https://github.com/dmetivie/smoothperiodicstatsmodels.jl
https://github.com/dmetivie/smoothperiodicstatsmodels.jl
Last synced: about 1 month ago
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- Host: GitHub
- URL: https://github.com/dmetivie/smoothperiodicstatsmodels.jl
- Owner: dmetivie
- License: mit
- Created: 2023-09-21T13:56:15.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-11-28T13:21:13.000Z (5 months ago)
- Last Synced: 2025-02-05T09:21:15.052Z (3 months ago)
- Language: Julia
- Size: 186 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 5
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# SmoothPeriodicStatsModels
[](https://github.com/dmetivie/SmoothPeriodicStatsModels.jl/actions/workflows/CI.yml?query=branch%3Amaster)
This package is primarily built to be an extension of the [StochasticWeatherGenerators](https://github.com/dmetivie/StochasticWeatherGenerators.jl) package. See the [tutorial](https://dmetivie.github.io/StochasticWeatherGenerators.jl/dev/examples/tuto_paper/) for example of usage.
It builds several smooth versions of stats models for time series, for now:
- AR(1) Auto Regressive model of order 1
- Mixture Models
- Auto Regressive Periodic Hidden Markov Model. For now, it only has Bernoulli mixtures emission distributions, i.e. conditionally independent distributions.
**Smooth** means that temporal coefficients of the models e.g. $p(t)\in [0,1]$ for Bernoulli parameter and $t\in [1,T]$ have a periodic functional form to enforce smoothness i.e. $p(t)\simeq p(t+1)$.
Note that the package [PeriodicHiddenMarkovModels.jl](https://github.com/dmetivie/PeriodicHiddenMarkovModels.jl) also deals with Periodic HMM, but right now, it does not enforce the smoothness hence if you don't have a lot of observations you can have $p(t)$ very different from $p(t+1)$. Moreover, this cause identifiability issues of the hidden states.
The HMM part of this package should be moved at some point to [PeriodicHiddenMarkovModels.jl](https://github.com/dmetivie/PeriodicHiddenMarkovModels.jl) making use under the hood of the very nice and flexible [HiddenMarkovModels.jl](https://github.com/gdalle/HiddenMarkovModels.jl) package.
This is inspired by seasonal Hidden Markov Model, see [A. Touron (2019)](https://link.springer.com/article/10.1007/s11222-019-09854-4).
## Example
### Set up
```julia
Random.seed!(2020)
K = 3 # Number of Hidden states
T = 11 # Period
N = 49_586 # Length of observation
D = 6 # dimension of observed variables
autoregressive_order = 1
size_order = 2^autoregressive_order
degree_of_P = 1
size_degree_of_P = 2*degree_of_P + 1
trans_θ = 4*(rand(K, K - 1, size_degree_of_P) .- 1/2)
Bernoulli_θ = 2*(rand(K, D, size_order, size_degree_of_P) .- 1/2)
hmm = Trig2ARPeriodicHMM([1/3, 1/6, 1/2], trans_θ, Bernoulli_θ, T)
```
### Simulations
```julia
z_ini = 1
y_past = rand(Bool, autoregressive_order, D)
n2t = SmoothPeriodicStatsModels.n_to_t(N,T)
z, y = rand(hmm, n2t; y_ini=y_past, z_ini=z_ini, seq=true)
```
### Fit
```julia
trans_θ_guess = rand(K, K-1, size_degree_of_P)
Bernoulli_θ_guess = zeros(K, D, size_order, size_degree_of_P)
trans_θ_guess[:,:,1] .= trans_θ[:,:,1] # cheating on initial guess to recover very good mle maxima
Bernoulli_θ_guess[:,:,:,1] = Bernoulli_θ[:,:,:,1]
hmm_guess = Trig2ARPeriodicHMM([1/4, 1/4, 1/2], trans_θ_guess, Bernoulli_θ_guess, T)
@time "FitMLE SHMM (Baum Welch)" hmm_fit, θq_fit, θy_fit, hist, histo_A, histo_B = fit_mle(hmm_guess, trans_θ_guess, Bernoulli_θ_guess, y, y_past, maxiter=10000, robust=true; display=:iter, silence=true, tol=1e-3, θ_iters=true, n2t=n2t);
# EM converged in 317 iterations, logtot = -194299.4177103428
# FitMLE SHMM (Baum Welch): 72.532794 seconds (344.65 M allocations: 27.641 GiB, 3.59% gc time)
```
### Plots
```julia
using LaTeXStrings, Plots
begin
pA = [plot(legendfont=14, foreground_color_legend=nothing, background_color_legend=nothing) for k in 1:K]
for k in 1:K
[plot!(pA[k], hmm.A[k, l, :], c=l, label=L"Q_{%$(k)\to %$(l)}", legend=:topleft) for l in 1:K]
[plot!(pA[k], hmm_fit.A[k, l, :], c=l, label=:none, legend=:topleft, s = :dot) for l in 1:K]
hline!(pA[k], [0.5], c=:black, label=:none, s=:dot)
ylims!(0,1)
end
pallA = plot(pA..., size=(1000, 500))
end
begin
mm = 1
pB = [plot() for j in 1:D]
for j in 1:D
[plot!(pB[j], succprob.(hmm.B[k, :, j, mm]), c=k, label=:none) for k in 1:K]
[plot!(pB[j], succprob.(hmm_fit.B[k, :, j, mm]), c=k, label=:none, s = :dot) for k in 1:K]
hline!(pB[j], [0.5], c=:black, label=:none, s=:dot)
ylims!(pB[j], (0, 1))
end
pallB = plot(pB...)
end
begin
mm = 2
pB = [plot() for j in 1:D]
for j in 1:D
[plot!(pB[j], succprob.(hmm.B[k, :, j, mm]), c=k, label=:none) for k in 1:K]
[plot!(pB[j], succprob.(hmm_fit.B[k, :, j, mm]), c=k, label=:none, s = :dot) for k in 1:K]
hline!(pB[j], [0.5], c=:black, label=:none, s=:dot)
ylims!(pB[j], (0, 1))
end
pallB = plot(pB...)
end
```
