Add logistic regression <-> Variational Inference

[Nandini-Jaiswal]

This PR adds Variational Inference for logistic regression.

This PR closely follows and depends on:

• Add VI for linear regression #154

And must not be merged before this.

[Nandini-Jaiswal]

@ShouvikGhosh2048 @sourish-cmi Please take a look!

[sourish-cmi]

Looks okay to me

[sourish-cmi]

Looks okay to me

[Nandini-Jaiswal]

Hello @sourish-cmi sir, can you suggest how to fix this error?

[ShouvikGhosh2048]

The error is:

using CRRao, StableRNGs, RDatasets, StatsModels, GLM, Statistics

CRRao.set_rng(StableRNG(123))
turnout = dataset("Zelig", "turnout")[1:100,:]
model = fit(@formula(Vote ~ Age + Race + Income + Educate), turnout, LogisticRegression(), Logit(), Prior_Ridge(), VI())

Logistic Regression: Error During Test at /home/runner/work/CRRao.jl/CRRao.jl/test/runtests.jl:41
  Got exception outside of a @test
  LoadError: DomainError with Dual{ForwardDiff.Tag{AdvancedVI.var"#f#1"{AdvancedVI.ELBO, AdvancedVI.ADVI{ADTypes.AutoForwardDiff{nothing, Nothing}}, Bijectors.MultivariateTransformed{DistributionsAD.TuringDiagMvNormal{Vector{Float64}, Vector{Float64}}, Bijectors.Stacked{Vector{Function}, Vector{UnitRange{Int64}}}}, Base.Fix1{typeof(LogDensityProblems.logdensity), DynamicPPL.LogDensityFunction{DynamicPPL.TypedVarInfo{NamedTuple{(:λ, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:λ, typeof(identity)}, Int64}, Vector{Distributions.InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:λ, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, typeof(identity)}, Int64}, Vector{DistributionsAD.TuringScalMvNormal{Vector{Float64}, Float64}}, Vector{AbstractPPL.VarName{:β, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{CRRao.var"#LogisticRegression#18"{Logit, Float64}, (:X, :y), (), (), Tuple{Matrix{Float64}, Vector{Int32}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.MiniBatchContext{DynamicPPL.DefaultContext, Float64}}}, Tuple{Int64}}, Float64}}(NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN):
  Normal: the condition σ >= zero(σ) is not satisfied.