Data scaling
length 60, 8 states, 12 iterations| sequences | observations | hmmlearn | mixle | speedup |
|---|---|---|---|---|
| 250 | 15,000 | 352 ms | 23 ms | 15.5x |
| 1,000 | 60,000 | 1,405 ms | 79 ms | 17.8x |
| 4,000 | 240,000 | 5,695 ms | 316 ms | 18.0x |
Benchmarks
Measured against the specialists.
Fit-time scaling results for full-covariance Gaussian mixtures, Gaussian-emission HMMs, GPU fits, and profiling runs. Every comparison uses shared data, shared initialization, fixed iteration counts, and final log-likelihood checks.
HMM
15-25x vs hmmlearn
GMM
1.41x vs sklearn at 200k
GPU
500k full-cov points
Method
correctness-gated fits
Methodology
The timing is only reported when the answer matches.
The harness measures comparable work: the same input arrays, the same initial parameters, and the same number of EM or Baum-Welch iterations.
Same data
One workload array is handed to each package.
Same initialization
Means, covariances, weights, and transitions are computed once and reused.
Same iteration count
Early stopping is disabled so no package wins by doing fewer steps.
Same answer
GMM likelihoods match to about 1e-7; HMM mean likelihoods match to about 1e-5.
Gaussian HMM
mixle is 15-25x faster than hmmlearn.
Many sequences from a latent regime process, Gaussian emissions, shared initialization, and fixed Baum-Welch iterations.
State scaling
1,000 sequences, length 60, 12 iterations| states | hmmlearn | mixle | speedup |
|---|---|---|---|
| 4 | 876 ms | 45 ms | 19.4x |
| 8 | 1,403 ms | 78 ms | 17.9x |
| 16 | 3,448 ms | 158 ms | 21.8x |
| 32 | 10,886 ms | 435 ms | 25.0x |
Full-covariance GMM
mixle matches the optimum and crosses over at scale.
scikit-learn and pomegranate are faster on small fits. mixle carries more fixed overhead, but its covariance accumulation scales better and crosses over near N=140k.
Data scaling
dim 32, 16 components, 15 iterations| N | sklearn | pomegranate | mixle | vs sklearn |
|---|---|---|---|---|
| 5,000 | 101 ms | 125 ms | 144 ms | 0.70x |
| 20,000 | 399 ms | 316 ms | 615 ms | 0.65x |
| 80,000 | 2,227 ms | 2,318 ms | 2,870 ms | 0.78x |
| 200,000 | 5,522 ms | 5,812 ms | 3,919 ms | 1.41x |
Dimension scaling
N 20,000, 8 components, 12 iterations| dim | sklearn | pomegranate | mixle |
|---|---|---|---|
| 8 | 85 ms | 57 ms | 89 ms |
| 16 | 105 ms | 71 ms | 122 ms |
| 32 | 170 ms | 152 ms | 241 ms |
| 64 | 384 ms | 362 ms | 540 ms |
| 128 | 835 ms | 881 ms | 1,206 ms |
The stable crossover check measured mixle at 0.78x at N=80k, then 1.42x / 1.42x / 1.41x at 140k / 200k / 350k, with the same final likelihood.
GPU engine
The same full-covariance model runs on CUDA.
This is a capability panel, not a cross-machine speedup claim. The data-scaling run used an RTX 2080 Ti at dim 64 with 16 components.
GPU data scaling
full-covariance GMM, 12 iterations| N | fit time | peak GPU memory |
|---|---|---|
| 50,000 | 3.3 s | 1.7 GB |
| 200,000 | 8.9 s | 6.8 GB |
| 500,000 | 20.2 s | 16.9 GB |
The dim-128 memory fix reduced a failing 21 GB intermediate to a 2.7 GB peak on an RTX 3060, with CPU parity at 2.5e-13. N=1M at dim 64 still needs chunking over N.
Scaling profile
The current bottlenecks are visible.
A separate A4000 + 16-core profiling run measured empirical slopes and cProfile hotspots across model families.
Data scaling
- GMM: slope 0.95, about 0.9M rows/s.
- MVN mixture: slope 1.03, about 0.14M rows/s.
- HMM: slope 1.07, about 0.01M rows/s.
Hotspots
- MVN: covariance second moment dominated by einsum.
- GMM: mixture responsibility accumulation.
- HMM: forward-backward plus NumPy reductions.
Open limits
- Torch CPU is 11-31x slower than NumPy for these MVN fits.
- Single-node model parallelism was 0.89x at N=200k.
- Large high-dimensional GPU batches still need N chunking.