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1dexperiments.jl
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using LinearAlgebra
using HCubature
using SpecialFunctions
using PyPlot
using SparseArrays
using ProgressBars
using StatsBase
using AlphaStableDistributions
using AdvancedHMC
using Dates
using MAT
using Optim
using MCMCDiagnostics
using Dates
function difference1(X)
N = length(X);
M = zeros(N,N);
for i = 2:N
M[i,i] = -1;
M[i,i-1] = 1;
end
M[1,1] = 1;
return M
end
function difference2(X)
N = length(X);
M = zeros(N,N);
for i = 3:N
M[i,i] = -1;
M[i,i-1] = 2;
M[i,i-2] = -1;
end
M[1,1] = 1; M[2,1] = 1; M[2,2] = -1;
return M
end
function smatrix(X0,a,b)
N = length(X0);
dx = X0[2]-X0[1];
M = zeros(N,N);
for i=2:N-1
M[i,i-1] = -a/dx^2;
M[i,i+1] = -a/dx^2;
M[i,i] = 2*a/dx^2 +b;
end
#M[1,:] = [b+2*a/dx^2 -a/dx^2 zeros(1,N-3) -a/dx^2];
#M[N,:] = [-a/dx^2 zeros(1,N-3) -a/dx^2 b+2*a/dx^2];
M[1,1] = 1;
#M(N,1) = 1/dx;
#M(N,2) = -1/dx;
M[N,N] = 1
return M
end
function measurementmatrix(X,MX,kernel)
s = X[2]-X[1];
F = zeros(size(MX)[1],size(X)[1])
for i = 1:size(MX)[1]
F[i,:] = s.*kernel.(X,MX[i]);
end
return F
end
function divide(N,NT)
even = mod(N,NT) == 0
k = Int64(floor(N/NT))
t = 0
if(even)
q = Vector{Vector{Int64}}(undef,k)
t = k
else
q = Vector{Vector{Int64}}(undef,k+1)
t = k +1
end
for i = 1:t
q[i] = Vector(NT*(i-1)+1:min(NT*i,N))
end
return q
end
function partialreplace(orig,replace,ix)
a = copy(orig)
a[ix] = replace
return a
end
function logpcauchy(W,arguments)
Mat = arguments.Mat;
noisesigma = arguments.noisesigma
scale = arguments.scale; y = arguments.y; #F = arguments.F
G = 1;
r = Mat*(W);
#r = F*U;
logp = -0.5/noisesigma^2*sum((r-y).^2);
logp = logp + sum(log.(scale./(pi*(scale^2.0.+W.^2))));
return logp;
end
function logpcauchygradi(W,arguments;both=false)
logp = 0.0
Mat = arguments.Mat;
noisesigma = arguments.noisesigma
scale = arguments.scale; y = arguments.y; #F = arguments.F
r = Mat*(W);
#r = F*U;
if(both)
logp = -0.5/noisesigma^2*sum((r-y).^2);
logp = logp + sum(log.(scale./(pi*(scale^2.0.+W.^2))));
end
Gr = Mat
nt = length(y); N =size(W)[1];
G = zeros(N,);
G = -1/noisesigma^2*Mat'*(r-y)
# for i = 1:nt
# q =(-((r[i]-y[i])./noisesigma.^2))*Gr[i,:]';
# G = G + dropdims(q, dims = tuple(findall(size(q) .== 1)...))
# end
G = G -2*W./(scale^2 .+ W.^2);
return logp,G
end
function logpdiff(U,args,cache)
M = args.Mat;
noisesigma = args.noisesigma
scale = args.scale; y = args.y; F = args.F
Fxprop = cache.Fxprop
Dxprop = cache.Dxprop
res = cache.residual
Fxprop .= F*U;
Dxprop .= M*U;
res .= Fxprop-y
logp = -0.5/noisesigma^2*dotitself(res);
logp = logp + sum(log.(scale./((scale^2 .+ Dxprop.^2))));
return logp
end
function logpdiffgradi(U,arguments,cache;both=true)
M = arguments.Mat;
noisesigma = arguments.noisesigma
scale = arguments.scale; y = arguments.y; F = arguments.F
Fxprop = cache.Fxprop
Dxprop = cache.Dxprop
res = cache.residual
Fxprop .= F*U;
Dxprop .= M*U;
res .= Fxprop-y
logp = -0.5/noisesigma^2*dotitself(res);
logp = logp + sum(log.(scale./((scale^2 .+ Dxprop.^2))));
#nt = length(y); N = length(U);
#for i = 1:nt
#println(Gr[i,:]')
#q = (-((r[i]-y[i])./noisesigma.^2))*Gr[i,:]';
#G = G + dropdims(q, dims = tuple(findall(size(q) .== 1)...))
