Goodness-of-fit diagnostics for Hawkes EM algorithm (#507)

* Hawkes EM qq plots - first commit * Hawkes EM qq plots - workings * HawkesEM - Compute time integral of intensities * HawkesEM - Time-changed interarrival * debugging * debugging * debugging * Update configure_env.sh and gtest.sh * HawkesEM gtest - ok till implicit abscissa * HawkesEM Gtest - pass till data with explicit abscissa * HawkesEM Gtest - pass till values with explicit abscissa * HawkesEM - Py unittest of fit method with simulated data * HawkesEM - test with simulated data * HawkesEM - basic unit tests for inter-arrival times * try get more python working on windows * Fix usage of threshold in _index_left and _t_left * Hawkes EM qq plots - first commit * Hawkes EM qq plots - workings * HawkesEM - Compute time integral of intensities * HawkesEM - Time-changed interarrival * debugging * debugging * debugging * Update configure_env.sh and gtest.sh * HawkesEM gtest - ok till implicit abscissa * HawkesEM Gtest - pass till data with explicit abscissa * HawkesEM Gtest - pass till values with explicit abscissa * HawkesEM - Py unittest of fit method with simulated data * HawkesEM - test with simulated data * HawkesEM - basic unit tests for inter-arrival times * Fix usage of threshold in _index_left and _t_left * Example - QQplot of simulated Hawkes process * Examples - QQ plot of Hawkes EM algo * TimeFunction - fix future max * HawkesEM test - test 3 rtol * HawkesKernelTiemFunc - get norm using time_func * Clean comments in hawkes em test] --------- Co-authored-by: dekken <philip.deegan@gmail.com> Co-authored-by: claudio <claudio.bellani01@gmail.com>
X-DataInitiative · Mar 5, 2023 · 04dbb37 · 04dbb37
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diff --git a/examples/qq_plot_hawkes_em.py b/examples/qq_plot_hawkes_em.py
@@ -0,0 +1,53 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+from tick.hawkes import (SimuHawkes, HawkesKernelTimeFunc, HawkesKernelExp,
+                         HawkesEM)
+from tick.base import TimeFunction
+from tick.plot import qq_plots
+
+run_time = 30000
+
+t_values1 = np.array([0, 1, 1.5, 2., 3.5], dtype=float)
+y_values1 = np.array([0, 0.2, 0, 0.1, 0.], dtype=float)
+tf1 = TimeFunction([t_values1, y_values1],
+                   inter_mode=TimeFunction.InterConstRight, dt=0.1)
+kernel1 = HawkesKernelTimeFunc(tf1)
+
+t_values2 = np.linspace(0, 4, 20)
+y_values2 = np.maximum(0., np.sin(t_values2) / 4)
+tf2 = TimeFunction([t_values2, y_values2])
+kernel2 = HawkesKernelTimeFunc(tf2)
+
+baseline = np.array([0.1, 0.3])
+
+hawkes = SimuHawkes(baseline=baseline, end_time=run_time, verbose=False,
+                    seed=2334)
+
+hawkes.set_kernel(0, 0, kernel1)
+hawkes.set_kernel(0, 1, HawkesKernelExp(.5, .7))
+hawkes.set_kernel(1, 1, kernel2)
+
+hawkes.simulate()
+
+em = HawkesEM(4, kernel_size=16, n_threads=8, verbose=False, tol=1e-3)
+em.fit(hawkes.timestamps)
+
+hawkes.store_compensator_values()
+residuals_list = em.time_changed_interarrival_times()
+
+fig, axs = plt.subplots(2, 2)
+
+_ = qq_plots(
+    point_process=hawkes,
+    ax=[axs[0, 0], axs[0, 1]],
+    node_names=['node 0 - simulation', 'node 1 - simulation'],
+    show=False
+)
+_ = qq_plots(
+    residuals=residuals_list[0],
+    ax=[axs[1, 0], axs[1, 1]],
+    node_names=['node 0 - estimation', 'node 1 - estimation'],
+    show=False
+)
+plt.show()
diff --git a/examples/qq_plot_hawkes_nonparam.py b/examples/qq_plot_hawkes_nonparam.py
