intensify 0.3.1

Point process library with Hawkes specialization. Rust-accelerated MLE, EM, online, and Bayesian inference.

intensify

A modern Python library for point processes broadly — Poisson, Cox, and Hawkes — with deep Hawkes specialization. Built for quantitative finance and computational neuroscience, tested on real spike-train recordings, and Rust-accelerated on the likelihood and simulation hot paths.

pip install intensify

Binary wheels are published for Linux (x86_64, aarch64), macOS (Intel and Apple Silicon), and Windows (x86_64) on Python 3.10 – 3.12. Source builds require a Rust toolchain — install via pip install 'intensify[fast]'.

Quickstart

import numpy as np
import intensify as its

# Simulate event times from a self-exciting process.
model = its.Hawkes(mu=0.6, kernel=its.ExponentialKernel(alpha=0.55, beta=1.4))
events = model.simulate(T=80.0, seed=1)

# Fit μ, α, and β jointly from the observed events.
result = model.fit(events, T=80.0)

print(f"Branching ratio: {result.branching_ratio_:.3f}")
print(f"Log-likelihood:  {result.log_likelihood:.3f}")
print(f"Fitted params:   {result.flat_params()}")

# Visualize fitted intensity and diagnostics
fig = its.plot_intensity(result)
fig.savefig("quickstart_intensity.png", dpi=160)

Representative output:

Branching ratio: 0.547
Log-likelihood:  -66.671
Fitted params:   {'mu': 0.6271952244498643, 'alpha': 0.5470266035451343, 'beta': 1.0562059205150198}

Other common workflows:

# Multivariate connectivity: estimate directed excitation strengths.
kernels = [
    [its.ExponentialKernel(0.20, 1.0), its.ExponentialKernel(0.05, 1.0)],
    [its.ExponentialKernel(0.10, 1.0), its.ExponentialKernel(0.25, 1.0)],
]
mh = its.MultivariateHawkes(n_dims=2, mu=[0.5, 0.6], kernel=kernels)
mv_events = mh.simulate(T=100.0, seed=4)
mv_result = mh.fit(mv_events, T=100.0, fit_decay=False)
print(mv_result.connectivity_matrix())

# Goodness of fit: time-rescaling theorem residuals.
from intensify.core.diagnostics.goodness_of_fit import time_rescaling_test

ks_stat, p_value = time_rescaling_test(result)
print(f"KS stat={ks_stat:.3f}, p={p_value:.3f}")

# Cox process: latent, time-varying intensity for spike-train style data.
lgcp = its.LogGaussianCoxProcess(n_bins=80, mu_prior=-0.2, sigma_prior=0.6)
spikes = lgcp.simulate(T=10.0, seed=11)
print(len(spikes), "events from an LGCP prior sample")

Features

• Process families (full point-process spectrum, not just Hawkes):
  • Poisson: HomogeneousPoisson, InhomogeneousPoisson (callable intensity or piecewise-constant rates).
  • Cox: LogGaussianCoxProcess (LGCP), ShotNoiseCoxProcess.
  • Hawkes: univariate, multivariate, marked, nonlinear (softplus / sigmoid / relu / identity links), multivariate-nonlinear, signed (inhibitory).
• Kernel family: Exponential, Sum-of-Exponentials, Power-Law, Approximate Power-Law (Bacry–Muzy), Nonparametric (piecewise-constant). Every kernel is supported in every MLE path.
• Inference: MLE with hand-derived closed-form gradients (no autodiff in the hot path); recursive O(N) likelihood for exponential-family kernels; EM and online (streaming) updates route through the same Rust core; Bayesian MCMC via numpyro (optional [bayesian] extra).
• Diagnostics: time-rescaling theorem (KS + QQ on inter-compensator increments — the mathematically correct form), AIC/BIC, residual intensity.
• Simulation: Ogata thinning (general) and cluster/branching (Galton–Watson) — both Rust-backed.
• Stationarity enforcement: projected gradient for multivariate Hawkes; spectral radius of the kernel-norm matrix stored as branching_ratio_ on every multivariate FitResult.
• Architecture: Rust core (intensify._libintensify) for kernel, likelihood, gradient, and simulator hot paths. Pure-Python user API. Loud ImportError if the compiled extension is missing.

Why intensify?

intensify and tick solve partly overlapping problems. Pick the right tool:

Capability	intensify	tick
Inhomogeneous Poisson (arbitrary rate function or piecewise-constant)	✓	partial (sim only)
Log-Gaussian Cox Process (LGCP)	✓	—
Shot-Noise Cox Process	✓	—
Joint MLE of (μ, α, β) — fits the Hawkes decay for you	✓	— (decay must be supplied)
MLE for power-law, approx-power-law, nonparametric kernels	✓	—
Marked Hawkes fit with any kernel	✓	—
Nonlinear (softplus / sigmoid / relu) Hawkes, signed kernels	✓	—
Multivariate stationarity enforcement (projected gradient)	✓	—
Time-rescaling test on inter-compensator increments	✓	✓
Python 3.10 – 3.12 support, prebuilt wheels	✓	3.8 only, C++ build
Sub-millisecond fits for exp kernels with known decay	✓	✓
Faster than tick at every benchmarked N (decay-given mv_exp)	✓	—

The benchmark suite builds seeded synthetic Hawkes datasets, fits the same models repeatedly, and reports median wall time over three runs. The apples-to-apples tick comparison locks the exponential decay β, because tick requires the user to provide decay up front; intensify also reports joint-decay runs where it estimates β directly. Full methodology and reproduction commands are in docs/benchmarks.md. Short version, on the decay-given mv_exp_5d problem:

N	tick (ms)	intensify 0.3.0b1 (ms)	speedup
501	1.0	0.5	2.0×
9,271	6.0	2.4	2.5×
91,249	48.0	22.2	2.2×

Joint-decay (β fit per cell) — tick can't do this at all — went from 1100 ms to 14 ms at N=1099 (~80× vs the pre-Rust 0.2.0 baseline). For kernels tick doesn't ship (power-law, nonparametric, signed, marked, nonlinear) intensify is the only option. ISSUES.md #8 is fixed: the nonparametric path now finishes in <1 s at N=500 (previously killed after 7 minutes). End-to-end, the HC-3 real-spike-train stress suite (42 tests across every kernel × every process × diagnostics) dropped from 8m 13s to ~1.3 s — about 380× faster. pyhawkes is no longer usable — its transitive deps depend on APIs removed from SciPy 1.0 in 2017.

Documentation

Full docs: https://hillmatt7.github.io/intensify

• Getting started
• User guide: inference, kernels, simulation, diagnostics, quantitative finance, computational neuroscience
• API reference
• Tutorials (Jupyter notebooks)

Citation

If you use intensify in academic work, please cite it:

@software{intensify,
  author = {Hill, Matthew},
  title  = {intensify: A modern Python point process library with deep Hawkes specialization},
  year   = {2026},
  url    = {https://github.com/hillmatt7/intensify}
}

See CITATION.cff for the machine-readable form.

Contributing & changes

• Contributing guide
• Changelog
• Open issues

License

MIT — see LICENSE.