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Kernel (statistics)

Index Kernel (statistics)

The term kernel is a term in statistical analysis used to refer to a window function. [1]

39 relations: Bayesian inference, Bayesian statistics, Boxcar function, Cluster analysis, Conditional expectation, Conjugate prior, Density estimation, 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, Periodogram, 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, Sigmoid function, Sign (mathematics), Spectral density, Statistical classification, Statistics, Support (mathematics), 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 more evidence or information becomes available.

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Bayesian statistics

Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief known as Bayesian probabilities.

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Boxcar function

In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant, A. The boxcar function can be expressed in terms of the uniform distribution as where f(a,b;x) is the uniform distribution of x for the interval and H(x) is the Heaviside step function.

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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) to each other than to those in other groups (clusters).

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Conditional expectation

In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take “on average” over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur.

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Conjugate prior

In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same probability distribution 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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Integrable system

In the context of differential equations to integrate an equation means to solve it from initial conditions.

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Kernel (statistics)

The term kernel is a term in statistical analysis used to refer to a window function.

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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

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 to estimate a real valued function f: \mathbb^p \to \mathbb as the weighted average of neighboring observed data.

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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 subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.

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Markov kernel

In probability theory, a Markov kernel (also known as a stochastic kernel or probability 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 is the branch of statistics that is not based solely on parameterized families of probability distributions (common examples of parameters are the mean and variance).

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) 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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A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

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In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898.

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Point process

In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on some underlying mathematical space such as the real line, the Cartesian plane, or more abstract 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, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Probability mass function

In probability 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, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Real-valued function

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

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Regression analysis

In statistical modeling, regression analysis is a set of statistical processes 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 of functions in which point evaluation is a continuous linear functional.

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Sigmoid function

A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.

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Sign (mathematics)

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

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Spectral density

The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that 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 is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Support (mathematics)

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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Time series

A time series is a series of data points indexed (or listed or graphed) in time order.

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

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