Contains all definitions in the statistics directory. More...

Classes
struct	BernoulliDistribution

struct	BernoulliMAPModel

struct	BetaDistribution

struct	BoxProbabilityDistribution

struct	CategoricalDistribution

struct	CategoricalMAPModel

class	DataSet

struct	DiracDistribution

struct	DiracMultivariateDistribution

struct	DistributionCollector
	Incrementally collects samples from a univariate distribution. More...

class	DistributionCollectorND
	Incrementally collects samples from a multivariate distribution. More...

struct	GaussianDistribution

class	GaussianHMM
	A model of a temporal sequence consisting of k discrete states each with a gaussian emission probability. More...

class	GaussianHMMRegression

class	GaussianMixtureModel
	A model of a probability distribution consisting of k gaussians. More...

class	GaussianMixtureModelRaw
	A more ``raw'' model of a GMM that does not perform a cholesky decomposiition. More...

class	GaussianMixtureRegression

struct	GaussianMultivariateDistribution

class	GaussianRegression

class	HierarchicalClustering

class	Histogram
	1-D histogram class More...

class	Histogram2D
	2-D histogram class More...

class	Histogram3D
	3-D histogram class More...

class	HistogramND
	N-D histogram class. More...

struct	IndexHash

class	IntervalMap
	Division of the real numbers into interval sets. Each interval is assigned data of type Data. More...

class	IntervalMap2D

class	KMeans
	A simple clustering method to choose k clusters from a set of data. More...

class	LeastSquares1D
	1-D least squares y = ax+b More...

class	LinearModel
	A linear model of n-dimensional data. More...

class	LinearProcess

class	LinearProcessHMM
	A model of a temporal sequence consisting of k discrete states each with a gaussian emission probability depending on the prior continuous state. More...

class	LinearProcessHMMRegression

class	LinearProcessHMMState

class	LogisticModel
	Models the probability of a boolean outcome using a logit. More...

struct	MultivariateProbabilityDistribution

struct	OnlineLeastSquares
	Online estimation of least-squares solution to y = A x. More...

struct	OnlineMoments
	Online calculation of mean, covariance, min/max of vectors. More...

struct	StochasticLeastSquares
	Stochastic gradient descent estimation of least-squares solution to y = A x. More...

struct	StochasticPseudoLASSO
	Stochastic estimation of solution to y = A x via a LASSO-like procedure min_x \|\|b-A x\|\|^2 + alpha*\|\|x\|\|_1. More...

struct	UniformProbabilityDistribution

struct	UnivariateProbabilityDistribution

Functions
Real	Normalize (vector< Real > &w)

Real	NormalizeProbability (Vector &w)

Real	ExpNormalize (vector< Real > &w)

Real	ExpNormalize (Vector &w)

Real	logDot (const Gaussian< Real > &g, const Vector &xmean, const Matrix &xcov)

void	AddOuterProduct (Matrix &A, const Vector &u, const Vector &v)

std::ostream &	operator<< (std::ostream &out, const GaussianHMM &gmm)

std::istream &	operator>> (std::istream &in, GaussianHMM &gmm)

void	Subsample (vector< Real > &weights, vector< int > &values)

Real	LogDotProduct (const Vector &mu1, const Matrix &K1, const Vector &mu2, const Matrix &K2)
	Computes int_x b1(x)b2(x) dx with b1(x) = N(x;mu1,K1), b2 = N(x;mu2,K2) More...

Real	LogCosAngle (const Vector &mu1, const Matrix &K1, const Vector &mu2, const Matrix &K2)

Real	LogCosAngle (const Gaussian< Real > &g1, const Gaussian< Real > &g2)

ostream &	operator<< (ostream &out, const GaussianMixtureModel &gmm)

ostream &	operator<< (ostream &out, const GaussianMixtureModelRaw &gmm)

istream &	operator>> (istream &in, GaussianMixtureModel &gmm)

istream &	operator>> (istream &in, GaussianMixtureModelRaw &gmm)

std::ostream &	operator<< (std::ostream &out, const GaussianMixtureModel &gmm)

std::istream &	operator>> (std::istream &in, GaussianMixtureModel &gmm)

