Mixture (Smile Math 1.0.3 API)

java.lang.Object
- smile.stat.distribution.AbstractDistribution
- - smile.stat.distribution.Mixture

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ExponentialFamilyMixture
```
public class Mixture
extends AbstractDistribution
```
A finite mixture model is a probabilistic model for density estimation using a mixture distribution. A mixture model can be regarded as a type of unsupervised learning or clustering.
The Expectation-maximization algorithm can be used to compute the parameters of a parametric mixture model distribution. The EM algorithm is a method for finding maximum likelihood estimates of parameters, where the model depends on unobserved latent variables. EM is an iterative method which alternates between performing an expectation (E) step, which computes the expectation of the log-likelihood evaluated using the current estimate for the latent variables, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter estimates are then used to determine the distribution of the latent variables in the next E step.

Author:

Haifeng Li

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class Mixture.Component
A component in the mixture distribution is defined by a distribution and its weight in the mixture.

Nested Classes
Modifier and Type	Class and Description
`static class`	`Mixture.Component` A component in the mixture distribution is defined by a distribution and its weight in the mixture.

Constructor Summary

Constructors
Constructor and Description

Mixture(List<Mixture.Component> mixture)
Constructor.

Constructors
Constructor and Description
`Mixture(List<Mixture.Component> mixture)` Constructor.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`bic(double[] data)` BIC score of the mixture for given data.
`double`	`cdf(double x)` Cumulative distribution function.
`double`	`entropy()` Shannon entropy.
`List<Mixture.Component>`	`getComponents()` Returns the list of components in the mixture.
`double`	`logp(double x)` The density at x in log scale, which may prevents the underflow problem.
`double`	`mean()` The mean of distribution.
`int`	`npara()` The number of parameters of the distribution.
`double`	`p(double x)` The probability density function for continuous distribution or probability mass function for discrete distribution at x.
`double`	`quantile(double p)` The quantile, the probability to the left of quantile is p.
`double`	`rand()` Generates a random number following this distribution.
`double`	`sd()` The standard deviation of distribution.
`int`	`size()` Returns the number of components in the mixture.
`String`	`toString()`
`double`	`var()` The variance of distribution.

Methods inherited from class smile.stat.distribution.AbstractDistribution
inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rejection

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - Mixture
```
public Mixture(List<Mixture.Component> mixture)
```
    Constructor.
    
    Parameters:
    mixture - a list of distributions.
- Method Detail
  - mean
```
public double mean()
```
    Description copied from interface: Distribution
    
    The mean of distribution.
  - var
```
public double var()
```
    Description copied from interface: Distribution
    
    The variance of distribution.
  - sd
```
public double sd()
```
    Description copied from interface: Distribution
    
    The standard deviation of distribution.
  - entropy
```
public double entropy()
```
    Shannon entropy. Not supported.
  - p
```
public double p(double x)
```
    Description copied from interface: Distribution
    
    The probability density function for continuous distribution or probability mass function for discrete distribution at x.
  - logp
```
public double logp(double x)
```
    Description copied from interface: Distribution
    
    The density at x in log scale, which may prevents the underflow problem.
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Cumulative distribution function. That is the probability to the left of x.
  - rand
```
public double rand()
```
    Description copied from interface: Distribution
    
    Generates a random number following this distribution.
  - quantile
```
public double quantile(double p)
```
    Description copied from interface: Distribution
    
    The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.
  - npara
```
public int npara()
```
    Description copied from interface: Distribution
    
    The number of parameters of the distribution.
  - size
```
public int size()
```
    Returns the number of components in the mixture.
  - bic
```
public double bic(double[] data)
```
    BIC score of the mixture for given data.
  - getComponents
```
public List<Mixture.Component> getComponents()
```
    Returns the list of components in the mixture.
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object

Class Mixture

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class smile.stat.distribution.AbstractDistribution

Methods inherited from class java.lang.Object

Constructor Detail

Mixture

Method Detail

mean

var

sd

entropy

p

logp

cdf

rand

quantile

npara

size

bic

getComponents

toString