Standard Hawkes Process #59

JoseKling · 2025-07-10T15:59:17Z

src/hawkes/hawkes_process.jl
- HawkesProcess type
- Methods: rand, fit, time_change, ground_intensity, integrated_ground_intensity, logdensityof
tests/hawkes.jl
- Some unit tests for Hawkes processes
history.jl
- added 'event_times(h, tmin, tmax)'
- added 'event_marks(h, tmin, tmax)'
simulation.jl
- added 'simulate_poisson' - for other methods to use

- src/hawkes/hawkes_process.jl - Methods: rand, fit, time_change, ground_intensity, integrated_ground_intensity, logdensityof - tests/hawkes.jl - Some unit tests for Hawkes processes - history.jl - added 'event_times(h, tmin, tmax)' - added 'event_marks(h, tmin, tmax)' - simulation.jl - added 'simulate_poisson' - for other methods to use

codecov · 2025-07-10T16:20:19Z

Codecov Report

✅ All modified and coverable lines are covered by tests.

📢 Thoughts on this report? Let us know!

jucheval

I did not check every line, but there are already lots of changes requested and questions.

src/hawkes/hawkes_process.jl

src/simulation.jl

jucheval · 2025-07-10T20:07:07Z

test/hawkes.jl

+@test isa(h_sim, History{Nothing,Float64})
+# Estimation
+hp_est = fit(HawkesProcess, h_sim)
+@test isa(hp_est, HawkesProcess)


add a test to check that the estimated parameters are close to the real ones ?

I am no sure how to do this, to be honest.

One way would be to simulate many processes with known parameters and then get the mean/median of the estimations, but how would I define a bound for how far off this can be from the true parameters?

The idea is to give us a warning in case of a harmful change in a future update.
You could chose a history and a rng seed such that the estimation is "close" to the true parameters. Then, add a unit test to check that this distance to the true parameters do not deteriorate in the next updates.

Not sure if this is the best approach, but, in principle, this would show us if something changes the algorithm too much.

Could make it simpler by just fixing a seed and checking if it is close to the median, if this is too much.

Also, I saved the result of a simulation in a text file, because this is recommended in the Random.jl documentation, as they might change the algorithm and, therefore, change the results in the future.

Julien is right, checking proximity between estimated and true parameters is an excellent way to guard against mistakes or breaking changes.
You can use StableRNGs.jl to get reproducible random seeds across versions and platforms, which makes text files unnecessary.

Room for improvement is good ; )

About your question, the problem is just a poor explanation in the comments.
In reality this t90 is the inverse of the time it takes for a 90% decay. The only reason for sampling the inverse of t90 instead of t90 is that this ensures that the distribution of $\omega$ will be uniform. The thing is that, because t90 is chosen from the interval (1/2, 2), both t90 and its inverse are inside this interval.

Okay, got it. I assumed it was something like this but wanted to make sure there wasn't a bug. I'll move forward on optimizing a bit!

I optimized to significantly improve performance and increase memory efficiency. The main change replaces the previous O(n²) double loop used to compute descendant probabilities with an O(n) recurrence formulation based on running sums (A and S). This eliminates redundant computations and scales efficiently with the number of events. I also introduced a few small buffers to avoid unnecessary array allocations and removed redundant exponential recalculations within the EM loop. This caused the fit time to go from 55s for ~8k events to 10.53 ms without changing the final estimates. All tests still pass as well

Thanks @rsenne!
Completely missed that! It is even in the paper, actually. Anyway, that's the good thing about having extra pair of eyes going through it.

Happens to the best of us, glad I could help :)

test/history.jl

test/hawkes.jl

src/hawkes/hawkes_process.jl

- Fixed `logdensityof` - HawkesProcess is now parametric and has as check in the inner constructor - Added explanation for `generate_descendants` and choice of initial guess in `fit`

- Fixed logdensityof - HawkesProcess is now parametric and has as check in the inner constructor - Added explanation for generate_descendants and choice of initial guess in fit Fixed formatting

- Changed parameter names of `HawkesProcess` - Added test for estimation

- Changed parameter names of `HawkesProcess` - Added test for estimation Forgot to run the formatter

- Changed parameter names of `HawkesProcess` - Added test for estimation Forgot to run the formatter Removed the docstring from `simulate_poisson_times` causing docs deployment problem.

gdalle

Awesome that you're getting started with new processes!
I left a few comments to try and guide you towards idiomatic Julia code, let me know what you think!