#end
G= F'*(-((res)./noisesigma.^2))
Gd = M'*(-2.0*Dxprop./(scale^2 .+ Dxprop.^2));
#Gd = Gd'*M;
G = G + Gd;
return logp,G
end
function logpdiffpartial(ix,U,args,cache,current)
D = @view args.Mat[:,ix];
noisesigma = args.noisesigma
scale = args.scale; y = args.y;
F = @view args.F[:,ix]
logp = 0.0
currx = @view current.xcurr[ix]
Fxcurr = current.Fxcurr
Dxcurr = current.Dxcurr
xprop = cache.xprop
xprop[ix] = U
compx = U-currx
Fxprop = cache.Fxprop
Fxprop .= Fxcurr
Fxprop .+= F*compx
Dxprop = cache.Dxprop
Dxprop .= Dxcurr
Dxprop .+= D*compx
res = cache.residual
res .= Fxprop
res .-= y
logp = -0.5/noisesigma^2*dotitself(res);
logp = logp + sum(log.(scale./((scale^2 .+ Dxprop.^2))));
return logp
end
function logpdiffpartialgradi(ix,U,arguments,cache,current;both=true)
D = @view arguments.Mat[:,ix];
noisesigma = arguments.noisesigma
scale = arguments.scale; y = arguments.y; F = @view arguments.F[:,ix]
#(Fxcurr=(F*X0),Dxcurr=(Md1*X0), xcurr = copy(X0))
currx = @view current.xcurr[ix]
Fxcurr = current.Fxcurr
Dxcurr = current.Dxcurr
xprop = cache.xprop
xprop[ix] = U
compx = U-currx
Fxprop = cache.Fxprop
Fxprop .= Fxcurr
Fxprop .+= F*compx
Dxprop = cache.Dxprop
Dxprop .= Dxcurr
Dxprop .+= D*compx
res = cache.residual
res .= Fxprop
res .-= y
logp = 0.0
if (both)
logp = -0.5/noisesigma^2*dotitself(res);
logp = logp + sum(log.(scale./((scale^2 .+ Dxprop.^2))));
end
G = cache.gradiprop
G[ix] = -F'*res/noisesigma^2
G[ix] = G[ix] + D'*(-2.0*Dxprop./(scale^2 .+ Dxprop.^2));
return logp,G[ix]
end
function refreshcurrent!(cache,current;mode=1)
if (mode ==1)
current.Mxcurr .= cache.Mxprop
current.noisecurr .= cache.noiseprop
elseif (mode==2)
current.xcurr .= cache.xprop
current.Fxcurr .= cache.Fxprop
current.Dxcurr .= cache.Dxprop
end
end
function repatpartial(lpdf,placeholder,ix,x0,args,cache,current,tuning;mode=1,Np=1,Nruns=1,T=-Inf,extra=copy(x0))::Vector{Float64}
x = copy(x0[ix])
dim = length(x)
logpdf(xp) = lpdf(ix,xp,args,cache,current)
#logpdf(xp) = lpdf(partialreplace(x0,xp,ix),args,cache)
density = logpdf(x)
z = copy(extra[ix])
u = randn(dim)
densityz = logpdf(z)
for i = 1:Nruns
R = tuning.Cho.L/sqrt(2)
u .= randn(dim)
xtilde = x + R * u
densitytilde = logpdf(xtilde)
while (log(rand()) >= density - densitytilde)
u .= randn(dim)
xtilde .= x + R * u
densitytilde = logpdf(xtilde)
end
u .= randn(dim)
xstar = xtilde + R * u
densitystar = logpdf(xstar)
while (log(rand()) >= densitystar - densitytilde)
u .= randn(dim)
xstar .= x + R * u
densitystar = logpdf(xstar)
end
u .= randn(dim)
zstar = xstar + R * u
densityzstar = logpdf(zstar)
while (log(rand()) >= densitystar - densityzstar)
u .= randn(dim)
zstar .= xstar + R * u
densityzstar = logpdf(zstar)
end
ratio = densitystar + min(0,density-densityz) - density - min(0,densitystar-densityzstar)
