condmixt (version 1.1)

condmixt.quant: Quantile computation for conditional mixtures.

Description

Quantile computation for conditional mixtures requires to solve numerically F(y)=p where F is the distribution function of the conditional mixture and p is a probability level.

Usage

condhparetomixt.quant(theta, h, m, x, p, a, b, trunc = TRUE)
condhparetomixt.dirac.quant(theta,h,m,x,p,a,b)
condhparetomixt.dirac.condquant(theta,h,m,x,p,a,b)
condgaussmixt.quant(theta,h,m,x,p,a,b,trunc=TRUE)
condgaussmixt.dirac.quant(theta,h,m,x,p,a,b)
condgaussmixt.dirac.condquant(theta,h,m,x,p,a,b)
condlognormixt.quant(theta,h,m,x,p,a,b)
condlognormixt.dirac.quant(theta,h,m,x,p,a,b)
condlognormixt.dirac.condquant(theta,h,m,x,p,a,b)
condbergamixt.quant(theta,h,x,p)

Arguments

theta

Vector of neural network parameters

h

Number of hidden units

m

Number of components

x

Matrix of explanatory (independent) variables of dimension d x n, d is the number of variables and n is the number of examples (patterns)

p

Probability level in [0,1]

a

Approximate lower bound on quantile value.

b

Approximate upper bound on quantile value.

trunc

Logical variable, if true, density is truncated below zero and re-weighted to make sure it integrates to one.

Value

Computed quantiles are stored in a matrix whose rows correspond to the probability levels and whose columns correspond to the number of examples n.

Details

condhparetomixt indicates a mixture with hybrid Pareto components, condgaussmixt for Gaussian components, condlognormixt for Log-Normal components, condbergam for a Bernoulli-Gamma two component mixture, dirac indicates that a discrete dirac component is included in the mixture condquant applies for mixtures with a dirac component at zero : quantiles are computed given that the variable is strictly positive, that is the quantile is computed for the continuous part of the mixture only : P(Y <= y | Y >0, X)

References

Bishop, C. (1995), Neural Networks for Pattern Recognition, Oxford

Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Mixture for Conditional Asymmetric Fat-Tailed Distributions, 20, IEEE Transactions on Neural Networks

See Also

condmixt.train,condmixt.nll, condmixt.init

Examples

# NOT RUN {
# generate train data
ntrain <- 200
xtrain <- runif(ntrain)
ytrain <- rfrechet(ntrain,loc = 3*xtrain+1,scale =
0.5*xtrain+0.001,shape=xtrain+2)
plot(xtrain,ytrain,pch=22) # plot train data
qgen <- qfrechet(0.99,loc = 3*xtrain+1,scale = 0.5*xtrain+0.001,shape=xtrain+2)
points(xtrain,qgen,pch="*",col="orange")

# generate test data
ntest <- 200
xtest <- runif(ntest)
ytest <- rfrechet(ntest,loc = 3*xtest+1,scale =
0.5*xtest+0.001,shape=xtest+2)

h <- 2 # number of hidden units
m <- 4 # number of components

# train a mixture with hybrid Pareto components
thetaopt <- condhparetomixt.train(h,m,t(xtrain),ytrain, nstart=2,iterlim=100)
qmod <- condhparetomixt.quant(thetaopt,h,m,t(xtest),0.99,0,10,trunc=TRUE)
points(xtest,qmod,pch="o",col="blue")

# }