Likelihood maximization

In this notebook, we are going to look over likelihood maximisation and how it is implemented in folie

The next step is to choose a discretisation of the likelihood

for trj in data:
    transition.preprocess_traj(trj)

def log_likelihood_negative(coefficients, data):
    weightsum = data.weights.sum()
    return np.sum([transition(weight, coefficients)[0] * weight / weightsum for weight, trj in zip(data.weights, data)])

KramersMoyalEstimator(self.model).fit(data)
coefficients0 = self.model.coefficients


transition.use_jac = False
res = minimize(log_likelihood_negative, coefficients0, args=(data,), callback=callback, **minimize_kwargs)

self.model.coefficients = res.x

We can also use the jacobian

def log_likelihood_negative_w_jac(transition, weights, data, coefficients):
    weightsum = weights.sum()
    array_res = [transition(weight, trj, coefficients, jac=True) * weight / weightsum for weight, trj in zip(data.weights, data)]
    likelihood = np.sum([val[0] for val in array_res])
    likelihood_jac = np.sum([val[1] for val in array_res], axis=0)
    return likelihood,likelihood_jac

res = minimize(log_likelihood_negative_w_jac, coefficients0, args=(data,), jac=True, **minimize_kwargs)
self.model.coefficients = res.x