
This is a contrast method for ProDenICA
. It fits a tilted
Gaussian density estimate by multiplying the Gaussian density by an
exponential tilt function using a cubic smoothing spline
GPois(x, df = 6, B = 500, order = 1, widen = 1.2, density.return = FALSE, ...)
vector of real values
degrees of freedom for the smoothing-spline fit; default is 6
number of grid points for density estimate; default is 500
A robustness parameter to avoid responding to outliers in
x
. The range of x
is estimated by the order
th
and n-order+1
th order statistics. Default is order=1
an expansion factor to widen the range of x
;
default is widen=1.2
logical variable, with default FALSE
. If
density.return=TRUE
, the estimated density is returned
additional arguments to GAM; typically not used
a list with components
estimated contrast function, which is the log of the tilting
function, evaluated at the original values of x
. mean(Gs)
is measure of negentropy
estimated first derivative of Gs
at x
estimated second derivative of Gs
at x
if density.return=TRUE
, a list with components
$x
the grid of B values of x
, and $y
the estimated
density.
See Section 14.7.4 of 'Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2009, 2nd Edition)' for details
Hastie, T. and Tibshirani, R. (2003) Independent Component Analysis through Product Density Estimation in Advances in Neural Information Processing Systems 15 (Becker, S. and Obermayer, K., eds), MIT Press, Cambridge, MA. pp 649-656 Hastie, T., Tibshirani, R. and Friedman, J. (2009) Elements of Statistical Learning (2nd edition), Springer. https://hastie.su.domains/ElemStatLearn/printings/ESLII_print12_toc.pdf
ProDenICA
, G1
and G0
# NOT RUN {
p=2
### Can use letters a-r below for dist
dist="n"
N=1024
A0<-mixmat(p)
s<-scale(cbind(rjordan(dist,N),rjordan(dist,N)))
x <- s %*% A0
fit=ProDenICA(x,Gfunc=GPois, whiten=TRUE, density=TRUE)
par(mfrow=c(2,1))
plot(fit)
# }
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