beach, Florida , United States
dual-enroll to obtain college credit while still in high school.[citation needed] The school's choir, Dimensional Harmony, was established in the first year the
Boynton Beach Community High School
Boynton_Beach_Community_High_School
Statistical method
Annals of Statistics. 14: 1261–1350. doi:10.1214/aos/1176350142. Mammen, E. (Mar 1993). "Bootstrap and wild bootstrap for high dimensional linear models"
Bootstrapping_(statistics)
Chinese statistician and academic
Perspective, and authored or coauthored over 300 articles on high-dimensional statistics, machine learning, AI, finance, economics, computational biology
Jianqing_Fan
Chart displaying multivariate data
Parallel Coordinates plots are a common method of visualizing high-dimensional datasets to analyze multivariate data having multiple variables, or attributes
Parallel_coordinates
Statistician and econometrician
understanding the Metropolis–Hastings algorithm and its extensions in high-dimensional settings. Central contributions of this work are the included derivations
Siddhartha_Chib
Dutch statistician
models, particularly in high-dimensional data from applications in biology and epidemiology. She is a professor of statistics at ETH Zurich in Switzerland
Marloes_Maathuis
of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector
Sufficient dimension reduction
Sufficient_dimension_reduction
History of crystallography to 1895
published his results. Liquid crystals are now known to have one- or two-dimensional periodicity, with rod or layer symmetry respectively. From the 1830s
History of crystallography before X-rays
History_of_crystallography_before_X-rays
Statistical term, a compound measure in statistics
In statistics and research design, an index is a composite statistic – a measure of changes in a representative group of individual data points, or in
Index_(statistics)
Statistical method
run in an ensemble. This can be especially useful when the data is high-dimensional. The procedure involves running lasso on each of several random subsets
Lasso_(statistics)
American statistician and professor
in 2019 and Fellow of Institute of Mathematical Statistics for seminal contributions to high-dimensional inference, variable selection, classification,
Yingying_Fan
Topological space that locally resembles Euclidean space
homeomorphic to an open subset of n {\displaystyle n} -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not self-crossing
Manifold
Relation between sides of a right triangle
square of the measure of an m-dimensional set of objects in one or more parallel m-dimensional flats in n-dimensional Euclidean space is equal to the
Pythagorean_theorem
Relief map of ancient Rome
the product of an "intellectual ferment" and was not a mere "three-dimensional translation of monuments reconstructed by others." The Circus Maximus
Plan_of_Rome_(Bigot)
Multidimensional data visualization
is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot. Introduced in
Bagplot
Structure that categorizes facts and measures in a data warehouse
then diced by grouping by product. A dimensional data element is similar to a categorical variable in statistics. Typically dimensions in a data warehouse
Dimension_(data_warehouse)
Mathematics award
Retrieved 31 March 2017. "Laurent Moise Schwartz". School of Mathematics and Statistics University of St Andrews, Scotland. 24 June 2007. Archived from the original
Fields_Medal
Machine learning technique
Peter (25 April 2018). "Deep TAMER: Interactive Agent Shaping in High-Dimensional State Spaces". Proceedings of the AAAI Conference on Artificial Intelligence
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Journal. 17 (1): 15–26. ISSN 0738-0658. PMID 9642717. Official Statistics of Sweden: Statistics – Health and Medical Care: Induced abortions 2009 Archived
Timeline of women's legal rights (other than voting) in the 20th century
Timeline_of_women's_legal_rights_(other_than_voting)_in_the_20th_century
Grouping a set of objects by similarity
For high-dimensional data, many methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high-dimensional
Cluster_analysis
Length of a line segment
