From ab2993ba4043b58dbf2e50b07edbcd52ce3dbcc1 Mon Sep 17 00:00:00 2001 From: Martin B Date: Thu, 14 Dec 2017 15:45:37 +0100 Subject: [PATCH] Implement Hawkes Cumulant non parametric learner --- doc/modules/api.rst | 1 + doc/modules/hawkes.rst | 1 + examples/plot_hawkes_cumulants_matching.py | 55 ++ examples/plot_hawkes_em.py | 2 +- lib/cpp/hawkes/inference/CMakeLists.txt | 2 + lib/cpp/hawkes/inference/hawkes_cumulant.cpp | 122 ++++ .../hawkes/model/base/model_hawkes_list.cpp | 2 +- .../tick/hawkes/inference/hawkes_cumulant.h | 41 ++ .../hawkes/model/base/model_hawkes_list.h | 9 +- lib/swig/hawkes/inference/hawkes_cumulant.i | 26 + .../inference/hawkes_inference_module.i | 1 + .../hawkes/model/base/model_hawkes_list.i | 2 + tick/base/base.py | 3 +- tick/hawkes/__init__.py | 4 +- tick/hawkes/inference/__init__.py | 4 +- .../inference/hawkes_cumulant_matching.py | 679 ++++++++++++++++++ ...wkes_cumulant_matching_test-train_data.pkl | Bin 0 -> 452322 bytes .../tests/hawkes_cumulant_matching_test.py | 206 ++++++ tools/travis/docker_run.sh | 1 + tools/travis/osx_install.sh | 1 + 20 files changed, 1154 insertions(+), 8 deletions(-) create mode 100644 examples/plot_hawkes_cumulants_matching.py create mode 100644 lib/cpp/hawkes/inference/hawkes_cumulant.cpp create mode 100644 lib/include/tick/hawkes/inference/hawkes_cumulant.h create mode 100644 lib/swig/hawkes/inference/hawkes_cumulant.i create mode 100644 tick/hawkes/inference/hawkes_cumulant_matching.py create mode 100644 tick/hawkes/inference/tests/hawkes_cumulant_matching_test-train_data.pkl create mode 100644 tick/hawkes/inference/tests/hawkes_cumulant_matching_test.py diff --git a/doc/modules/api.rst b/doc/modules/api.rst index 33e9747d8..cd5ada2c2 100644 --- a/doc/modules/api.rst +++ b/doc/modules/api.rst @@ -50,6 +50,7 @@ Learners HawkesBasisKernels HawkesSumGaussians HawkesConditionalLaw + HawkesCumulantMatching Simulation ---------- diff --git a/doc/modules/hawkes.rst b/doc/modules/hawkes.rst index 2a49bbeec..7bbf7e1fc 100644 --- a/doc/modules/hawkes.rst +++ b/doc/modules/hawkes.rst @@ -96,6 +96,7 @@ These learners might be used to infer more exotic kernels. HawkesEM HawkesBasisKernels HawkesConditionalLaw + HawkesCumulantMatching Example ******* diff --git a/examples/plot_hawkes_cumulants_matching.py b/examples/plot_hawkes_cumulants_matching.py new file mode 100644 index 000000000..8a7bd3ce9 --- /dev/null +++ b/examples/plot_hawkes_cumulants_matching.py @@ -0,0 +1,55 @@ +""" +======================================= +Fit Hawkes kernel norms using cumulants +======================================= + +This non parametric Hawkes cumulants matching +(`tick.hawkes.HawkesCumulantMatching`) algorithm estimates directly +kernels norms without making any assumption on kernel shapes. + +It has been originally described in this paper: + +Achab, M., Bacry, E., Gaiffas, S., Mastromatteo, I., & Muzy, J. F. +(2017, July). Uncovering causality from multivariate Hawkes integrated +cumulants. +`In International Conference on Machine Learning (pp. 1-10)`_. + +.. _In International Conference on Machine Learning (pp. 1-10): http://proceedings.mlr.press/v70/achab17a.html +""" + +import numpy as np + +from tick.hawkes import (HawkesCumulantMatching, SimuHawkesExpKernels, + SimuHawkesMulti) +from tick.plot import plot_hawkes_kernel_norms + +np.random.seed(7168) + +n_nodes = 3 +baselines = 0.3 * np.ones(n_nodes) +decays = 0.5 + np.random.rand(n_nodes, n_nodes) +adjacency = np.array([ + [1, 1, -0.5], + [0, 1, 0], + [0, 0, 2], +], dtype=float) + +adjacency /= 4 + +end_time = 1e5 +integration_support = 5 +n_realizations = 5 + +simu_hawkes = SimuHawkesExpKernels( + baseline=baselines, adjacency=adjacency, decays=decays, + end_time=end_time, verbose=False, seed=7168) +simu_hawkes.threshold_negative_intensity(True) + +multi = SimuHawkesMulti(simu_hawkes, n_simulations=n_realizations, n_threads=-1) +multi.simulate() + +nphc = HawkesCumulantMatching(integration_support, cs_ratio=.15, tol=1e-10, + step=0.3) + +nphc.fit(multi.timestamps) +plot_hawkes_kernel_norms(nphc) diff --git a/examples/plot_hawkes_em.py b/examples/plot_hawkes_em.py index 74f0e5756..039865190 100644 --- a/examples/plot_hawkes_em.py +++ b/examples/plot_hawkes_em.py @@ -7,7 +7,7 @@ piecewise constant. Hence it can fit basically any kernel form. However it doesn't scale very well. -I has been originally described in this paper: +It has been originally described in this paper: Lewis, E., & Mohler, G. (2011). A nonparametric EM algorithm for multiscale Hawkes processes. diff --git a/lib/cpp/hawkes/inference/CMakeLists.txt b/lib/cpp/hawkes/inference/CMakeLists.txt