lokta-volterra inference module

README.md

@@ -61,3 +61,9 @@ python causal_inference/base/lv_simulator.py
 This will take all the default arguments and configuration to run a simulation instance of lotka-volterra population dynamics.
 
 - The simulation statistics will be saved in the `repo/results` directory by default.
+
+## Simulation and inference
+
+- The simulation and inference methods are separately implemented in `repo/causal_inference/base/lotka_volterra/lv_system.py`.
+- Currently, this inference method is experimental and may not always converge to correct optimal parameters.
+- More work is needed to find a good approximation schema to initiate the parameters of the LV-system.

causal_inference/base/lotka_volterra/lv_system.py

@@ -0,0 +1,129 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+
+import numpy as np
+from scipy import integrate
+from scipy.optimize import minimize
+
+from causal_inference.config import LV_PARAMS
+
+class LotkaVolterra():
+    '''
+    Base Lotka-Volterra Class that defines a predator-prey system.
+    '''
+    def __init__(self,
+                 A=LV_PARAMS['A'], B=LV_PARAMS['B'], C=LV_PARAMS['C'], D=LV_PARAMS['D'],
+                 prey_population=LV_PARAMS['INITIAL_PREY_POPULATION'],
+                 pred_population=LV_PARAMS['INITIAL_PREDATOR_POPULATION'],
+                 total_time=LV_PARAMS['TOTAL_TIME'], step_size=LV_PARAMS['STEP_SIZE'],
+                 max_iter=LV_PARAMS['MAX_ITERATIONS']):
+        # Lotka-Volterra parameters
+        self.A = A
+        self.B = B
+        self.C = C
+        self.D = D
+
+        self.prey_population = prey_population          # Initial prey population
+        self.predator_population = pred_population      # Initial predator population
+
+        self.init_time = 0                  # initial time
+        self.total_time = total_time        # total time in units
+        self.step_size = step_size          # increment for each time step
+        self.max_iterations = max_iter      # tolerance parameter
+
+        self.time_stamps = np.arange(self.init_time, self.total_time, self.step_size)
+
+@staticmethod
+def LV_derivative(t, Z, A, B, C, D):
+    '''
+    Returns the rate of change of predator and prey population
+
+    Simulates Lotka-Volterra dynamics
+
+    Parameters:
+    t (list): [t0, tf] initial and final time points for simulation (Not used but necessary for integration step)
+    Z (tuple): (x, y) state of the system
+    A: prey growth rate (model parameter)
+    B: predation rate (model parameter)
+    C: predator death rate (model parameter)
+    D: predator growth rate from eating prey (model parameter)
+
+    Returns:
+    array: rate of change of prey and predator population
+    '''
+    x, y = Z
+    dotx = x * (A - B * y)
+    doty = y * (-C + D * x)
+    return np.array([dotx, doty])
+
+def simulate_lotka_volterra(params, t, initial_conditions):
+    """
+    Simulates Lotka-Volterra dynamics
+
+    Parameters:
+    params (tuple): (A, B, C, D) model parameters
+        A: prey growth rate
+        B: predation rate
+        C: predator death rate
+        D: predator growth rate from eating prey
+    t (array): time points for simulation
+    initial_conditions (tuple): (prey0, predator0) initial populations
+
+    Returns:
+    population: (n, 2) array where each row is [prey_pop, predator_pop]
+    """
+    A, B, C, D = params
+
+    solution = integrate.solve_ivp(LV_derivative, [t[0], t[-1]], initial_conditions,
+                                   args=(A, B, C, D), dense_output=True)
+
+    population = solution.sol(t)
+    return population
+
+def fit_lotka_volterra(time_points, observed_data, initial_guess):
+    """
+    Fits Lotka-Volterra parameters to observed population data
+
+    Parameters:
+    time_points (array): time points of observations
+    observed_data (array): observed population data [prey, predator]
+    initial_guess (tuple): initial parameter guess (A, B, C, D)
+
+    Returns:
+    tuple: Fitted parameters (A, B, C, D) after optimization
+    """
+    def objective_function(params):
+        # Simulate with current parameters
+        simulated = simulate_lotka_volterra(params, time_points,
+                                            observed_data[:, 0])
+        # Calculate mean squared error
+        mse = np.mean((simulated - observed_data) ** 2)
+        return mse
+
+    # Parameter bounds (all parameters must be positive)
+    bounds = [(0, None) for _ in range(4)]
+
+    # Optimize parameters
+    result = minimize(objective_function, initial_guess,
+                      bounds=bounds, method='L-BFGS-B')
+
+    return result.x
+
+# Example usage:
+if __name__ == "__main__":
+    # Generate synthetic data
+    m = LotkaVolterra()
+    true_params = (m.A, m.B, m.C, m.D)
+    initial_conditions = (m.prey_population, m.predator_population)     # (prey0, predator0)
+
+    # Generate synthetic data with some noise
+    data = simulate_lotka_volterra(true_params, m.time_stamps, initial_conditions)
+    noisy_data = data + np.random.normal(0, 0.1, data.shape)
+
+    # Fit parameters
+    initial_guess = (0.5, 0.05, 0.05, 0.05) #FIXME Use more educated schema for initial guess
+
+    fitted_params = fit_lotka_volterra(m.time_stamps, noisy_data, initial_guess)
+
+    print("True parameters:", true_params)
+    print("Fitted parameters:", fitted_params)

