154 lines
5.4 KiB
Python
154 lines
5.4 KiB
Python
import numpy as np
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from scipy.stats import norm, multivariate_normal
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import matplotlib.pyplot as plt
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class PreferenceExpectedImprovement:
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def __init__(self, nr_samples, nr_dims, nr_likelihood_samples, lower_bound, upper_bound, init_var, seed=None):
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self.nr_samples = int(nr_samples)
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self.nr_dims = nr_dims
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self.nr_likelihood_samples = int(nr_likelihood_samples)
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# check if upper_bound and lower_bound are numpy arrays of shape (nr_dims, 1) or (nr_dims,) or if they are float
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self.upper_bound = upper_bound
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self.lower_bound = lower_bound
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self.initial_variance = init_var
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self.proposal_mean = np.zeros((nr_dims, 1))
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self.proposal_cov = np.diag(np.ones((nr_dims,)) * self.initial_variance)
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self.rng = np.random.default_rng(seed=seed)
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def rejection_sampling(self):
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samples = np.empty((0, self.nr_dims))
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while samples.shape[0] < self.nr_samples:
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# sample from the multi variate gaussian distribution
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sample = np.zeros((1, self.nr_dims))
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for i in range(self.nr_dims):
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check = False
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while not check:
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sample[0, i] = self.rng.normal(self.proposal_mean[i], self.proposal_cov[i, i])
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if self.lower_bound <= sample[0, i] <= self.upper_bound:
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check = True
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samples = np.append(samples, sample, axis=0)
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# sample = self.rng.multivariate_normal(
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# mean,
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# self.proposal_cov
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# )
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#
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# # check if the sample is within the bounds
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# if np.all(sample >= self.lower_bound) and np.all(sample <= self.upper_bound):
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# samples = np.append(samples, [sample], axis=0)
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return samples
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def expected_improvement(self, gp, X, kappa=0.01):
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X_sample = self.rejection_sampling()
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mu_sample, sigma_sample = gp.predict(X_sample, return_std=True)
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sigma_sample = sigma_sample.reshape(-1, 1)
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mu = gp.predict(X)
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mu_best = np.max(mu)
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with np.errstate(divide='warn'):
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imp = mu_sample - mu_best - kappa
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imp = imp.reshape(-1, 1)
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z = imp / sigma_sample
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ei = imp * norm.cdf(z) + sigma_sample * norm.pdf(z)
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ei[sigma_sample == 0.0] = 0.0
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idx = np.argmax(ei)
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x_next = X_sample[idx, :]
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return x_next
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def likelihood(self, preference):
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covariance_diag = np.ones((self.nr_dims,)) * self.initial_variance
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covariance_diag[preference] = 0.05
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covariance = np.diag(covariance_diag)
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return covariance
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def update_proposal_model(self, preference_mean, preference_bool):
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covariance_diag = np.ones((self.nr_dims,)) * self.initial_variance
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covariance_diag[preference_bool] = 0.05
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preference_cov = np.diag(covariance_diag)
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preference_mean = preference_mean.reshape(-1, 1)
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posterior_mean = np.linalg.inv(np.linalg.inv(self.proposal_cov) + np.linalg.inv(preference_cov)).dot(np.linalg.inv(self.proposal_cov).dot(self.proposal_mean) + np.linalg.inv(preference_cov).dot(preference_mean))
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posterior_cov = np.linalg.inv(np.linalg.inv(self.proposal_cov) + np.linalg.inv(preference_cov))
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print(posterior_mean, posterior_cov)
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self.proposal_mean = posterior_mean
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self.proposal_cov = posterior_cov
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def plot_2D(self, mean, cov):
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print(mean.shape, cov.shape)
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if mean.shape == (2, 1):
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mean = mean.squeeze()
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gaussian = multivariate_normal(mean, cov)
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x = np.random.uniform(self.lower_bound, self.upper_bound, (self.nr_likelihood_samples, self.nr_dims))
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pdf = gaussian.pdf(x)
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pdf = pdf / pdf.sum()
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plt.scatter(x[:, 0], x[:, 1], c=pdf, cmap='viridis')
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# Add a color bar
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plt.colorbar(label='PDF value')
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# Add labels
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plt.xlabel('x1')
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plt.ylabel('x2')
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# Show the plot
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plt.show()
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if __name__ == '__main__':
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# acquisition = PreferenceExpectedImprovement(10, 10, 10e4, -1.0, 1.0, 5.0)
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# sample_res = acquisition.rejection_sampling()
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# print(f"finished: {sample_res}")
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acquisition = PreferenceExpectedImprovement(10, 2, 10e4, -1.0, 1.0, 10.0)
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mean_ = np.array([0.5, 0.23])
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preference_ = [False, True]
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likelihood_cov = acquisition.likelihood(preference_)
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acquisition.plot_2D(acquisition.proposal_mean, acquisition.proposal_cov)
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acquisition.plot_2D(mean_, likelihood_cov)
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acquisition.update_proposal_model(mean_, preference_)
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acquisition.plot_2D(acquisition.proposal_mean, acquisition.proposal_cov)
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mean2 = np.array([0.33, 0.24])
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preference2 = [True, False]
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likelihood_cov2 = acquisition.likelihood(preference2)
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acquisition.plot_2D(mean2, likelihood_cov2)
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acquisition.update_proposal_model(mean2, preference2)
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acquisition.plot_2D(acquisition.proposal_mean, acquisition.proposal_cov)
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mean2 = np.array([-0.66, -0.5])
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preference2 = [False, False]
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likelihood_cov2 = acquisition.likelihood(preference2)
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acquisition.plot_2D(mean2, likelihood_cov2)
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acquisition.update_proposal_model(mean2, preference2)
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acquisition.update_proposal_model(mean2, preference2)
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acquisition.update_proposal_model(mean2, preference2)
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acquisition.update_proposal_model(mean2, preference2)
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acquisition.update_proposal_model(mean2, preference2)
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acquisition.plot_2D(acquisition.proposal_mean, acquisition.proposal_cov)
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