if (log(rand()) <= ratio)
x .= xstar
z .= zstar
extra[ix] = zstar
density = densitystar
densityz = densityzstar
end
tuning.n = tuning.n + 1
if (tuning.n <= tuning.Nadapt)
xmp = copy(tuning.xm)
tuning.xm .= tuning.xm + (x-tuning.xm)/tuning.n
xm = tuning.xm
tuning.C .= ((tuning.n-1)*tuning.C + (x-xm)*(x-xmp)')/tuning.n
tuning.Cho = cholesky(Hermitian(2.38^2/dim*tuning.C + 1e-11*I(dim)))
end
end
logpdf(x)
refreshcurrent!(cache,current;mode=mode)
return x
end
function mwgpartial(lpdf,gradilpdf,ix,x00,args,cache,current,tuning;Nruns=5,Np=3,T=5.0,mode=1,extra=nothing)
x0 = repeat(x00[ix],Np)
x = copy(x0)
Nall = length(x)
xnew = similar(x)
pnew = similar(xnew)
p = similar(xnew)
logpdf_can(xp) = lpdf(ix,xp,args,cache,current)
#logpdf_can(xp) = lpdf(partialreplace(x00,xp,ix),args,cache)
logpdf(x) = totallogpdf(x,logpdf_can,Np,T)
glpdf_can(xp) = gradilpdf(ix,xp,args,cache,current;both=false)[2]
#glpdf_can(xp) = gradilpdf(partialreplace(x00,xp,ix),args,cache)[2][ix]
glpdf(x) = totalloggrad(x,logpdf_can,glpdf_can,Np,T)[2]
glpdfboth(x) = totalloggrad(x,logpdf_can,glpdf_can,Np,T)
ll = logpdf(x)
for _ = 1:Nruns
tuning.n = tuning.n + 1
V=randn(Nall)
xnew .= x+ tuning.Cho.L*V
lnew = logpdf(xnew)
U = rand()
apr = min(1.0,exp(-ll + lnew))
if (U < apr)
ll = lnew
x .= xnew
tuning.acc = tuning.acc +1
end
if (tuning.n <= tuning.Nadapt)
xmp = copy(tuning.xm)
tuning.xm .= tuning.xm + (x-tuning.xm)/tuning.n
xm = tuning.xm
tuning.C .= ((tuning.n-1)*tuning.C + (x-xm)*(x-xmp)')/tuning.n
tuning.Cho = cholesky(Hermitian(2.38^2/Nall*tuning.C + 1e-11*I(Nall)))
# atarg = 0.3
# V = V/norm(V)
# z = sqrt(tuning.n^(-0.7) *abs(tuning.acc/tuning.n - atarg)) * tuning.Cho.L*V
# #println(z)
# if (tuning.acc/tuning.n >= atarg)
# lowrankupdate!(tuning.Cho, z)
# else
# lowrankdowndate!(tuning.Cho, z)
# end
end
end
xret = reweight(x,Np,logpdf_can,T)
logpdf_can(xret)
refreshcurrent!(cache,current;mode=mode)
return xret
end
mutable struct rram
n::Int64
acc::Int64
Nadapt::Int64
C::Array{Float64,2}
Cho::Cholesky{Float64,Array{Float64,2}}
xm::Vector{Float64}
end
function totalsample(lpdf,glpdf,x0,meas,arg,ix;N=1,Nadapt=1000,Nruns=5,thinning=10,algo=repatpartial,mode=1,Np=2,T=2.0)
x = copy(x0)
Npar = length(x0)
chain = zeros(Npar, Int(floor(N / thinning)))
Nix = length(ix)
if (mode==2)
cache=(xprop=copy(x0),Fxprop=(arg.F*x0),Dxprop=(arg.Mat*x0), residual=similar(meas),gradiprop=similar(x0))
current = (Fxcurr=(arg.F*x0),Dxcurr=(arg.Mat*x0), xcurr = copy(x0))
else
cache = []
current = []
end
if algo == repatpartial
extra = copy(x0)
tuning = Vector{rram}(undef,Nix)
for k = 1:Nix
n = length(ix[k])
C = 0.1*Array(I(n))
Cho = cholesky(C)
xm = copy(x0[ix[k]])
tuning[k] = rram(1,0,Nadapt,C,Cho,xm)
end
elseif (algo==mwgpartial)
extra = []
