MixFit.jl Documentation

Structure of mixture model parameters.

Variables

• α::Vector{Float32}: Weights of the components
• μ::Vector{Float32}: Means of the components
• σ::Vector{Float32}: SDs of the components

mixfit(x::Vector{<:Real},
        m::Int;
        rtol::AbstractFloat = 0.00001,
        α::Vector{<:Real} = fill(1/m, m),
        μ::Vector{<:Real} = quantile!(x, (1:m)/m),
        σ::Vector{<:Real} = fill(std(x) / √(m), m),
        maxswap::Int = 5 * m^2,
        maxiter_inner::Int = 0,
        maxiter::Int = 0,
        silent::Bool = false,
        kernel::Function = dnorm)

Get the maximum likelihood estimate of an m-component mixture model using random-swap EM. Random-swap EM avoids local optimums by randomly replacing components and using the result with the maximum likelihood ^[1]. The component distributions are given by kernel. The maximum number of swaps is given by maxswap. If results vary across runs, then maxswap is too low - the default is $5m^2$. maxiter_inner is the maximum number of iterations for the estimates that go through the swapping process, and maxiter is the maximum for the final estimate. Similarly, rtol is for the final estimate, while the inner estimates use 0.1. To supress output, simply set silent to true. Starting values can be provided via the α, μ, and σ arguments, but this shouldn't be necassary due to the use of random swapping.

See also: densfit, em_run!

densfit(x::Vector{<:Real};
        wait::Int = 3,
        rtol_em::AbstractFloat = 0.00001,
        criterion::Function = AIC,
        silent::Bool = false,
        maxiter::Int = 0,
        maxiter_inner::Int = 0,
        maxswap::Int = 0,
        kernel::Function = dnorm)

Estimate the density of x by a mixture model. Successive mixture model estimates are done via random swap EM with increasing number of clusters until criterion decreases for 3 iterations. By default, criterion uses AIC, which performs well for density estimation ^[2]. However, AIC2 should be used instead if one wants to actually estimate the number of clusters in a true mixture model. The relative tolerance for EM convergence is given by rtol_em. To disable output, set silent to true.

See also: densfit, em_run!

em_run!(est::MixModel, x::Vector{<:Real}, rtol::AbstractFloat = 0.00001, maxiter::Int = 0)

Run EM steps until the percent increase in log-likelihood is below rtol or the number of iterations is greater than maxiter. If maxiter is set to zero, EM steps will continue until the increase is below rtol regardless of the number of iterations.

See also: em_run!, mixfit

em_step!(est::MixModel, x::Vector{<:Real})

Run a single EM step.

See also: em_run!, mixfit

LL(x::Vector{<:Real}, est::MixModel)

Get the log-likelihood of a mixture model detailed in est, using the data x.

See also: AIC, AIC3, BIC

AIC(x::Vector{<:Real}, est::MixModel)

Get the AIC of a mixture model, using the data x. The AIC for a model $M$ is given by: $AIC(M) = 2*l(M) - 2*k$ Where $k$ is the number of parameters.

See also: AIC3, BIC, LL

AIC3(x::Vector{<:Real}, est::MixModel)

Get the modified AIC, "AIC3", of a mixture model using the data x. The AIC3 for a model $M$ is given by ^[3]: $AIC(M) = 2*l(M) - 3*k$ Where $k$ is the number of parameters.

See also: AIC, BIC, LL

BIC(x::Vector{<:Real}, est::MixModel)

Get the BIC of a mixture model using the data x.

See also: AIC, AIC3, LL

describe(est::MixModel; data::Vector{<:Real})

Pretty-print the parameters and fit indicies for the mixture model est. If data is not specified, fit indicies will not be printed.

dnorm(x::Real, μ::Real, σ::Real)

Normal distribution density function

dgumbel(x::Real, μ::Real, σ::Real)

Gumbel density, parameterized by mean (μ) and SD (σ) of x.

dgamma(x::Real, μ::Real, σ::Real)

Gamma density, parameterized by mean (μ) and sigma(σ) of x.

dlognorm(x::Real, μ::Real, σ::Real)

Lognormal density, parameterized by mean (μ) and SD (σ) of x, NOT of log(x).