# libhmm: A Modern C++20 Library for Hidden Markov Models with Correct MLE Emission M-Steps

arXiv: https://arxiv.org/abs/2605.29208 · HTML: https://mlsanity.com/paper/2605.29208/

## Key facts

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- First posted on arXiv 28 May 2026.

## Abstract (arXiv)

We describe libhmm, a C++20 library for Hidden Markov Model parameter estimation, sequence decoding, and model selection. libhmm addresses two gaps in existing software: the absence of a well-maintained, zero-dependency C++ HMM library suitable for embedding in production systems, and the widespread use of method-of-moments (MOM) approximations in the emission distribution M-step of the Baum-Welch algorithm. The library implements correct maximum likelihood estimators for sixteen scalar emission distributions, including an ECME algorithm for the location-scale Student-t distribution, Newton-Raphson maximization for Gamma, Beta, Weibull, and Negative Binomial distributions, and the von Mises distribution for circular data. All forward-backward and Viterbi calculations operate in full log-space. SIMD acceleration is provided for AVX-512, AVX2, SSE2, and ARM NEON via compile-time dispatch with scalar fallback. Version 4 adds multivariate observation support via the BasicHmm<Obs> template, with three multivariate emission families (diagonal Gaussian, full-covariance Gaussian, and independent components) each with correct weighted MLE M-steps. Python bindings are available via the companion package pylibhmm. We compare libhmm against established C and C++ HMM libraries and against published R reference packages on seven real-data benchmarks, and discuss the architectural tradeoffs made in the design.