tuning = Vector{rram}(undef,Nix)
#tuning = Vector{dahmc2}(undef,Nix)
#tuning = Vector{ahmc}(undef,Nix)
for k = 1:Nix
n = length(ix[k])*Np
C = 5*Array(I(n))
Cho = cholesky(C)
xm = repeat(copy(x0[ix[k]]),Np)
tuning[k] = rram(1,0,Nadapt,C,Cho,xm)
end
pb = ProgressBar(1:N)
for i in pb
for k = 1:Nix
x[ix[k]] = algo(lpdf,glpdf,ix[k],x,arg,cache,current,tuning[k];mode=mode,Nruns=Nruns,extra=extra,Np=Np,T=T)#lpdf,ix,x0,args,cache,current,tuning
if (i % thinning == 0)
chain[ix[k], Int(i / thinning)] = x[ix[k]]
end
end
end
return chain,tuning
end
function savechain(c,prefix)
p = pwd()
f = p*"/chains/"*prefix*"_"*Dates.format(Dates.now(), "yyyy_mm_dd_HH_MM_SS")*".mat"
matwrite(f,Dict("chain"=>c))
end
N = 200;
x = Vector(range(-0.0,stop=1.0,length=N)); dx = x[2]-x[1];
xi = copy(x)
measxi = copy(xi[1:3:end])
triangle(x) = 1.0*(x+1)*(x<=0)*(x>=-1) + 1.0*(-x+1)*(x>0)*(x<=1);
heavi(x) = 1.0*(x>=0);
tf(x) = 0+ 0.2*heavi(x-0.1)*heavi(-x+0.15) - 0.5*heavi(x-0.65)*heavi(-x+0.7)+ 0*exp(-60*abs(x-0.2)) - 0*exp(-180*abs(x-0.8)) + 0*triangle(10*(x-0.8)) + 1*heavi(x-0.3)*heavi(-x+0.6);
tf(x) = heavi(x-0.75)*heavi(-x+0.9)+ triangle(10*(x-0.15)) + triangle(10*(x-0.55))*heavi(x-0.55) + 0*triangle(30*(x-0.65))*heavi(-x+0.65) + exp(-70*abs(x-0.4)) # heavi(x-0.45)*heavi(-x+0.55)
sigma = 0.1; # Standard deviation of the measurement noise.
cw = 500;
kernel(x,y) = sqrt(cw)/sqrt(π)*exp(-cw*(x-y)^2)
tfc(x) = quadgk(y -> tf(y)*kernel(x,y), 0, 1, rtol=1e-9)[1]
tfc(x) = HCubature.hquadrature(y -> tf(y)*kernel(x,y), 0.0, 1.0; rtol=1e-6,atol=1e-6,initdiv=7)[1]
F = measurementmatrix(xi,measxi,kernel); # Theory matrix.
gt = tf.(xi);
gtc = tfc.(measxi); #F*gt
gtc2 = F*gt
Random.seed!(100)
meas = gtc .+ sigma.*randn(size(measxi)); # Simulate the measurements.
lcauchy = 0.015;
acauchy = lcauchy^2; bcauchy = 1;
cauchypriorscale = 0.5;
cd1scale = 0.05;
cd2scale = 0.01;
Md1=difference1(xi);
Md2=difference2(xi);
Mcauchy = smatrix(x,acauchy,bcauchy); MN = size(Mcauchy)[1];
measnoisescaling = 1.0
diff1arg = (F=F, y=meas,Mat=sparse(Md1),scale=cd1scale,noisesigma=measnoisescaling*sigma)
diff2arg = (F=F, y=meas,Mat=sparse(Md2),scale=cd2scale,noisesigma=measnoisescaling*sigma)
varg = (Mat=Mcauchy,F=F,y=meas,scale=cauchypriorscale,noisesigma=measnoisescaling*sigma)
cached=(xprop=similar(xi),Fxprop=(F*xi),Dxprop=(Md1*xi), residual=similar(meas),gradiprop=similar(xi))
cache2d=(xprop=similar(xi),Fxprop=(F*xi),Dxprop=(Md2*xi), residual=similar(meas),gradiprop=similar(xi))
cachev =(xprop = similar(xi), Fxprop = F*xi, Dxprop = Mcauchy*xi,residual=similar(meas),gradiprop=similar(xi))
targetdiff1(w) =-logpdiff(w,diff1arg,cached)
targetdiffgrad1(w) = -logpdiffgradi(w,diff1arg,cached;both=false)[2]#-logpcauchygradi(w,cauchyarg)[2]#