causal_inference/base/lv_simulator.py

@@ -25,15 +25,19 @@
         raise AssertionError(f'{method} is not implemented!')
     return solver
 
+def simulate_lotka_volterra(method):
+    log_LV_params()
+    solver = get_solver(method)
+    prey_list, predator_list = solver._solve()
+    return prey_list, predator_list, solver.time_stamps
+
 def main(method, results_dir):
     '''
     Main function that solves LV system.
     '''
-    log_LV_params()
-    solver = get_solver(method)
-    prey_list, predator_list = solver._solve()
-    _save_population(prey_list, predator_list, solver.time_stamps, results_dir)
-    plot_population_over_time(prey_list, predator_list, solver.time_stamps, results_dir)
+    prey_list, predator_list, t = simulate_lotka_volterra(method)
+    _save_population(prey_list, predator_list, t, results_dir)
+    plot_population_over_time(prey_list, predator_list, t, results_dir)
 
 if __name__ == '__main__':
     PARSER = argparse.ArgumentParser()

causal_inference/base/ode_solver.py

@@ -2,10 +2,9 @@
 # -*- coding: utf-8 -*-
 
 import logging
-import numpy as np
 from scipy import integrate
 
-from causal_inference.base.lv_system import LotkaVolterra
+from causal_inference.base.lotka_volterra.lv_system import LotkaVolterra, LV_derivative
 
 class ODE_solver(LotkaVolterra):
     '''
@@ -15,24 +14,14 @@
         super().__init__()
         logging.info('Simulating Lotka-Volterra predator-prey dynamics with odeint solver')
 
-    @staticmethod
-    def LV_derivative(t, Z, A, B, C, D):
-        '''
-        Returns the rate of change of predator and prey population
-        '''
-        x, y = Z
-        dotx = x * (A - B * y)
-        doty = y * (-C + D * x)
-        return np.array([dotx, doty])
-
     def _solve(self):
         '''
         ODE solver that returns the predator and prey populations at each time step in time series.
         '''
         logging.info(f'Computing population over {self.total_time} generation with step size of {self.step_size}...')
 
         INIT_POP = [self.prey_population, self.predator_population]
-        sol = integrate.solve_ivp(self.LV_derivative, [self.init_time, self.total_time], INIT_POP, args=(self.A, self.B, self.C, self.D), dense_output=True)
+        sol = integrate.solve_ivp(LV_derivative, [self.init_time, self.total_time], INIT_POP, args=(self.A, self.B, self.C, self.D), dense_output=True)
         prey_list, predator_list = sol.sol(self.time_stamps)
 
         logging.info('done!')

causal_inference/base/runge_kutta_solver.py

@@ -1,7 +1,7 @@
 #!/usr/bin/python
 # -*- coding: utf-8 -*-
 import logging
-from causal_inference.base.lv_system import LotkaVolterra
+from causal_inference.base.lotka_volterra.lv_system import LotkaVolterra
 
 class RungeKuttaSolver(LotkaVolterra):
     '''

causal_inference/config.py

@@ -7,15 +7,15 @@
 
 # Lotka-Volterra Parameters
 LV_PARAMS = {
-'A' : 10.0,
-'B' : 7.0,
-'C' : 3.0,
-'D' : 5.0,
+'A' : 1.0,
+'B' : 0.1,
+'C' : 0.3,
+'D' : 0.4,
 'STEP_SIZE' : 0.01,
-'TOTAL_TIME' : 20,
-'INITIAL_PREY_POPULATION' : 60,
+'TOTAL_TIME' : 10,
+'INITIAL_PREY_POPULATION' : 40,
 'INITIAL_PREDATOR_POPULATION' : 25,
-'MAX_ITERATIONS' : 200
+'MAX_ITERATIONS' : 100
 }
 
 # PATHS

causal_inference/tests/test_lv_simulator.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python3
 # flake8: noqa
-from causal_inference.base.lv_system import LotkaVolterra
+from causal_inference.base.lotka_volterra.lv_system import LotkaVolterra
 from causal_inference.config import LV_PARAMS
 
 def test_lotka_volterra():