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Kernel (statistics)

The term kernel has several distinct meanings in statistics. [1]

37 relations: Bayesian inference, Bayesian statistics, Cluster analysis, Conditional expectation, Conjugate prior, Density estimation, Indicator function, Integrable system, Kernel (statistics), Kernel density estimation, Kernel method, Kernel regression, Kernel smoother, Logistic distribution, Machine learning, Markov kernel, Multivariate kernel density estimation, Nonparametric statistics, Normal distribution, Normalizing constant, Parameter, Point process, Probability density function, Probability distribution, Probability mass function, Pseudo-random number sampling, Random variable, Real-valued function, Regression analysis, Reproducing kernel Hilbert space, Sign (mathematics), Spectral density, Spectral density estimation, Statistical classification, Statistics, Time series, Window function.

Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as evidence is acquired.

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Bayesian statistics

Bayesian statistics is a subset of the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities.

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Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters).

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Conditional expectation

In probability theory, the conditional expectation of a random variable is another random variable equal to the average of the former over each possible "condition".

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Conjugate prior

In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function.

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Density estimation

In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function.

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Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a bold or blackboard bold 1 symbol with a subscript describing the event of inclusion.

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Integrable system

In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems.

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Kernel (statistics)

The term kernel has several distinct meanings in statistics.

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Kernel density estimation

In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable.

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Kernel method

In machine learning, kernel methods are a class of algorithms for pattern analysis, whose best known member is the support vector machine (SVM).

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Kernel regression

The kernel regression is a non-parametric technique in statistics to estimate the conditional expectation of a random variable.

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Kernel smoother

A kernel smoother is a statistical technique for estimating a real valued function f(X)\,\,\left(X\in \mathbb^ \right) by using its noisy observations, when no parametric model for this function is known.

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Logistic distribution

In probability theory and statistics, the logistic distribution is a continuous probability distribution.

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Machine learning

Machine learning is a subfield of computer sciencehttp://www.britannica.com/EBchecked/topic/1116194/machine-learning that evolved from the study of pattern recognition and computational learning theory in artificial intelligence.

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Markov kernel

In probability theory, a Markov kernel (or stochastic kernel) is a map that plays the role, in the general theory of Markov processes, that the transition matrix does in the theory of Markov processes with a finite state space.

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Multivariate kernel density estimation

Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics.

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Nonparametric statistics

Nonparametric statistics are statistics not based on parameterized families of probability distributions.

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Normal distribution

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution.

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Normalizing constant

The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics.

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Parameter

A parameter (from the Ancient Greek παρά, "para", meaning "beside, subsidiary" and μέτρον, "metron", meaning "measure"), in its common meaning, is a characteristic, feature, or measurable factor that can help in defining a particular system.

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Point process

In statistics and probability theory, a point process is a type of random process for which any one realisation consists of a set of isolated points either in time or geographical space, or in even more general spaces.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

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Probability distribution

In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Probability mass function

In probability theory and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

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Pseudo-random number sampling

Pseudo-random number sampling or non-uniform pseudo-random variate generation is the numerical practice of generating pseudo-random numbers that are distributed according to a given probability distribution.

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Random variable

In probability and statistics, a random variable, aleatory variable or stochastic variable is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense).

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Real-valued function

In mathematics, a real-valued function or real function is a function whose values are real numbers.

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Regression analysis

In statistics, regression analysis is a statistical process for estimating the relationships among variables.

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Reproducing kernel Hilbert space

In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space associated with a kernel that reproduces every function in the space or, equivalently, where every evaluation functional is bounded.

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Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number to be positive or negative.

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Spectral density

The power spectrum of a time series x(t) describes how the variance of the data x(t) is distributed over the frequency domain, into spectral components which the series x(t) may be decomposed.

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Spectral density estimation

In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal.

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Statistical classification

In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations (or instances) whose category membership is known.

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Statistics

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data.

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Time series

A time series is a sequence of data points, typically consisting of successive measurements made over a time interval.

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Window function

In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.

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References

[1] https://en.wikipedia.org/wiki/Kernel_(statistics)

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