src/hawkes/hawkes_process.jl

gdalle · 2025-07-18T09:16:34Z

src/hawkes/hawkes_process.jl

+Expectation-Maximization algorithm from [E. Lewis, G. Mohler (2011)](https://api.semanticscholar.org/CorpusID:2105771)).
+The relevant calculations are in page 4, equations 6-13.
+
+Let (t_1 < ... < t_N) be the event times over the interval [0, T). We use the immigrant-descendant representation,


If possible, one should refrain from using LaTeX in docstrings because it renders badly in the REPL. If you have to include formulas or symbols, it's better to put them inside backticks so that they display as monospace code, and then add a page to the Documenter.jl documentation for proper LaTeX equations

You can visualize the docstring by typing

?fit

in a Julia REPL

gdalle · 2025-07-18T09:18:44Z

src/hawkes/hawkes_process.jl

+    max_iter::Int=1000,
+)
+    N = nb_events(h)
+    N == 0 && return HawkesProcess(0.0, 0.0, 0.0)


Note that this should return a process of the same type as the one provided to fit, otherwise the function will be type-unstable. Are you familiar with that concept?
So here we should put something like

return HawkesProcess(zero(T), zero(T), zero(T))

and parametrize T inside

::Type{HawkesProcess{T}}

Careful about the notation conflict with T = duration(h) on line 58

Yes, I am familiar with it, although it is sometimes hard to spot.

From what I understand, the method is not type stable because the first return statement always returns a HawkesProcess{Float64}, but the second could return a BigFloat (or something Float64 could promote to), and the compiler cannot know in advance which of the statements will be hit.

In my code I was fixing the types of everything to be Float64, so I did not have to worry about this. But it is good to have to deal with it.

gdalle · 2025-07-18T09:21:14Z

src/hawkes/hawkes_process.jl

+    T = duration(h)
+    norm_ts = h.times .* (N / T) # Average inter-event time equal to 1. Numerical stability
+    n_iters = 0
+    step = step_tol + 1.0


Whenever you use floating point numbers like 1.0, you're forcing the entire computation to happen in Float64, even if the user provided Float32 everywhere. This could be replaced by one(T) for the right choice of T.

What is the right choice of T? Probably the result of the promotion between the time type of the History and the parameter type of the HawkesProcess

Fixed the types returned by rand and time_change too. The rule I used is the following:

time_change(hp::HawkesProcess{HP}, h::{M,H})

Returns a History{M,H}, same type as argument

fit(::Type{HawkesProcess{HP}}, h::History{M,H})

Returns a HawkesProcess{HP}, the exact type passed as an argument

If argument passed is HawkesProcess (without a type parmeter), return HawkesProcess{T}, where T == promote_type(Float64, H).

rand(hp::HawkesProcess{HP}, tmin, tmax)

Returns a History{M,H} where H == promote_type(typeof(tmin), typeof(tmax))

gdalle · 2025-07-18T09:26:17Z

src/hawkes/hawkes_process.jl

+# Internal function for simulating Hawkes processes
+# The first generation, gen_0, is the `immigrants`, which is a set of event times.
+# For each t_g ∈ gen_n, simulate an inhomogeneous Poisson process over the interval [t_g, T]
+# with intensity λ(t) = α exp(-ω(t - t_g)) with the inverse method.
+# gen_{n+1} is the set of all events simulated from all events in gen_n.
+# The algorithm stops when the simulation from one generation results in no further events.


You can use block comments like so:

#= First line second line =#

gdalle · 2025-07-18T09:26:34Z

src/hawkes/hawkes_process.jl

+function generate_descendants(rng::AbstractRNG, immigrants::Vector, T, α, ω)
+    descendants = eltype(immigrants)[]
+    next_gen = immigrants
+    while ~isempty(next_gen)


Suggested change

while ~isempty(next_gen)

while !isempty(next_gen)

gdalle · 2025-07-18T09:26:57Z

src/history.jl

+Return the sorted vector of event times between `tmin` and `tmax` for `h`.
+"""
+function event_times(h::History, tmin, tmax)
+    h.times[searchsortedfirst(h.times, tmin):(searchsortedfirst(h.times, tmax) - 1)]


this could be a @view?

gdalle · 2025-07-18T09:28:31Z

test/hawkes.jl

+@test isa(h_sim, History{Nothing,Float64})
+# Estimation
+hp_est = fit(HawkesProcess, h_sim)
+@test isa(hp_est, HawkesProcess)