res1 = Optim.optimize(targetdiff1, targetdiffgrad1,0*randn(N,),Optim.LBFGS(), Optim.Options(allow_f_increases=true,show_trace=false,iterations=1000); inplace = false)
MAP_diff1 = res1.minimizer
targetdiff2(w) =-logpdiff(w,diff2arg,cache2d)
targetdiffgrad2(w) = -logpdiffgradi(w,diff2arg,cached;both=false)[2]#-logpcauchygradi(w,cauchyarg)[2]#
res2 = Optim.optimize(targetdiff2, targetdiffgrad2,0*randn(N,),Optim.LBFGS(), Optim.Options(allow_f_increases=true,show_trace=false,iterations=30000); inplace = false)
MAP_diff2 = res2.minimizer
targetv(w) = -logpdiff(w,varg,cachev)
targetvgrad(w) = -logpdiffgradi(w,varg,cachev;both=false)[2]#-logpcauchygradi(w,cauchyarg)[2]#
res2 = Optim.optimize(targetv, targetvgrad,0.00*randn(N,),Optim.LBFGS(), Optim.Options(allow_f_increases=true,show_trace=false,iterations=30000); inplace = false)
MAP_v = res2.minimizer
Ntot = length(xi)
function NUTS_sample(N,arg,cac)
n_samples, n_adapts = 100, 30
ss = Vector{Any}(undef,N)
st = Vector{Any}(undef,N)
Np = 1
T = 3.0
for i = 1:N
Ntot = length(xi)*Np
Random.seed!(i)
initial_θ = repeat(MAP_v,Np)
global c
targetdiff(w) = logpdiff(w,arg,cac)
targetdiffgrad(w) = logpdiffgradi(w,arg,cac;both=true)
metric = DiagEuclideanMetric(Ntot)# DenseEuclideanMetric(Ntot)# DiagEuclideanMetric(Ntot)
hamiltonian = Hamiltonian(metric, targetdiff, targetdiffgrad)
initial_ϵ = find_good_stepsize(hamiltonian, initial_θ)
integrator = Leapfrog(initial_ϵ)# TemperedLeapfrog(initial_ϵ, 1.05)# Leapfrog(initial_ϵ)
proposal = NUTS{MultinomialTS, GeneralisedNoUTurn}(integrator,10,1000.0)
adaptor = StanHMCAdaptor(MassMatrixAdaptor(metric), StepSizeAdaptor(0.8, integrator))
c, stats = sample(hamiltonian, proposal, initial_θ, n_samples, adaptor, n_adapts; progress=true)
ss[i] = hcat(c...)
# ss[i] = c
st[i] = stats
pr="NUTS_"*string("diff1_NUTS_")
savechain(c,pr)
end
return ss, st
end
#c,b = NUTS_sample(10,diff1arg,cached)
ix = divide(N,1)
algo = repatpartial#mwgpartial
grfunk = logpdiffpartialgradi# logpcauchyreppartialgradi#
funk = logpdiffpartial#logpcauchyreppartial#logpdiffpartial#
par = diff1arg
mode = 2# 1
x000 = copy(MAP_diff1) #randn(N,)
cached=(xprop=copy(x000),Fxprop=(F*x000),Dxprop=(Md1*x000), residual=copy(meas),gradiprop=copy(gt))
currentd = (Fxcurr=(F*MAP_diff1),Dxcurr=(Md1*MAP_diff1), xcurr = copy(MAP_diff1))
for t=1:0
Random.seed!(t)
xz = copy(MAP_v)#0.1*randn(N,)
Nsamples = 1500; Nadapt = 1250; thinning = 20
Np = 1; Nruns = 5; T = 1.0
c,tun=totalsample(funk,grfunk,xz,meas,par,ix;N=Nsamples,Nadapt=Nadapt,thinning=thinning,algo=algo,mode=mode,Np=Np,T=T,Nruns=Nruns)
savechain(c,"diff1_"*string(nameof(algo))*"_"*string(nameof(funk))*"_N"*string(Nsamples)*"_Nadapt"*string(Nadapt)*"_thin"*string(thinning)*"_Np"*string(Np)*"_Nruns"*string(Nruns)*"_T"*string(T))
println(effective_sample_size(c[1,:]))
global c
global tun
end