Here's the code in that attachment:
using Winston
using Distributions
# nonparametric regression, using pre-generated weights
# can be local constant, local linear, or local quadratic
#
# y is n X p
# x is n X dimx
# xeval is neval X dimx
# weights is n X neval (different weights for each eval. point)
#
# weights should sum to one by columns, they are typical
# nonparametric weights from a kernel.
function npreg(y, x, xeval, weights, order)
weights = sqrt(weights)
neval, dimx = size(xeval)
n, dimy = size(y)
stacked = [x; xeval]
# local constant
if order==0
X = ones(n,1)
Xeval = ones(neval,1)
end
# local linear
if order==1
X = [ones(n,1) x]
Xeval = [ones(neval,1) xeval]
end
# local quadratic
if order==2
# cross products
CP = zeros(n+neval, Int((dimx-1)*dimx/2))
cpind = 0
@inbounds for i = 1:dimx-1
for j = i+1:dimx
cpind += 1
CP[:,cpind] = stacked[:,i].*stacked[:,j]
end
end
ZZ = [ones(n+neval,1) stacked CP]
X = sub(ZZ,1:n,:)
Xeval = sub(ZZ,(n+1):n+neval,:)
end
# do the fit
yhat = zeros(neval, dimy)
@inbounds for i = 1:neval
WX = weights[:,i] .* X
Wy = weights[:,i] .* y
b = WX\Wy
yhat[i,:] = Xeval[i,:]*b
end
return yhat
end
function main()
order = 2 # 0 for local constant, 1 for local linear, 2 for local quadratic
k = 5 # number of regressors
bandwidth = 0.2
n = 10000
neval = 1000
x = rand(n,k)*pi*2.
xeval = [pi*ones(neval,k-1) linspace(0,pi*2.,neval)]
y = cos(sum(x,2)) + cos(2. * sum(x,2)) + randn(n,1)
ytrue = cos(sum(xeval,2)) + cos(2. * sum(xeval,2))
P = inv(chol(cov(x)))
x *=P
xeval *=P
weights = zeros(n,neval)
@time for i = 1:neval
z = x .- xeval[i,:]
z = z/bandwidth
weights[:,i] = prod(pdf(Normal(), z),2)
end
weights ./= sum(weights,1)
@time yhat = npreg(y, x, xeval, weights, order)
plot(xeval[:,k], [yhat ytrue])
end
main()
On Thursday, December 17, 2015 at 11:45:41 AM UTC+1, [email protected]
wrote:
>
> I am working on some code for nonparametric regression using local
> constant, local linear, and local quadratic fits. I would like to speed up
> the function npreg, which is contained in the attached code. This function
> gets the fit by weighted least square regression. I suspect that there may
> be better ways of doing this. Any pointers would be very welcome!
>