@@ -0,0 +1,35 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+from tick.hawkes import (SimuHawkes, HawkesKernelTimeFunc, HawkesKernelExp,
+                         HawkesEM)
+from tick.base import TimeFunction
+from tick.plot import qq_plots
+
+run_time = 30000
+
+t_values1 = np.array([0, 1, 1.5, 2., 3.5], dtype=float)
+y_values1 = np.array([0, 0.2, 0, 0.1, 0.], dtype=float)
+tf1 = TimeFunction([t_values1, y_values1],
+                   inter_mode=TimeFunction.InterConstRight, dt=0.1)
+kernel1 = HawkesKernelTimeFunc(tf1)
+
+t_values2 = np.linspace(0, 4, 20)
+y_values2 = np.maximum(0., np.sin(t_values2) / 4)
+tf2 = TimeFunction([t_values2, y_values2])
+kernel2 = HawkesKernelTimeFunc(tf2)
+
+baseline = np.array([0.1, 0.3])
+
+hawkes = SimuHawkes(baseline=baseline, end_time=run_time, verbose=False,
+                    seed=2334)
+
+hawkes.set_kernel(0, 0, kernel1)
+hawkes.set_kernel(0, 1, HawkesKernelExp(.5, .7))
+hawkes.set_kernel(1, 1, kernel2)
+
+hawkes.simulate()
+hawkes.store_compensator_values()
+
+fig = qq_plots(hawkes, show=False)
+plt.show()
diff --git a/lib/cpp-test/base/time_func_gtest.cpp b/lib/cpp-test/base/time_func_gtest.cpp
@@ -0,0 +1,133 @@
+// License: BSD 3 clause
+
+#include <gtest/gtest.h>
+#include "tick/base/time_func.h"
+#include <iostream>
+#include <cmath>
+
+class TimeFunctionTest : public ::testing::Test {
+ protected:
+  ArrayDouble T;
+  ArrayDouble Y;
+  double dt = .25;
+  double time_horizon = 1.;
+  double border_value = .0;
+  ulong sample_size = 5;
+  void SetUp() override {
+    T = ArrayDouble{.0, .25, .5, .75, 1.};
+    Y = ArrayDouble{1., 2., 3., 4., 5.};
+  }
+};
+
+TEST_F(TimeFunctionTest, implicit_abscissa_data) {
+  TimeFunction tf(Y, TimeFunction::BorderType::Border0, TimeFunction::InterMode::InterConstRight,
+                  dt, border_value);
+  EXPECT_DOUBLE_EQ(tf.get_t0(), T[0]);
+  SArrayDoublePtr sampled_y = tf.get_sampled_y();
+  EXPECT_EQ(tf.get_sample_size(), sample_size);
+  EXPECT_EQ(sampled_y->size(), Y.size());
+  for (ulong i = 0; i < Y.size(); i++) {
+    EXPECT_DOUBLE_EQ((*sampled_y)[i], Y[i]);
+  }
+}
+TEST_F(TimeFunctionTest, explicit_abscissa_data) {
+  TimeFunction tf(T, Y, TimeFunction::BorderType::Border0,
+                  TimeFunction::InterMode::InterConstRight);
+  EXPECT_DOUBLE_EQ(tf.get_t0(), T[0]);
+  SArrayDoublePtr sampled_y = tf.get_sampled_y();
+  EXPECT_EQ(tf.get_sample_size(), sample_size);
+  EXPECT_EQ(sampled_y->size(), Y.size());
+  for (ulong i = 0; i < Y.size(); i++) {
+    EXPECT_DOUBLE_EQ((*sampled_y)[i], Y[i]);
+  }
+}
+
+TEST_F(TimeFunctionTest, border0_interconstright_implicit_node_values) {
+  TimeFunction tf(Y, TimeFunction::BorderType::Border0, TimeFunction::InterMode::InterConstRight,
+                  dt, border_value);
+  double s = 0;
+  for (int k = 0; k < T.size(); k++) {
+    double t_k = T[k];
+    double y_k = Y[k];
+    EXPECT_DOUBLE_EQ(tf.value(t_k), y_k) << "error at k=" << k << ", t_k=" << t_k << "\n";
+    if (k > 0) s += Y[k - 1] * dt;
+    EXPECT_DOUBLE_EQ(tf.primitive(t_k), s) << "error at k=" << k << ", t_k=" << t_k << "\n";
+  }
+
+  EXPECT_DOUBLE_EQ(tf.get_norm(), tf.primitive(time_horizon));
+}
+
+TEST_F(TimeFunctionTest, border0_interconstright_explicit_node_values) {
+  TimeFunction tf(T, Y, TimeFunction::BorderType::Border0,
+                  TimeFunction::InterMode::InterConstRight);
+  double s = 0;