Julien is right, checking proximity between estimated and true parameters is an excellent way to guard against mistakes or breaking changes.
You can use StableRNGs.jl to get reproducible random seeds across versions and platforms, which makes text files unnecessary.

gdalle · 2025-07-18T09:28:41Z

test/hawkes_times.txt

@@ -0,0 +1 @@
+[0.01017337415246089, 0.013640560097159748, 0.013925428236956083, 0.014608995173263944, 0.015735173436628665, 0.017731455643465788, 0.018173140414903033, 0.019398584582704777, 0.02169310038049055, 0.026539311564590558, 0.03535296046523939, 0.035385747642310054, 0.04888791827373706, 0.049245437622213895, 0.05207317680771159, 0.05417399567567511, 0.06282683568521101, 0.07081244234996387, 0.0791015159737285, 0.0861333024505229, 0.087551141093, 0.08772509630067638, 0.09411335483093886, 0.09724491891582732, 0.0988625084503767, 0.10010837332313449, 0.10135018373031557, 0.10363364868768966, 0.10592656977963455, 0.10715180725875367, 0.11028563316661419, 0.1134331444864608, 0.12272955724493595, 0.12726221430956405, 0.12836304084244704, 0.12844801940952075, 0.13597112047166005, 0.15072073156516308, 0.15114633616168527, 0.15451628188316555, 0.1615175726493574, 0.17404961232856206, 0.19135505688083287, 0.22076206529908327, 0.23982012455994361, 0.24316977218179758, 0.24474350243009585, 0.24644188741540635, 0.24758741892662547, 0.26335250468309224, 0.2657968651067172, 0.26846031955131877, 0.2714547249648518, 0.2752925737618863, 0.27565342198838594, 0.27609484665183454, 0.2793520184225446, 0.28043167139411607, 0.28266772707753685, 0.2892355684930643, 0.28935629867942364, 0.2910561718681186, 0.29157899048672486, 0.30523440749876696, 0.31427715680728796, 0.3160799465423002, 0.3186409783533404, 0.31928256511258085, 0.3561905127846101, 0.35726422828011145, 0.37542826109696614, 0.3761737738905845, 0.383211879818265, 0.38412250885804855, 0.3892202718510143, 0.38973687161088244, 0.3903222364578105, 0.3921460092118373, 0.3927565640326585, 0.3929931412548428, 0.39550199927854035, 0.4004287509915203, 0.4012584947658139, 0.4188933113083467, 0.4222797931631154, 0.42547015568968916, 0.43096758007962505, 0.4318550285906202, 0.44109809732147987, 0.4411113062102109, 0.4414891960155095, 0.4419159595553975, 0.4455996720525952, 0.4496160036372285, 0.4498795159779206, 0.45469339795091446, 0.45799213961322816, 0.4582125417978449, 0.4593459923561455, 0.460330625273055, 0.46151099501089304, 0.4663379688495272, 0.4668223709854475, 0.4689158086068933, 0.47513195296839694, 0.48261581524557473, 0.5018848417890917, 0.5082613332032163, 0.5098025975578675, 0.5103574120239697, 0.5105994460715356, 0.5251305262758121, 0.5394744828867348, 0.5398929198384044, 0.5451644369828262, 0.5456458484033474, 0.5461471626817158, 0.5562494823653819, 0.5577837518050861, 0.5629099224574312, 0.5639313234396448, 0.5652484663007217, 0.56579448745316, 0.569761662149659, 0.5772534932071732, 0.57747271973829, 0.581312103742883, 0.5897117080989583, 0.6042594925582441, 0.6062770267185059, 0.6146506742853325, 0.619164121825413, 0.6233280853442464, 0.6562295767400433, 0.657191314194358, 0.6683396665157701, 0.6934098253153014, 0.7098168085084123, 0.7142551495263125, 0.7149292250425998, 0.7222898663646184, 0.7230225303240918, 0.7258703766070407, 0.7329257086975677, 0.734965964575541, 0.7367052753163055, 0.7369917675462134, 0.7377952054108926, 0.7431668020456873, 0.7442335599332027, 0.7494356056840505, 0.7592464069425915, 0.76513378821372, 0.7778400193541839, 0.783570871666886, 0.7892533149681009, 0.8151907848154715, 0.8163624371624438, 0.8203512192351479, 0.8231907075189483, 0.8254450315531231, 0.8327541619684787, 0.8340446391585701, 0.8365483397626655, 0.8380870238704485, 0.8396006152087313, 0.8424109556863868, 0.8449279007257848, 0.8493882720082039, 0.8499247624654398, 0.8570201197254786, 0.8708262595580382, 0.8757516578617132, 0.8851984472410247, 0.8943124667367437, 0.9099513775965703, 0.9158323560687229, 0.916124781335173, 0.9186099384299968, 0.9207850430116301, 0.9261702419474741, 0.9266763718478324, 0.927525059408, 0.9326181870421033, 0.9332024579347786, 0.9369755618858636, 0.9371907441403706, 0.9389797249122629, 0.939953948070523, 0.9420001470511369, 0.943798275663379, 0.9466861545841257, 0.947173907438536, 0.94880346770712, 0.9500849345227314, 0.953356815578679, 0.9535829930299445, 0.9596111063743575, 0.9686141854288621, 0.9810644372158931]