index e33ade626..fec21687f 100644 --- a/lib/cpp/hawkes/inference/CMakeLists.txt +++ b/lib/cpp/hawkes/inference/CMakeLists.txt @@ -6,11 +6,13 @@ add_library(tick_hawkes_inference EXCLUDE_FROM_ALL ${TICK_HAWKES_INFERENCE_INCLUDE_DIR}/hawkes_adm4.h ${TICK_HAWKES_INFERENCE_INCLUDE_DIR}/hawkes_basis_kernels.h ${TICK_HAWKES_INFERENCE_INCLUDE_DIR}/hawkes_sumgaussians.h + ${TICK_HAWKES_INFERENCE_INCLUDE_DIR}/hawkes_cumulant.h hawkes_adm4.cpp hawkes_basis_kernels.cpp hawkes_conditional_law.cpp hawkes_em.cpp hawkes_sumgaussians.cpp + hawkes_cumulant.cpp ) target_link_libraries(tick_hawkes_inference diff --git a/lib/cpp/hawkes/inference/hawkes_cumulant.cpp b/lib/cpp/hawkes/inference/hawkes_cumulant.cpp new file mode 100644 index 000000000..7fa89fbd3 --- /dev/null +++ b/lib/cpp/hawkes/inference/hawkes_cumulant.cpp @@ -0,0 +1,122 @@ +#include "tick/hawkes/inference/hawkes_cumulant.h" + +HawkesCumulant::HawkesCumulant(double integration_support) + : integration_support(integration_support), are_cumulants_ready(false) { } + +SArrayDoublePtr HawkesCumulant::compute_A_and_I_ij(ulong r, ulong i, ulong j, + double mean_intensity_j) { + auto timestamps_i = timestamps_list[r][i]; + auto timestamps_j = timestamps_list[r][j]; + + ulong n_i = timestamps_i->size(); + ulong n_j = timestamps_j->size(); + double res_C = 0; + double res_J = 0; + double width = 2 * integration_support; + double trend_C_j = mean_intensity_j * width; + double trend_J_j = mean_intensity_j * width * width; + + ulong last_l = 0; + for (ulong k = 0; k < n_i; ++k) { + double t_i_k = (*timestamps_i)[k]; + double t_i_k_minus_half_width = t_i_k - integration_support; + double t_i_k_minus_width = t_i_k - width; + + if (t_i_k_minus_half_width < 0) continue; + + // Find next t_j_l that occurs width before t_i_k + while (last_l < n_j) { + if ((*timestamps_j)[last_l] <= t_i_k_minus_width) ++last_l; + else + break; + } + + ulong l = last_l; + ulong timestamps_in_interval = 0; + + double sub_res = 0.; + + while (l < n_j) { + double t_j_l_minus_t_i_k = (*timestamps_j)[l] - t_i_k; + double abs_t_j_l_minus_t_i_k = fabs(t_j_l_minus_t_i_k); + + if (abs_t_j_l_minus_t_i_k < width) { + sub_res += width - abs_t_j_l_minus_t_i_k; + + if (abs_t_j_l_minus_t_i_k < integration_support) timestamps_in_interval++; + } else { + break; + } + l += 1; + } + + if (l == n_j) continue; + res_C += timestamps_in_interval - trend_C_j; + res_J += sub_res - trend_J_j; + } + + res_C /= (*end_times)[r]; + res_J /= (*end_times)[r]; + + ArrayDouble return_array{res_C, res_J}; + return return_array.as_sarray_ptr(); +} + +double HawkesCumulant::compute_E_ijk(ulong r, ulong i, ulong j, ulong k, + double mean_intensity_i, double mean_intensity_j, + double J_ij) { + auto timestamps_i = timestamps_list[r][i]; + auto timestamps_j = timestamps_list[r][j]; + auto timestamps_k = timestamps_list[r][k]; + + double L_i = mean_intensity_i; + double L_j = mean_intensity_j; + + double res = 0; + ulong last_l = 0; + ulong last_m = 0; + ulong n_i = timestamps_i->size(); + ulong n_j = timestamps_j->size(); + ulong n_k = timestamps_k->size(); + + double trend_i = L_i * 2 * integration_support; + double trend_j = L_j * 2 * integration_support; + + for (ulong t = 0; t < n_k; ++t) { + double tau = (*timestamps_k)[t]; + + if (tau - integration_support < 0) continue; + + while (last_l < n_i) { + if ((*timestamps_i)[last_l] <= tau - integration_support) last_l += 1; + else + break; + } + ulong l = last_l; + + while (l < n_i) { + if ((*timestamps_i)[l] < tau + integration_support) l += 1; + else + break; + } + + while (last_m < n_j) { + if ((*timestamps_j)[last_m] <= tau - integration_support) last_m += 1; + else + break; + } + ulong m = last_m; + + while (m < n_j) { + if ((*timestamps_j)[m] < tau + integration_support) m += 1; + else + break; + } + + if ((m == n_j) || (l == n_i)) continue; + + res += (l - last_l - trend_i) * (m - last_m - trend_j) - J_ij; + } + res /= (*end_times)[r]; + return res; +} diff --git a/lib/cpp/hawkes/model/base/model_hawkes_list.cpp b/lib/cpp/hawkes/model/base/model_hawkes_list.cpp index f35bb8e60..54573f8a7 100644 --- a/lib/cpp/hawkes/model/base/model_hawkes_list.cpp +++ b/lib/cpp/hawkes/model/base/model_hawkes_list.cpp @@ -6,7 +6,7 @@ ModelHawkesList::ModelHawkesList( const int max_n_threads, const unsigned int optimization_level) - : ModelHawkes(max_n_threads, optimization_level), n_realizations(0) { + : ModelHawkes(max_n_threads, optimization_level), n_realizations(0), timestamps_list(0) { n_jumps_per_realization = VArrayULong::new_ptr(n_realizations); end_times = VArrayDouble::new_ptr(n_realizations); } diff --git