std::ostream &	operator<< (std::ostream &out, const GaussianMixtureModelRaw &gmm)

std::istream &	operator>> (std::istream &in, GaussianMixtureModelRaw &gmm)

std::istream &	operator>> (std::istream &in, LinearModel &model)

std::ostream &	operator<< (std::ostream &out, const LinearModel &model)

std::ostream &	operator<< (std::ostream &out, const LinearProcessHMM &gmm)

std::istream &	operator>> (std::istream &in, LinearProcessHMM &gmm)

void	MixtureCollapse (GaussianMixtureModelRaw &x, int k, bool refit)

ostream &	operator<< (ostream &out, const LogisticModel &model)

istream &	operator>> (istream &in, LogisticModel &model)

std::ostream &	operator<< (std::ostream &out, const LogisticModel &model)

std::istream &	operator>> (std::istream &in, LogisticModel &model)

bool	LeastSquares (const Matrix &data, const Vector &outcome, Vector &coeffs, Real &offset)
	Calculate a least squares fit of the outcome given data. More...

bool	LeastSquares (const vector< Vector > &data, int dependentVariable, Vector &coeffs)
	Calculate a least squares fit of some dependent variable. More...

bool	LeastSquaresPickDependent (const vector< Vector > &data, int &dependentVariable, Vector &coeffs)
	Calculate a least squares fit and pick some dependent variable. More...

bool	LeastSquares (const std::vector< Vector > &data, int dependentVariable, Vector &coeffs)
	Calculate a least squares fit of some dependent variable. More...

bool	LeastSquaresPickDependent (const std::vector< Vector > &data, int &dependentVariable, Vector &coeffs)
	Calculate a least squares fit and pick some dependent variable. More...

void	Sum (const vector< Vector > &data, Vector &sum)

void	Sum (const Matrix &data, Vector &sum)

Real	Mean (const vector< Real > &data)

Real	Mean (const Vector &data)

void	Mean (const vector< Vector > &data, Vector &mean)

void	Mean (const Matrix &data, Vector &mean)

Real	Variance (const vector< Real > &data)

Real	Variance (const Vector &data)

void	Variance (const vector< Vector > &data, Vector &var)

void	Variance (const Matrix &data, Vector &var)

Real	StdDev (const vector< Real > &data)

Real	StdDev (const Vector &data)

void	StdDev (const vector< Vector > &data, Vector &stddev)

void	StdDev (const Matrix &data, Vector &stddev)

Real	StdDev_Robust (const vector< Real > &data)

Real	StdDev_Robust (const Vector &data)

void	StdDev_Robust (const vector< Vector > &data, Vector &stddev)

void	StdDev_Robust (const Matrix &data, Vector &stddev)

Real	WeightedSum (const Vector &data, const Vector &w)

void	WeightedSum (const Matrix &data, const Vector &w, Vector &sum)

Real	WeightedMean (const Vector &data, const Vector &w)

void	WeightedMean (const Matrix &data, const Vector &w, Vector &mean)

Real	WeightedVariance (const Vector &data, const Vector &w)

void	WeightedVariance (const Matrix &data, const Vector &w, Vector &var)

Real	WeightedStdDev (const Vector &data, const Vector &w)

void	WeightedStdDev (const Matrix &data, const Vector &w, Vector &stddev)

Real	Sum (const std::vector< Real > &data)

Real	Sum (const Vector &data)

void	Sum (const std::vector< Vector > &data, Vector &sum)

Real	Mean (const std::vector< Real > &data)

void	Mean (const std::vector< Vector > &data, Vector &mean)

Real	Variance (const std::vector< Real > &data)

void	Variance (const std::vector< Vector > &data, Vector &var)

Real	StdDev (const std::vector< Real > &data)

void	StdDev (const std::vector< Vector > &data, Vector &stddev)

Real	StdDev_Robust (const std::vector< Real > &data)

void	StdDev_Robust (const std::vector< Vector > &data, Vector &stddev)

Detailed Description

Contains all definitions in the statistics directory.

Function Documentation

Real Statistics::ExpNormalize ( vector< Real > & w )

Given input of log(p)'s, perform exponentiation and normalization in a numerically stable way. Return the sum probability of the p[i]'s

References ExpNormalize(), Math::IsFinite(), and Statistics::GaussianMixtureModel::phi.