See above, this is not needed

jucheval · 2025-07-18T12:35:08Z

src/simulation.jl

I think that it's more common to use uppercases at the beginning of sentences in Julia documentation

Sorry, I probably hit u (vim shortcut to make everything lowercase) by mistake while having the docstring selected.

- Added docstring to `HawkesProcess` - Avoided LaTeX in docstrings - Remove all `@inbounds`

- Reference parameters inside `hawkes_times.txt` file, instead of hard coded in tests. - Fixed return types for `rand`, `fit`, and `time_change` and added tests.

JoseKling · 2025-10-07T08:12:19Z

Hello.
Any problems left here? Had some issues lately but I am back.
Cheers

…r O(n)

rsenne · 2025-10-24T23:58:29Z

Anything else we want to do for this PR?

JoseKling · 2025-10-27T01:21:26Z

I think all issues were resolved...

rsenne · 2025-10-27T13:28:48Z

I think all issues were resolved...

Are we good to merge then? What would be good to work on next?

JoseKling force-pushed the hawkes branch from 6ed7e71 to d3abeb3 Compare July 10, 2025 16:18

jucheval reviewed Jul 10, 2025

View reviewed changes

JoseKling added 5 commits July 14, 2025 14:03

- Added missing unit tests

51088ed

- Fixed `logdensityof` - HawkesProcess is now parametric and has as check in the inner constructor - Added explanation for `generate_descendants` and choice of initial guess in `fit`

- Added missing unit tests

71bb1d5

- Fixed logdensityof - HawkesProcess is now parametric and has as check in the inner constructor - Added explanation for generate_descendants and choice of initial guess in fit Fixed formatting

- HawkesProcess is now parametric and has checks

4be2ba4

- Changed parameter names of `HawkesProcess` - Added test for estimation

- HawkesProcess is now parametric and has checks

245294d

- Changed parameter names of `HawkesProcess` - Added test for estimation Forgot to run the formatter

- HawkesProcess is now parametric and has checks

f5ac1db

- Changed parameter names of `HawkesProcess` - Added test for estimation Forgot to run the formatter Removed the docstring from `simulate_poisson_times` causing docs deployment problem.

gdalle reviewed Jul 18, 2025

View reviewed changes

jucheval reviewed Jul 18, 2025

View reviewed changes

- Fixed type instability in fit

99e6672

- Added docstring to `HawkesProcess` - Avoided LaTeX in docstrings - Remove all `@inbounds`

JoseKling mentioned this pull request Jul 21, 2025

Plan for next features #55

Open

JoseKling added 2 commits July 24, 2025 12:19

- Fixed estimation test for Hawkes processes.

4ac7659

- Reference parameters inside `hawkes_times.txt` file, instead of hard coded in tests. - Fixed return types for `rand`, `fit`, and `time_change` and added tests.

Stable Hawkes estimation. Changed step_tol

9cb7a4d

JoseKling and others added 2 commits October 20, 2025 13:16

Test for Hawkes process estimation based on simulated events

b0793df

Remove double loop causing O(n^2) time complexity to a single pass fo…

ee4a88c

…r O(n)

		@@ -0,0 +1 @@
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Standard Hawkes Process #59

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Standard Hawkes Process #59

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JoseKling commented Jul 10, 2025

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JoseKling commented Oct 7, 2025

codecov bot commented Jul 10, 2025 •

edited

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JoseKling Jul 18, 2025 •

edited

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