+  for (int k = 0; k < T.size(); k++) {
+    double t_k = T[k];
+    double y_k = Y[k];
+    EXPECT_DOUBLE_EQ(tf.value(t_k), y_k) << "error at k=" << k << ", t_k=" << t_k << "\n";
+    if (k > 0) s += Y[k - 1] * dt;
+    EXPECT_DOUBLE_EQ(tf.primitive(t_k), s) << "error at k=" << k << ", t_k=" << t_k << "\n";
+  }
+
+  EXPECT_DOUBLE_EQ(tf.get_norm(), tf.primitive(time_horizon));
+}
+
+TEST_F(TimeFunctionTest, border0_interconstleft_implicit_node_values) {
+  TimeFunction tf(Y, TimeFunction::BorderType::Border0, TimeFunction::InterMode::InterConstLeft, dt,
+                  border_value);
+  double s = 0;
+  for (int k = 0; k < T.size(); k++) {
+    double t_k = T[k];
+    double y_k = Y[k];
+    EXPECT_DOUBLE_EQ(tf.value(t_k), y_k) << "error at k=" << k << ", t_k=" << t_k << "\n";
+    if (k > 0) s += y_k * dt;
+    EXPECT_DOUBLE_EQ(tf.primitive(t_k), s) << "error at k=" << k << ", t_k=" << t_k << "\n";
+  }
+  EXPECT_DOUBLE_EQ(tf.get_norm(), tf.primitive(time_horizon));
+}
+
+TEST_F(TimeFunctionTest, border0_interconstleft_explicit_node_values) {
+  TimeFunction tf(T, Y, TimeFunction::BorderType::Border0, TimeFunction::InterMode::InterConstLeft);
+  double s = 0;
+  for (int k = 0; k < T.size(); k++) {
+    double t_k = T[k];
+    double y_k = Y[k];
+    EXPECT_DOUBLE_EQ(tf.value(t_k), y_k) << "error at k=" << k << ", t_k=" << t_k << "\n";
+    if (k > 0) s += y_k * dt;
+    EXPECT_DOUBLE_EQ(tf.primitive(t_k), s) << "error at k=" << k << ", t_k=" << t_k << "\n";
+  }
+  EXPECT_DOUBLE_EQ(tf.get_norm(), tf.primitive(time_horizon));
+}
+
+TEST_F(TimeFunctionTest, border0_interlinear_implicit_node_values) {
+  TimeFunction tf(Y, TimeFunction::BorderType::Border0, TimeFunction::InterMode::InterLinear, dt,
+                  border_value);
+  double s = 0;
+  for (int k = 0; k < T.size(); k++) {
+    double t_k = T[k];
+    double y_k = Y[k];
+    EXPECT_DOUBLE_EQ(tf.value(t_k), y_k) << "error at k=" << k << ", t_k=" << t_k << "\n";
+    if (k > 0) s += .5 * (y_k + Y[k - 1]) * dt;
+    EXPECT_DOUBLE_EQ(tf.primitive(t_k), s) << "error at k=" << k << ", t_k=" << t_k << "\n";
+  }
+  EXPECT_DOUBLE_EQ(tf.get_norm(), tf.primitive(time_horizon));
+}
+
+TEST_F(TimeFunctionTest, border0_interlinear_explicit_node_values) {
+  TimeFunction tf(T, Y, TimeFunction::BorderType::Border0, TimeFunction::InterMode::InterLinear);
+  double s = 0;
+  for (int k = 0; k < T.size(); k++) {
+    double t_k = T[k];
+    double y_k = Y[k];
+    EXPECT_DOUBLE_EQ(tf.value(t_k), y_k) << "error at k=" << k << ", t_k=" << t_k << "\n";
+    if (k > 0) s += .5 * (y_k + Y[k - 1]) * dt;
+    EXPECT_DOUBLE_EQ(tf.primitive(t_k), s) << "error at k=" << k << ", t_k=" << t_k << "\n";
+  }
+  EXPECT_DOUBLE_EQ(tf.get_norm(), tf.primitive(time_horizon));
+}
+#ifdef ADD_MAIN
+int main(int argc, char** argv) {
+  ::testing::InitGoogleTest(&argc, argv);
+  return RUN_ALL_TESTS();
+}
+#endif  // ADD_MAIN
diff --git a/lib/cpp-test/hawkes/inference/CMakeLists.txt b/lib/cpp-test/hawkes/inference/CMakeLists.txt
@@ -0,0 +1,16 @@
+add_executable(tick_test_hawkes_inference
+        hawkes_em_gtest.cpp
+        )
+
+target_link_libraries(tick_test_hawkes_inference
+        ${TICK_LIB_ARRAY}
+        ${TICK_LIB_BASE}
+        ${TICK_LIB_CRANDOM}
+        ${TICK_LIB_BASE_MODEL}
+        ${TICK_LIB_LINEAR_MODEL}
+	${TICK_LIB_HAWKES_INFERENCE}
+        ${TICK_LIB_HAWKES_MODEL}
+        ${TICK_TEST_LIBS}
+        )
+
+