first commit here

src/ExpFamilyPCA.jl

@@ -1,5 +1,87 @@
 module ExpFamilyPCA
 
-# Write your package code here.
+using Optim
+using CompressedBeliefMDPs
 
+# TODO: make this an imutable struct
+mutable struct EPCA <: CompressedBeliefMDPs.Compressor
+    n::Int  # number of samples
+    d::Int  # size of each sample
+    l::Int  # number of components
+    A::Matrix  # n x l matrix
+    V::Matrix  # l x d basis matrix
+
+    G  # convex function that induces g, F, f, and Bregman
+    g  # g(θ) = G'(θ)
+    F  # F(g(θ)) + G(θ) = g(θ)θ
+    f  # f(x) = F'(x)
+    Bregman  # generalized Bregman divergence induced by F
+
+    μ0::Real  # for numerical stability; must be in the range of g
+    ϵ::Real  # controls weight of stabilizing term in loss function
+
+    EPCA() = new()
 end
+
+
+# TODO: implement this with Symbolics of SymEnginer
+# """
+#     EPCA(G)
+
+# Return the EPCA induced by a convex function G.
+# """
+# function EPCA(G)
+#     return nothing
+# end
+
+# TODO: move this logic 
+function EPCA(l::Int, μ0::Real; ϵ::Float64=0.01)
+    epca = EPCA()
+    epca.l = l
+    epca.μ0 = μ0
+    epca.ϵ = ϵ
+    return epca
+end
+
+
+function CompressedBeliefMDPs.fit!(epca::EPCA, X; verbose=false, maxiter::Int=50)
+    @assert epca.l > 0
+    epca.n, epca.d = size(X)
+    epca.A = zeros(epca.n, epca.l)
+    epca.V = rand(epca.l, epca.d)
+
+    L(A, V) = sum(epca.Bregman(X, epca.g(A * V)) + epca.ϵ * epca.Bregman(epca.μ0, epca.g(A * V)))
+
+    for _ in 1:maxiter
+        if verbose println("Loss: ", L(epca.A, epca.V)) end
+        epca.V = Optim.minimizer(optimize(V->L(epca.A, V), epca.V))
+        epca.A = Optim.minimizer(optimize(A->L(A, epca.V), epca.A))
+    end
+end
+
+# TODO: make sure this works for both matrices and vectors!! also update the signature in compressed belief pomdps
+function CompressedBeliefMDPs.compress(epca::EPCA, X; maxiter=50, verbose=false)
+    n, d = size(X)
+    @assert d == epca.d
+    Â = zeros(n, epca.l)
+    L(A, V) = sum(epca.Bregman(X, epca.g(A * V)) + epca.ϵ * epca.Bregman(epca.μ0, epca.g(A * V)))
+    for _ in 1:maxiter
+        if verbose println("Loss: ", L(Â, epca.V)) end
+        Â = Optim.minimizer(optimize(A->L(A, epca.V), Â))
+    end
+    return  * epca.V
+end
+
+CompressedBeliefMDPs.decompress(epca::EPCA, compressed) = epca.g(compressed)
+
+
+export
+    PoissonPCA
+include("poisson.jl")
+
+export
+    BernoulliPCA
+include("bernoulli.jl")
+
+
+end # module ExpFamilyPCA

src/bernoulli.jl

@@ -0,0 +1,22 @@
+"""
+Best with binary data. 
+"""
+function BernoulliPCA(l::Int; μ0::Real=0.5, kwargs...)
+    epca = EPCA(l, μ0; kwargs...)
+    # TODO: eventually replace this w/ symbolic diff
+    ϵ = 10e-20
+    @. begin
+        G(θ) = log(1 + exp(θ))
+        g(θ) = exp(θ) / (1 + exp(θ))
+        F(x) = x * log(x) + (1 - x) * log(1 - x)
+        f(x) = log(x / (1 - x))
+        # TODO: look into when this value is negative
+        Bregman(p, q) = p * log((p + ϵ) / (q + ϵ)) + (1 - p) * log((1 - p + ϵ) / (1 - q + ϵ))  # with additive smoothing
+    end
+    epca.G = G
+    epca.g = g
+    epca.F = F
+    epca.f = f
+    epca.Bregman = Bregman
+    return epca
+end

src/poisson.jl

@@ -0,0 +1,22 @@
+function PoissonPCA(l::Int; μ0::Real=0, kwargs...)
+    epca = EPCA(l, μ0; kwargs...)
+    # TODO: eventually replace this w/ symbolic diff
+    # ϵ = 10e-20
+    ϵ = eps()
+    @. begin
+        G(θ) = exp(θ)
+        g(θ) = exp(θ)
+        F(x) = x * log(x) - x
+        f(x) = log(x)
+        Bregman(p, q) = p * log((p + ϵ) / (q + ϵ)) + q - p  # with additive smoothing
+    end
+    epca.G = G
+    epca.g = g
+    epca.F = F
+    epca.f = f
+    epca.Bregman = Bregman
+    return epca
+end
+
+
+# TODO: include a normalized Poisson w/ link function in footnote 5 of long paper