Referenced by ExpNormalize(), Statistics::GaussianHMM::Posterior(), Statistics::LinearProcessHMM::Posterior(), Statistics::GaussianMixtureModel::TrainEM(), Statistics::GaussianHMM::Update(), and Statistics::LinearProcessHMM::Update().

bool Statistics::LeastSquares	(	const std::vector< Vector > &	data,
		int	dependentVariable,
		Vector &	coeffs
	)

Calculate a least squares fit of some dependent variable.

Upon success, coeffs contains the coefficients of the independent variables, as well as the constant offset in coeffs(d) where d is the index of the dependent variable.

References LeastSquares().

bool Statistics::LeastSquares	(	const Matrix &	data,
		const Vector &	outcome,
		Vector &	coeffs,
		Real &	offset
	)

Calculate a least squares fit of the outcome given data.

The rows of data give the individual observations. Upon success, coeffs contains the coefficients of the independent variables, and offset contains a constant offset.

References LeastSquares().

Referenced by LeastSquares(), and LeastSquaresPickDependent().

bool Statistics::LeastSquares	(	const std::vector< Vector > &	data,
		int	dependentVariable,
		Vector &	coeffs
	)

Calculate a least squares fit of some dependent variable.

Upon success, coeffs contains the coefficients of the independent variables, as well as the constant offset in coeffs(d) where d is the index of the dependent variable.

References LeastSquares().

bool Statistics::LeastSquaresPickDependent	(	const std::vector< Vector > &	data,
		int &	dependentVariable,
		Vector &	coeffs
	)

Calculate a least squares fit and pick some dependent variable.

Upon success, dependentVariable contains the index of the dependent variable, coeffs contains the coefficients of the independent variables, as well as the constant offset in coeffs(d) where d is the index of the dependent variable.

References LeastSquares(), and LeastSquaresPickDependent().

Referenced by LeastSquaresPickDependent().

bool Statistics::LeastSquaresPickDependent	(	const std::vector< Vector > &	data,
		int &	dependentVariable,
		Vector &	coeffs
	)

Calculate a least squares fit and pick some dependent variable.

Upon success, dependentVariable contains the index of the dependent variable, coeffs contains the coefficients of the independent variables, as well as the constant offset in coeffs(d) where d is the index of the dependent variable.

References LeastSquares(), and LeastSquaresPickDependent().

Referenced by LeastSquaresPickDependent().

Real Statistics::LogDotProduct	(	const Vector &	mu1,
		const Matrix &	K1,
		const Vector &	mu2,
		const Matrix &	K2
	)

Computes int_x b1(x)b2(x) dx with b1(x) = N(x;mu1,K1), b2 = N(x;mu2,K2)

Method considers joint distribution of variables X1 ~ N(mu1,K1), X2 ~ N(mu2,K2), Y=X1-X2, X1 independent of X2: [X1;X2;Y] ~ N([mu1;mu2;mu1-mu2],[K1,0,K1; 0,K2,-K2; K1,-K2,K1+K2]) and then considers the probability that Y=0. Y ~= N(mu1-mu2,K1+K2) => N(0;mu1-mu2,K1+K2) = int_x b1(x)b2(x) dx

References Math::Gaussian< T >::L, LogDotProduct(), Math::Gaussian< T >::logProbability(), Math::Gaussian< T >::mu, Normalize(), Statistics::GaussianMixtureModel::phi, Statistics::GaussianMixtureModelRaw::phi, and Math::Gaussian< T >::setCovariance().

Referenced by LogDotProduct().

Real Statistics::Normalize ( vector< Real > & w )

Given input of nonnegative p's, perform normalization in a numerically stable way. Returns the sum of the p's. Specifically, if all p's are 0, then it returns a uniform distribution. If any p is infinite, then all non-infinite p's are set to 0 while the remaining weight is distributed evenly among all infinite p's

References Math::IsInf(), and Normalize().

Referenced by LogDotProduct(), Normalize(), Statistics::LinearProcessHMM::Posterior(), and Statistics::GaussianMixtureModel::TrainEM().

Classes

Functions

Detailed Description

Function Documentation