distance from a point to a plane in three-dimensional Euclidean space The distance between two lines in three-dimensional Euclidean space The distance from a
Euclidean_distance
States of matter for water as a solid
grown on substrates at low temperature without the use of dopants. One-dimensional nano-confined ferroelectric ice XI was created in 2010. Although the
Phases_of_ice
Set of methods for supervised statistical learning
reason, it was proposed that the original finite-dimensional space be mapped into a much higher-dimensional space, presumably making the separation easier
Support_vector_machine
Statement in computational learning theory
pattern-classification problem, cast in a high-dimensional space nonlinearly, is more likely to be linearly separable than in a low-dimensional space, provided that the
Cover's_theorem
Province of Canada
2016". Statistics Canada. August 4, 2017. Archived from the original on June 3, 2021. Retrieved June 6, 2021. Government of Canada, Statistics Canada
Quebec
Chinese and American biostatistician
biostatistician focusing on metagenomics and associated problems in high-dimensional inference and data analysis including the multiple comparisons problem
Xinping_Cui
Simultaneous observation and analysis of more than one outcome variable
Structured data analysis (statistics) Structural equation modeling RV coefficient Bivariate analysis Design of experiments (DoE) Dimensional analysis Exploratory
Multivariate_statistics
Graphical representation of data
of a pie; first introduced by William Playfair. A line chart is a two-dimensional scatterplot of ordered observations where the observations are connected
Chart
Chinese-American statistician
Chinese and American statistician. Her research applies Bayesian statistics to high-dimensional and complex data from genomics and electronic health records
Yanxun_Xu
American basketball player (born 1990)
referred to the "one-dimensional" jab from James while talking with the media at a basketball camp he was hosting for elite high school players. "AS Monaco
Mike James (basketball, born 1990)
Mike_James_(basketball,_born_1990)
HIGH DIMENSIONAL-STATISTICS
HIGH DIMENSIONAL-STATISTICS
Boy/Male
Hindu, Indian
Dimensions
Boy/Male
French Teutonic American Shakespearean English Welsh
Intelligent.
Boy/Male
English
Son of Hugh.
Girl/Female
Hindu, Indian
Three Dimension
Male
English
English form of Old French Hugues, HUGH means "heart," "mind," or "spirit."
Surname or Lastname
English (chiefly Yorkshire)
English (chiefly Yorkshire) : topographic name for someone who lived by a hedged or fenced enclosure (Old English haga), or a habitational name from a place named with this word (or its Old Norse cognate hagi), especially three places called Haigh, two in West Yorkshire and the other near Manchester.
Girl/Female
Tamil
Triguni | தà¯à®°à¯€à®•à¯‚நீ
The three dimensions
Triguni | தà¯à®°à¯€à®•à¯‚நீ
Girl/Female
Indian, Telugu
Uni-dimensional
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Three Dimensions
Girl/Female
Tamil
Trikaya | தà¯à®°à®¿à®•à®¾à®¯à®¾
Three dimensional
Trikaya | தà¯à®°à®¿à®•à®¾à®¯à®¾
Girl/Female
Hindu
Three dimensional
Surname or Lastname
English (chiefly East Anglia and northern England)
English (chiefly East Anglia and northern England) : nickname for a tall man, from Middle English hegh, hie ‘high’, ‘tall’, Old English hēah (compare Hay 2), or a topographic name for a dweller on a hilltop or high place, from the same word used in a topographical sense. This second use is supported by early forms such as Richard atte High (Sussex 1332).
Surname or Lastname
English
English : topographic name for someone who lived at the top of a hill or on a piece of raised ground, from Middle English heyt ‘summit’, ‘height’.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Three Dimensions
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Three Dimentional
Boy/Male
Irish
Hugh is a translation of an ancient name Aodh meaning “â€fire.â€â€ A name with nationalistic connotations as Hugh O’Neill, Earl of Tyrone and Red Hugh O’Donnell, Earl of Tyrconnell together led a rebellion and won some major battles against the forces of the English queen Elizabeth 1st, before being defeated at the Battle of Kinsale in 1601.
