Distributions fit_mle of distribution type vs distributions with parameters

General Usage
, ,
1

I try the following, but it does not work.

using Distributions
p = 0.2
x = rand(Bernoulli(0.2),50)
fit_mle(Bernoulli(p), x)
 MethodError: no method matching fit_mle(::Bernoulli{Float64}, ::Vector{Bool})

I know that

fit_mle(Bernoulli, x)

works.
Adding the following seems to do what I want

function fit_mle(g::Distribution{Univariate,Discrete}, args...)
    fit_mle(typeof(g), args...)
end

function fit_mle(g::Distribution{Univariate,Continuous}, args...)
    fit_mle(typeof(g), args...)
end

However, I don’t understand why fit_mle(Bernoulli(p), x) is not authorized (or coded this way)?
Sure, the parameter p does not matter for the usual function where the MLE is explicit.
In my applications, I write extensions of fit_mle to other distributions where the actual parameter p is useful. It can be an initialization for an optimization algorithm.
Or when the distributions are Products or Mixture, the type is not enough and the whole distribution structure is needed.

2

I’d be more surprised if that did work - the point of fit_mle(Bernoulli, x) is to find p.

This is the same with any type of optimization scheme I know. Say in Optim if I want to find the x that minimizes a function, I would do:

rosenbrock(x) =  (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
result = optimize(rosenbrock, zeros(2), BFGS())

and not optimize(rosenbrock([1.5, 2.5]), zeros(2), BFGS()).

1 Like
3

I get your point, the first p = p_ini is just an initial point here not what you look for.
In optimization, it would not work because rosenbrock([1.5, 2.5]) is a scalar and not a function.
For distribution fitting Bernoulli(p) carries the same info as just the type Bernoulli.
In fact, it carries more info because of the p_ini, in some situation it might be useless I agree (like for Benoulli).
Imagine a Product distribution of an Exponential and Normal distribution.
If one were to write a fit_mle(::Type{<:Product}, x) how do you extract the informations over the component of the Product if you just accept the type ? Whereas fit_mle(g::Product, x) has everything you need.
Same thing for a Mixture distribution.

I am still uncomfortable with the types, so there might be a way to do that I do not understand.

4

Actually product types are parametrized:

julia> typeof(product_distribution(Gamma(),Normal()))
Distributions.ProductDistribution{1, 0, Tuple{Gamma{Float64}, Normal{Float64}}, Continuous, Float64}

julia>

I agree with you for mixtures though.

5

Thanks for the heads-up, I did not notice it got updated with v0.25.65 on July 22.

However, note that

# v0.25.64 and bellow
julia> typeof(product_distribution([Gamma(),Normal()]...))
ERROR: MethodError: no method matching product_distribution(::Gamma{Float64}, ::Normal{Float64})

julia> typeof(product_distribution([Gamma(),Normal()]))
Product{Continuous, Distribution{Univariate, Continuous}, Vector{Distribution{Univariate, Continuous}}}

# v0.25.65 and above
julia> typeof(product_distribution([Gamma(),Normal()]...))
Distributions.ProductDistribution{1, 0, Tuple{Gamma{Float64}, Normal{Float64}}, Continuous, Float64}

julia> typeof(product_distribution([Gamma(),Normal()]))
Product{Continuous, Distribution{Univariate, Continuous}, Vector{Distribution{Univariate, Continuous}}}
# -> still use the old (depreacated) Product interface

Indeed, having a similar update for MixtureModels would answer my concern and unify the interface.

6 
# v0.25.65 and above
julia> typeof(product_distribution([Gamma(),Normal()]...))
Distributions.ProductDistribution{1, 0, Tuple{Gamma{Float64}, Normal{Float64}}, Continuous, Float64}

julia> typeof(product_distribution([Gamma(),Normal()]))
Product{Continuous, Distribution{Univariate, Continuous}, Vector{Distribution{Univariate, Continuous}}}
# -> still use the old (depreacated) Product interface

This looks like a bug and should be reported.

7

I opened an issue.