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funHMM: Hidden Markov Models for Functional Data

funHMM fits topological hidden Markov models to time-ordered sequences of curves (functional data, sample paths of stochastic processes) without first projecting the curves onto a finite basis. The emission functions are Onsager-Machlup functionals of Gaussian measures on function spaces, as developed in

Kashlak, A. B., Loliencar, P. and Heo, G. (2023). Topological Hidden Markov Models. Journal of Machine Learning Research, 24(340), 1-49. https://jmlr.org/papers/v24/22-0685.html

Three emission models are available:

• "bmwd": Brownian motion with a state-dependent linear drift, including fractional Brownian motion with a fixed Hurst parameter;
• "ou": the Ornstein-Uhlenbeck process with state-dependent mean and mean-reversion rate;
• "nonpar": non-parametric state mean curves under an L2, W21 (Sobolev) or W22 Cameron-Martin norm.

The Baum-Welch (EM) and Viterbi algorithms are implemented in C and run on the log scale, so they are fast and numerically stable for long sequences.

Installation

# from CRAN (once accepted)
install.packages("funHMM")

# from a source tarball
install.packages("funHMM_0.1.0.tar.gz", repos = NULL, type = "source")

Example

library(funHMM)
set.seed(137)
A <- matrix(0.09, 5, 5) + 0.55 * diag(5)          # transition matrix A1 of the paper
sim <- rthmm(200, init.prob = c(1, 0, 0, 0, 0), trans = A,
             type = "bmwd", par = c(-8, -4, 0, 4, 8), len = 100)

fit <- thmm(sim$data, nstates = 5, type = "bmwd")
fit
table(fit$states, sim$states)      # decoded vs true states
ari(fit$states, sim$states)        # adjusted Rand index
plot(fit)

See vignette("funHMM") for a tour of all three models that reproduces the simulation studies of the paper.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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