Boy/Male
Tamil
Trigun | தà¯à®°à®¿à®•à¯à®£
The three dimensions
Trigun | தà¯à®°à®¿à®•à¯à®£
Girl/Female
Gujarati, Indian, Kannada
Dimension; Purity
Boy/Male
Tamil
Dimensions
Surname or Lastname
English
English : from the Old French personal name Hu(gh)e, introduced to Britain by the Normans. This is in origin a short form of any of the various Germanic compound names with the first element hug ‘heart’, ‘mind’, ‘spirit’. Compare, for example, Howard 1, Hubble, and Hubert. It was a popular personal name among the Normans in England, partly due to the fame of St. Hugh of Lincoln (1140–1200), who was born in Burgundy and who established the first Carthusian monastery in England.In Ireland and Scotland this name has been widely used as an equivalent of Celtic Aodh ‘fire’, the source of many Irish surnames (see for example McCoy).
HIGH DIMENSIONAL-STATISTICS
HIGH DIMENSIONAL-STATISTICS
Boy/Male
Irish
“â€without enemy.â€â€ The name of early kings, legendary heroes and saints, Diarmuid was the lover of Grainne and the most beloved of that warrior band, the Fianna (read the legend). Grainne, as the daughter of Cormac Mac Airt, the High King of Tara, was betrothed to a much older man, the legendary Fionn Mac Cool (read the legend). When Grainne saw Fionn at the wedding banquet she realised he “â€was not for herâ€â€ and put a a “â€geis,â€â€ a spell, on his nephew, Diarmuid, to run away with her. For sixteen years the lovers were forced to roam the countryside, all the time knowing that they were being constantly pursued by the furious Fionn. Each night they made a fresh bed in a sheltered spot and legend has it that these beds can still be seen today in many remote places. (Read the legend of Diarmuid and Grainne).
Girl/Female
Hindu, Indian, Traditional
Star
Boy/Male
Hindu, Indian
Another Name for Krishna's Bansari; Flute
Boy/Male
Hindu, Indian
Goddess of Learning; River Ganga
Girl/Female
Hebrew
Grace.
Boy/Male
Tamil
Parijat | பாரிஜாத
Divine tree, A celestial flower
Boy/Male
Muslim/Islamic
Spinner
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Hebrew, Irish, Italian, Jewish, Latin, Swedish, Swiss, Teutonic
Guide; Staff of the God; Warrior; Wood; Valley; Forest; Wide
Surname or Lastname
English (Sussex)
English (Sussex) : probably a variant of Pullen.
Boy/Male
Arabic, Hindu, Indian, Muslim
Lion
HIGH DIMENSIONAL-STATISTICS
HIGH DIMENSIONAL-STATISTICS
HIGH DIMENSIONAL-STATISTICS
HIGH DIMENSIONAL-STATISTICS
HIGH DIMENSIONAL-STATISTICS
n.
The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.
n.
Extent; reach; scope; importance; as, a project of large dimensions.
a.
High as the breast.
a.
Having dimensions.
superl.
Costly; dear in price; extravagant; as, to hold goods at a high price.
adv.
In a high manner; in a high place; to a great altitude; to a great degree; largely; in a superior manner; eminently; powerfully.
n.
High-priesthood.
superl.
Acute or sharp; -- opposed to grave or low; as, a high note.
superl.
Strong-scented; slightly tainted; as, epicures do not cook game before it is high.
superl.
Of great strength, force, importance, and the like; strong; mighty; powerful; violent; sometimes, triumphant; victorious; majestic, etc.; as, a high wind; high passions.
adv. & a.
Very high.
n.
People of rank or high station; as, high and low.
a.
Strung to a high pitch; spirited; sensitive; as, a high-strung horse.
n.
A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree.
superl.
Of noble birth; illustrious; as, of high family.
a.
Pertaining to dimension.
a.
High in tone or sound.
superl.
Possessing a characteristic quality in a supreme or superior degree; as, high (i. e., intense) heat; high (i. e., full or quite) noon; high (i. e., rich or spicy) seasoning; high (i. e., complete) pleasure; high (i. e., deep or vivid) color; high (i. e., extensive, thorough) scholarship, etc.
adv.
On high.
a.
Elevated; high-principled; honorable.