.~ seems to give incorrect answers #28
Description
using Turing
@model naive_bayes(image, label, D, N, C, ::Type{T}=Float64) where {T<:Real} = begin
m = Matrix{T}(undef, D, C)
for c = 1:C
m[:,c] ~ MvNormal(fill(0, D), 10)
end
# m .~ Normal(0, 10) # this gives incorrect answer
for n = 1:N
image[:,n] ~ MvNormal(m[:,label[n]], 1)
end
end
Checking answer via
using MLDatasets
image_raw = reshape(MNIST.traintensor(Float64), 28*28, :)
label = MNIST.trainlabels() .+ 1
# Pre-processing
using MultivariateStats
D_pca = 40
pca = fit(PCA, image_raw; maxoutdim=D_pca)
image = transform(pca, image_raw)
@info "Peformed PCA to reduce the dimension to $D_pca"
# Data function
get_data(n=100) = Dict(
"C" => 10,
"D" => D_pca,
"N" => n,
"image" => image[:,1:n],
"label" => label[1:n]
)
data = get_data()
model = naive_bayes(data["image"], data["label"], data["D"], data["N"], data["C"])
alg = HMC(0.1, 4)
n_samples = 2_000
chain = sample(model, alg, n_samples)
m_data = Array(group(chain, :m))
m_bayes = mean(
map(
i -> reconstruct(pca, Matrix{Float64}(reshape(m_data[i,:], D_pca, 10))),
1_000:100:2_000
)
)
using PyPlot
function make_imggrid(imgs, n_rows, n_cols; gap::Int=1)
n = length(imgs)
d_row, d_col = size(first(imgs))
imggrid = 0.5 * ones(n_rows * (d_row + gap) + gap, n_cols * (d_col + gap) + gap)
i = 1
for row = 1:n_rows, col = 1:n_cols
if i <= n
i_row = (row - 1) * (d_row + gap) + 1
i_col = (col - 1) * (d_col + gap) + 1
imggrid[i_row+1:i_row+d_row,i_col+1:i_col+d_col] .= imgs[i]
else
break
end
i += 1
end
return imggrid
end
imgs = [reshape(m_bayes[:,i], 28, 28)' for i in 1:size(m_bayes, 2)]
plt.figure(figsize=(5, 2))
plt.imshow(make_imggrid(imgs, 2, 5), cmap="gray")It should give something like below:
Edit (05/2021): Updated example