a/lib/include/tick/hawkes/inference/hawkes_cumulant.h b/lib/include/tick/hawkes/inference/hawkes_cumulant.h new file mode 100644 index 000000000..9aad1ad12 --- /dev/null +++ b/lib/include/tick/hawkes/inference/hawkes_cumulant.h @@ -0,0 +1,41 @@ +#ifndef LIB_INCLUDE_TICK_HAWKES_INFERENCE_HAWKES_CUMULANT_H_ +#define LIB_INCLUDE_TICK_HAWKES_INFERENCE_HAWKES_CUMULANT_H_ + +// License: BSD 3 clause + +#include "tick/base/base.h" +#include "tick/hawkes/model/base/model_hawkes_list.h" + +class HawkesCumulant : public ModelHawkesList { + double integration_support; + bool are_cumulants_ready; + + public: + explicit HawkesCumulant(double integration_support); + + SArrayDoublePtr compute_A_and_I_ij(ulong r, ulong i, ulong j, double mean_intensity_j); + + double compute_E_ijk(ulong r, ulong i, ulong j, ulong k, + double mean_intensity_i, double mean_intensity_j, + double J_ij); + + double get_integration_support() const { + return integration_support; + } + + void set_integration_support(const double integration_support) { + if (integration_support <= 0) TICK_ERROR("Kernel support must be positive"); + this->integration_support = integration_support; + are_cumulants_ready = false; + } + + bool get_are_cumulants_ready() const { + return are_cumulants_ready; + } + + void set_are_cumulants_ready(const bool are_cumulants_ready) { + this->are_cumulants_ready = are_cumulants_ready; + } +}; + +#endif // LIB_INCLUDE_TICK_HAWKES_INFERENCE_HAWKES_CUMULANT_H_ diff --git a/lib/include/tick/hawkes/model/base/model_hawkes_list.h b/lib/include/tick/hawkes/model/base/model_hawkes_list.h index f5aab987e..b4f745124 100644 --- a/lib/include/tick/hawkes/model/base/model_hawkes_list.h +++ b/lib/include/tick/hawkes/model/base/model_hawkes_list.h @@ -20,7 +20,7 @@ class DLL_PUBLIC ModelHawkesList : public ModelHawkes { SArrayDoublePtrList2D timestamps_list; //! @brief Ending time of the realization - VArrayDoublePtr end_times; + VArrayDoublePtr end_times = nullptr; //! @brief Number of jumps of the process per realization (size=n_realizations) VArrayULongPtr n_jumps_per_realization; @@ -33,7 +33,8 @@ class DLL_PUBLIC ModelHawkesList : public ModelHawkes { ModelHawkesList(const int max_n_threads = 1, const unsigned int optimization_level = 0); - void set_data(const SArrayDoublePtrList2D ×tamps_list, const VArrayDoublePtr end_times); + virtual void set_data(const SArrayDoublePtrList2D ×tamps_list, + const VArrayDoublePtr end_times); //! @brief returns the number of jumps per realization SArrayULongPtr get_n_jumps_per_realization() const { @@ -46,6 +47,10 @@ class DLL_PUBLIC ModelHawkesList : public ModelHawkes { virtual unsigned int get_n_threads() const; + SArrayDoublePtrList2D get_timestamps_list() const { + return timestamps_list; + } + public: template void serialize(Archive &ar) { diff --git a/lib/swig/hawkes/inference/hawkes_cumulant.i b/lib/swig/hawkes/inference/hawkes_cumulant.i new file mode 100644 index 000000000..ee1807a3c --- /dev/null +++ b/lib/swig/hawkes/inference/hawkes_cumulant.i @@ -0,0 +1,26 @@ + + +%include std_shared_ptr.i +%shared_ptr(HawkesCumulant); + +%{ +#include "tick/hawkes/inference/hawkes_cumulant.h" +%} + + +class HawkesCumulant : public ModelHawkesList { + +public: + HawkesCumulant(double integration_support); + + SArrayDoublePtr compute_A_and_I_ij(ulong r, ulong i, ulong j, double mean_intensity_j); + + double compute_E_ijk(ulong r, ulong i, ulong j, ulong k, + double mean_intensity_i, double mean_intensity_j, + double J_ij); + + double get_integration_support() const; + void set_integration_support(const double integration_support); + bool get_are_cumulants_ready() const; + void set_are_cumulants_ready(const bool recompute_cumulants); +}; \ No newline at end of file diff --git a/lib/swig/hawkes/inference/hawkes_inference_module.i b/lib/swig/hawkes/inference/hawkes_inference_module.i index fa7c3520d..2c05a10a2 100644 --- a/lib/swig/hawkes/inference/hawkes_inference_module.i +++ b/lib/swig/hawkes/inference/hawkes_inference_module.i @@ -23,3 +23,4 @@ %include hawkes_adm4.i %include hawkes_basis_kernels.i %include hawkes_sumgaussians.i +%include hawkes_cumulant.i diff --git a/lib/swig/hawkes/model/base/model_hawkes_list.i b/lib/swig/hawkes/model/base/model_hawkes_list.i index b3c7abd04..8fe234e50 100644 --- a/lib/swig/hawkes/model/base/model_hawkes_list.i +++ b/lib/swig/hawkes/model/base/model_hawkes_list.i @@ -18,5 +18,7 @@ class ModelHawkesList : public ModelHawkes { ulong get_n_threads() const; SArrayULongPtr get_n_jumps_per_realization() const; + SArrayDoublePtrList2D get_timestamps_list() const; + void set_n_threads(const int max_n_threads); }; diff --git a/tick/base/base.py b/tick/base/base.py index 5403c4c84..66299dbe7 100644 --- a/tick/base/base.py +++ b/tick/base/base.py @@ -249,7 +249,8 @@ def find_documented_attributes(class_name, attrs): current_class_doc = inspect.cleandoc(attrs['__doc__']) parsed_doc = nd.docscrape.ClassDoc(None, doc=current_class_doc) - attr_docs = parsed_doc['Parameters'] + parsed_doc['Attributes'] + attr_docs = parsed_doc['Parameters'] + parsed_doc['Attributes'] + \ + parsed_doc['Other Parameters'] attr_and_doc = [] diff --git a/tick/hawkes/__init__.py b/tick/hawkes/__init__.py index f696b1590..a4befb26b 100644 --- a/tick/hawkes/__init__.py +++ b/tick/hawkes/__init__.py @@ -12,7 +12,7 @@ ) from .inference import ( HawkesADM4, HawkesExpKern, HawkesSumExpKern, HawkesBasisKernels, - HawkesConditionalLaw, HawkesEM, HawkesSumGaussians + HawkesConditionalLaw, HawkesEM, HawkesSumGaussians, HawkesCumulantMatching ) __all__ = [ @@ -23,5 +23,5 @@ "SimuPoissonProcess", "SimuInhomogeneousPoisson", "SimuHawkes", "SimuHawkesMulti", "SimuHawkesExpKernels", "SimuHawkesSumExpKernels", "HawkesKernel0", "HawkesKernelExp", "HawkesKernelPowerLaw", - "HawkesKernelSumExp", "HawkesKernelTimeFunc" + "HawkesKernelSumExp", "HawkesKernelTimeFunc", "HawkesCumulantMatching", ] diff --git a/tick/hawkes/inference/__init__.py b/tick/hawkes/inference/__init__.py index c61e15f61..e09a33155 100644 --- a/tick/hawkes/inference/__init__.py +++ b/tick/hawkes/inference/__init__.py @@ -7,6 +7,7 @@ from .hawkes_expkern_fixeddecay import HawkesExpKern from .hawkes_sumexpkern_fixeddecay import HawkesSumExpKern from .hawkes_sumgaussians import HawkesSumGaussians +from .hawkes_cumulant_matching import HawkesCumulantMatching __all__ = [ "HawkesExpKern", @@ -15,5 +16,6 @@ "HawkesEM", "HawkesADM4", "HawkesBasisKernels", - "HawkesSumGaussians" + "HawkesSumGaussians", + "HawkesCumulantMatching", ] diff --git a/tick/hawkes/inference/hawkes_cumulant_matching.py b/tick/hawkes/inference/hawkes_cumulant_matching.py new file mode 100644 index 000000000..2b18c3ede --- /dev/null +++ b/tick/hawkes/inference/hawkes_cumulant_matching.py @@ -0,0 +1,679 @@ +from itertools import product + +import numpy as np +import scipy +from scipy.linalg import qr, sqrtm, norm + +from tick.base import Base +from tick.hawkes.inference.base import LearnerHawkesNoParam +from tick.hawkes.inference.build.hawkes_inference import ( + HawkesCumulant as _HawkesCumulant +) + +# Tensorflow is not a project requirement but is needed for this class +try: + import tensorflow as tf +except ImportError: + tf = None + pass + + +class HawkesCumulantMatching(LearnerHawkesNoParam): + """This class is used for performing non parametric estimation of + multi-dimensional Hawkes processes based cumulant matching. + + It does not make any assumptions on the kernel shape and recovers + the kernel norms only. + + This class relies on `Tensorflow`_ to perform the matching of the + cumulants. If `Tensorflow`_ is not installed, it will not work. + + Parameters + ---------- + integration_support : `float` + Controls the maximal lag (positive or negative) upon which we + integrate the cumulant densities (covariance and skewness), + this amounts to neglect border effects. In practice, this is a + good approximation if the support of the kernels is smaller than + integration support and if the spectral norm of the kernel norms + is sufficiently distant from the critical value, namely 1. + It denoted by :math:`H` in the paper. + + C : `float`, default=1e3 + Level of penalization + + penalty : {'l1', 'l2', 'elasticnet', 'none'}, default='none' + The penalization to use. By default no penalization is used. + Penalty is only applied to adjacency matrix. + + solver : {'momentum', 'adam', 'adagrad', 'rmsprop', 'adadelta', 'gd'}, default='adam' + Name of tensorflow solver that will be used. + + step : `float`, default=1e-2 + Initial step size used for learning. Also known as learning rate. + + tol : `float`, default=1e-8 + The tolerance of the solver (iterations stop when the stopping + criterion is below it). If not reached the solver does ``max_iter`` + iterations + + max_iter : `int`, default=1000 + Maximum number of iterations of the solver + + verbose : `bool`, default=False + If `True`, we verbose things, otherwise the solver does not + print anything (but records information in history anyway) + + print_every : `int`, default=100 + Print history information when ``n_iter`` (iteration number) is + a multiple of ``print_every`` + + record_every : `int`, default=10 + Record history information when ``n_iter`` (iteration number) is + a multiple of ``record_every`` + + elastic_net_ratio : `float`, default=0.95 + Ratio of elastic net mixing parameter with 0 <= ratio <= 1. + + * For ratio = 0 this is ridge (L2 squared) regularization. + * For ratio = 1 this is lasso (L1) regularization. + * For 0 < ratio < 1, the regularization is a linear combination + of L1 and L2. + + Used in 'elasticnet' penalty + + solver_kwargs : `dict`, default=`None` + Extra arguments that will be passed to tensorflow solver + + Attributes + ---------- + n_nodes : `int` + Number of nodes / components in the Hawkes model + + baseline : `np.array`, shape=(n_nodes,) + Inferred baseline of each component's intensity + + adjacency : `np.ndarray`, shape=(n_nodes, n_nodes) + Inferred adjacency matrix + + mean_intensity : list of `np.array` shape=(n_nodes,) + Estimated mean intensities, named :math:`\\widehat{L}` in the paper + + covariance : list of `np.array` shape=(n_nodes,n_nodes) + Estimated integrated covariance, named :math:`\\widehat{C}` + in the paper + + skewness : list of `np.array` shape=(n_nodes,n_nodes) + Estimated integrated skewness (sliced), named :math:`\\widehat{K^c}` + in the paper + + R : `np.array` shape=(n_nodes,n_nodes) + Estimated weight, linked to the integrals of Hawkes kernels. + Use to derive adjacency and baseline + + Other Parameters + ---------------- + cs_ratio : `float`, default=`None` + Covariance-skewness ratio. The higher it is, themore covariance + has an impact the result which leads to more symmetric + adjacency matrices. If None, a default value is computed based + on the norm of the estimated covariance and skewness cumulants. + + elastic_net_ratio : `float`, default=0.95 + Ratio of elastic net mixing parameter with 0 <= ratio <= 1. + For ratio = 0 this is ridge (L2 squared) regularization + For ratio = 1 this is lasso (L1) regularization + For 0 < ratio < 1, the regularization is a linear combination + of L1 and L2. + Used in 'elasticnet' penalty + + References + ---------- + Achab, M., Bacry, E., Gaïffas, S., Mastromatteo, I., & Muzy, J. F. + (2017, July). Uncovering causality from multivariate Hawkes integrated + cumulants. + `In International Conference on Machine Learning (pp. 1-10)`_. + + .. _In International Conference on Machine Learning (pp. 1-10): http://proceedings.mlr.press/v70/achab17a.html + .. _Tensorflow: https://www.tensorflow.org + """ + _attrinfos = { + '_cumulant_computer': {'writable': False}, + '_solver': {'writable': False}, + '_elastic_net_ratio': {'writable': False}, + '_tf_feed_dict': {}, '_tf_graph': {}, + '_events_of_cumulants': {'writable': False} + } + + def __init__(self, integration_support, C=1e3, penalty='none', solver='adam', + step=1e-2, tol=1e-8, max_iter=1000, verbose=False, + print_every=100, record_every=10, solver_kwargs=None, + cs_ratio=None, elastic_net_ratio=0.95): + try: + import tensorflow + except ImportError: + raise ImportError('`tensorflow` >= 1.4.0 must be available to use ' + 'HawkesCumulantMatching') + + self._tf_graph = tf.Graph() + + LearnerHawkesNoParam.__init__( + self, tol=tol, verbose=verbose, max_iter=max_iter, + print_every=print_every, record_every=record_every + ) + + self._elastic_net_ratio = None + self.C = C + self.penalty = penalty + self.elastic_net_ratio = elastic_net_ratio + self.step = step + self.cs_ratio = cs_ratio + self.solver_kwargs = solver_kwargs + if self.solver_kwargs is None: + self.solver_kwargs = {} + + self._cumulant_computer = _HawkesCumulantComputer( + integration_support=integration_support) + self._learner = self._cumulant_computer._learner + self._solver = solver + self._tf_feed_dict = None + self._events_of_cumulants = None + + self.history.print_order = ["n_iter", "objective", "rel_obj"] + + def compute_cumulants(self, force=False): + """Compute estimated mean intensity, covariance and sliced skewness + + Parameters + ---------- + force : `bool` + If `True` previously computed cumulants are not reused + """ + self._cumulant_computer.compute_cumulants(verbose=self.verbose, + force=force) + + @property + def mean_intensity(self): + if not self._cumulant_computer.cumulants_ready: + self.compute_cumulants() + + return self._cumulant_computer.L + + @property + def covariance(self): + if not self._cumulant_computer.cumulants_ready: + self.compute_cumulants() + + return self._cumulant_computer.C + + @property + def skewness(self): + if not self._cumulant_computer.cumulants_ready: + self.compute_cumulants() + + return self._cumulant_computer.K_c + + def objective(self, adjacency=None, R=None): + """Compute objective value for a given adjacency or variable R + + Parameters + ---------- + adjacency : `np.ndarray`, shape=(n_nodes, n_nodes), default=None + Adjacency matrix at which we compute objective. + If `None`, objective will be computed at `R` + + R : `np.ndarray`, shape=(n_nodes, n_nodes), default=None + R variable at which objective is computed. Superseded by + adjacency if adjacency is not `None` + + Returns + ------- + Value of objective function + """ + cost = self._tf_objective_graph() + L, C, K_c = self._tf_placeholders() + + if adjacency is not None: + R = scipy.linalg.inv(np.eye(self.n_nodes) - adjacency) + + with self._tf_graph.as_default(): + with tf.Session() as sess: + sess.run(tf.global_variables_initializer()) + sess.run(self._tf_model_coeffs.assign(R)) + + return sess.run(cost, feed_dict={L: self.mean_intensity, + C: self.covariance, + K_c: self.skewness}) + + @property + def _tf_model_coeffs(self): + """Tensorflow variable of interest, used to perform minimization of + objective function + """ + with self._tf_graph.as_default(): + with tf.variable_scope("model", reuse=tf.AUTO_REUSE): + return tf.get_variable("R", [self.n_nodes, self.n_nodes], + dtype=tf.float64) + + @property + def adjacency(self): + return np.eye(self.n_nodes) - scipy.linalg.inv(self.solution) + + @property + def baseline(self): + return scipy.linalg.inv(self.solution).dot(self.mean_intensity) + + def _tf_placeholders(self): + """Tensorflow placeholders to manage cumulants data + """ + d = self.n_nodes + if self._tf_feed_dict is None: + with self._tf_graph.as_default(): + L = tf.placeholder(tf.float64, d, name='L') + C = tf.placeholder(tf.float64, (d, d), name='C') + K_c = tf.placeholder(tf.float64, (d, d), name='K_c') + self._tf_feed_dict = L, C, K_c + + return self._tf_feed_dict + + def _tf_objective_graph(self): + """Objective fonction written as a tensorflow graph + """ + d = self.n_nodes + + if self.cs_ratio is None: + cs_ratio = self.approximate_optimal_cs_ratio() + else: + cs_ratio = self.cs_ratio + + with self._tf_graph.as_default(): + L, C, K_c = self._tf_placeholders() + R = self._tf_model_coeffs + I = tf.constant(np.eye(d), dtype=tf.float64) + + # Construct model + variable_covariance = \ + tf.matmul(R, tf.matmul(tf.diag(L), R, transpose_b=True)) + + variable_skewness = \ + tf.matmul(C, tf.square(R), transpose_b=True) \ + + 2.0 * tf.matmul(R, R * C, transpose_b=True) \ + - 2.0 * tf.matmul(R, tf.matmul( + tf.diag(L), tf.square(R), transpose_b=True)) + + covariance_divergence = tf.reduce_mean( + tf.squared_difference(variable_covariance, C)) + + skewness_divergence = tf.reduce_mean( + tf.squared_difference(variable_skewness, K_c)) + + cost = (1 - cs_ratio) * skewness_divergence + cost += cs_ratio * covariance_divergence + + # Add potential regularization + cost = tf.cast(cost, tf.float64) + if self.strength_lasso > 0: + reg_l1 = tf.contrib.layers.l1_regularizer(self.strength_lasso) + cost += reg_l1((I - tf.matrix_inverse(R))) + if self.strength_ridge > 0: + reg_l2 = tf.contrib.layers.l2_regularizer(self.strength_ridge) + cost += reg_l2((I - tf.matrix_inverse(R))) + + return cost + + def fit(self, events, end_times=None, adjacency_start=None, R_start=None): + """Fit the model according to the given training data. + + Parameters + ---------- + events : `list` of `list` of `np.ndarray` + List of Hawkes processes realizations. + Each realization of the Hawkes process is a list of n_node for + each component of the Hawkes. Namely `events[i][j]` contains a + one-dimensional `numpy.array` of the events' timestamps of + component j of realization i. + If only one realization is given, it will be wrapped into a list + + end_times : `np.ndarray` or `float`, default = None + List of end time of all hawkes processes that will be given to the + model. If None, it will be set to each realization's latest time. + If only one realization is provided, then a float can be given. + + adjacency_start : `str` or `np.ndarray, shape=(n_nodes + n_nodes * n_nodes,), default=`None` + Initial guess for the adjacency matrix. Will be used as + starting point in optimization. + If `None` and `R_start` is also `None`, a default starting point + is estimated from the estimated cumulants + If `"random"`, a starting point is estimated from estimated + cumulants with a bit a randomness + + R_start : `np.ndarray`, shape=(n_nodes, n_nodes), default=None + R variable at which we start optimization. Superseded by + adjacency_start if adjacency_start is not `None` + """ + LearnerHawkesNoParam.fit(self, events, end_times=end_times) + self.solve(adjacency_start=adjacency_start, R_start=R_start) + + def _solve(self, adjacency_start=None, R_start=None): + """Launch optimization algorithm + + Parameters + ---------- + adjacency_start : `str` or `np.ndarray, shape=(n_nodes + n_nodes * n_nodes,), default=`None` + Initial guess for the adjacency matrix. Will be used as + starting point in optimization. + If `None`, a default starting point is estimated from the + estimated cumulants + If `"random"`, as with `None`, a starting point is estimated from + estimated cumulants with a bit a randomness + + max_iter : `int` + The number of training epochs. + + step : `float` + The learning rate used by the optimizer. + + solver : {'adam', 'momentum', 'adagrad', 'rmsprop', 'adadelta', 'gd'}, default='adam' + Solver used to minimize the loss. As the loss is not convex, it + cannot be optimized with `tick.optim.solver` solvers + """ + self.compute_cumulants() + + if adjacency_start is None and R_start is not None: + start_point = R_start + elif adjacency_start is None or adjacency_start == 'random': + random = adjacency_start == 'random' + start_point = self.starting_point(random=random) + else: + start_point = scipy.linalg.inv( + np.eye(self.n_nodes) - adjacency_start) + + cost = self._tf_objective_graph() + L, C, K_c = self._tf_placeholders() + + # Launch the graph + with self._tf_graph.as_default(): + with tf.variable_scope("solver", reuse=tf.AUTO_REUSE): + tf_solver = self.tf_solver(self.step, **self.solver_kwargs) + optimization = tf_solver.minimize(cost) + + with tf.Session() as sess: + sess.run(tf.global_variables_initializer()) + sess.run(self._tf_model_coeffs.assign(start_point)) + # Training cycle + prev_obj = np.finfo(np.float).max + for n_iter in range(self.max_iter + 1): + # We don't use self.objective here as it would be very slow + obj = sess.run( + cost, feed_dict={L: self.mean_intensity, + C: self.covariance, + K_c: self.skewness}) + rel_obj = abs(obj - prev_obj) / abs(prev_obj) + prev_obj = obj + converged = rel_obj < self.tol + + force = converged or n_iter == self.max_iter + self._handle_history(n_iter, objective=obj, rel_obj=rel_obj, + force=force) + + if converged: + break + + sess.run(optimization, feed_dict={L: self.mean_intensity, + C: self.covariance, + K_c: self.skewness}) + + self._set('solution', sess.run(self._tf_model_coeffs)) + + def approximate_optimal_cs_ratio(self): + """Heuristic to set covariance skewness ratio close to its + optimal value + """ + norm_sq_C = norm(self.covariance) ** 2 + norm_sq_K_c = norm(self.skewness) ** 2 + return norm_sq_K_c / (norm_sq_K_c + norm_sq_C) + + def starting_point(self, random=False): + """Heuristic to find a starting point candidate + + Parameters + ---------- + random : `bool` + Use a random orthogonal matrix instead of identity + + Returns + ------- + startint_point : `np.ndarray`, shape=(n_nodes, n_nodes) + A starting point candidate + """ + sqrt_C = sqrtm(self.covariance) + sqrt_L = np.sqrt(self.mean_intensity) + if random: + random_matrix = np.random.rand(self.n_nodes, self.n_nodes) + M, _ = qr(random_matrix) + else: + M = np.eye(self.n_nodes) + initial = np.dot(np.dot(sqrt_C, M), np.diag(1. / sqrt_L)) + return initial + + def get_kernel_values(self, i, j, abscissa_array): + raise ValueError('Hawkes cumulant cannot estimate kernel values') + + def get_kernel_norms(self): + """Computes kernel norms. This makes our learner compliant with + `tick.plot.plot_hawkes_kernel_norms` API + + Returns + ------- + norms : `np.ndarray`, shape=(n_nodes, n_nodes) + 2d array in which each entry i, j corresponds to the norm of + kernel i, j + """ + return self.adjacency + + @property + def solver(self): + return self._solver + + @solver.setter + def solver(self, val): + available_solvers = ['momentum', 'adam', 'adagrad', 'rmsprop', + 'adadelta', 'gd'] + if val.lower() not in available_solvers: + raise ValueError('solver must be one of {}, recieved {}' + .format(available_solvers, val)) + + self._set('_solver', val) + + @property + def tf_solver(self): + if self.solver.lower() == 'momentum': + return tf.train.MomentumOptimizer + elif self.solver.lower() == 'adam': + return tf.train.AdamOptimizer + elif self.solver.lower() == 'adagrad': + return tf.train.AdagradOptimizer + elif self.solver.lower() == 'rmsprop': + return tf.train.RMSPropOptimizer + elif self.solver.lower() == 'adadelta': + return tf.train.AdadeltaOptimizer + elif self.solver.lower() == 'gd': + return tf.train.GradientDescentOptimizer + + @property + def elastic_net_ratio(self): + return self._elastic_net_ratio + + @elastic_net_ratio.setter + def elastic_net_ratio(self, val): + if val < 0 or val > 1: + raise ValueError("`elastic_net_ratio` must be between 0 and 1, " + "got %s" % str(val)) + else: + self._set("_elastic_net_ratio", val) + + @property + def strength_lasso(self): + if self.penalty == 'elasticnet': + return self.elastic_net_ratio / self.C + elif self.penalty == 'l1': + return 1. / self.C + else: + return 0. + + @property + def strength_ridge(self): + if self.penalty == 'elasticnet': + return (1 - self.elastic_net_ratio) / self.C + elif self.penalty == 'l2': + return 1. / self.C + return 0. + + +class _HawkesCumulantComputer(Base): + """Private class to compute Hawkes cumulants + """ + + _cpp_obj_name = '_learner' + _attrinfos = { + 'integration_support': {'cpp_setter': 'set_integration_support'}, + '_learner': {}, 'L': {}, 'C': {}, 'K_c': {}, + '_L_day': {}, '_J': {}, '_events_of_cumulants': {}, + } + + def __init__(self, integration_support=100.): + Base.__init__(self) + self.integration_support = integration_support + self._learner = _HawkesCumulant(self.integration_support) + + self.L = None + self.C = None + self.K_c = None + + self._L_day = None + self._J = None + self._events_of_cumulants = None + + def compute_cumulants(self, verbose=False, force=False): + """Compute estimated mean intensity, covariance and sliced skewness + + Parameters + ---------- + verbose : `bool` + If `True`, a message will be printed when previously computed + cumulants are reused + + force : `bool` + If `True` cumulants will always be recomputed + """ + if len(self.realizations) == 0: + raise RuntimeError('Cannot compute cumulants if no realization ' + 'has been provided') + + # Check if cumulants have already been computed + if self.cumulants_ready and not force: + if verbose: + print('Use previouly computed cumulants') + return + + # Remember for which realizations cumulants have been computed + self._events_of_cumulants = self.realizations + self.compute_L() + self.compute_C_and_J() + self.K_c = self.compute_E_c() + + self._learner.set_are_cumulants_ready(True) + + @staticmethod + def _same_realizations(events_1, events_2): + if len(events_1) != len(events_2): + return False + + for r in range(len(events_1)): + if len(events_1[r]) != len(events_2[r]): + return False + + # Fast check that both arrays share the same pointer + for i in range(len(events_1[r])): + if events_1[r][i].__array_interface__ != \ + events_2[r][i].__array_interface__: + return False + return True + + def compute_L(self): + self._L_day = np.zeros((self.n_realizations, self.n_nodes)) + + for day, realization in enumerate(self.realizations): + for i in range(self.n_nodes): + process = realization[i] + self._L_day[day][i] = len(process) / self.end_times[day] + + self.L = np.mean(self._L_day, axis=0) + + def compute_C_and_J(self): + self.C = np.zeros((self.n_nodes, self.n_nodes)) + self._J = np.zeros((self.n_realizations, self.n_nodes, self.n_nodes)) + + d = self.n_nodes + for day in range(len(self.realizations)): + C = np.zeros((d, d)) + J = np.zeros((d, d)) + for i, j in product(range(d), repeat=2): + res = self._learner.compute_A_and_I_ij( + day, i, j, self._L_day[day][j]) + C[i, j] = res[0] + J[i, j] = res[1] + # we keep the symmetric part to remove edge effects + C[:] = 0.5 * (C + C.T) + J[:] = 0.5 * (J + J.T) + self.C += C / self.n_realizations + self._J[day] = J.copy() + + def compute_E_c(self): + E_c = np.zeros((self.n_nodes, self.n_nodes, 2)) + + d = self.n_nodes + + for day in range(len(self.realizations)): + for i in range(d): + for j in range(d): + E_c[i, j, 0] += self._learner.compute_E_ijk( + day, i, j, j, self._L_day[day][i], self._L_day[day][j], + self._J[day][i, j]) + + E_c[i, j, 1] += self._learner.compute_E_ijk( + day, j, j, i, self._L_day[day][j], self._L_day[day][j], + self._J[day][j, j]) + + E_c /= self.n_realizations + + K_c = np.zeros((self.n_nodes, self.n_nodes)) + K_c += 2 * E_c[:, :, 0] + K_c += E_c[:, :, 1] + K_c /= 3. + + return K_c + + @property + def n_nodes(self): + return self._learner.get_n_nodes() + + @property + def n_realizations(self): + return len(self._learner.get_n_jumps_per_realization()) + + @property + def realizations(self): + return self._learner.get_timestamps_list() + + @property + def end_times(self): + return self._learner.get_end_times() + + @property + def cumulants_ready(self): + events_didnt_change = self._events_of_cumulants is not None and \ + _HawkesCumulantComputer._same_realizations( + self._events_of_cumulants, self.realizations) + + return self._learner.get_are_cumulants_ready() and events_didnt_change diff --git a/tick/hawkes/inference/tests/hawkes_cumulant_matching_test-train_data.pkl b/tick/hawkes/inference/tests/hawkes_cumulant_matching_test-train_data.pkl new file mode 100644 index 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