My attempt at reproducing the paper Deep Autoencoding Gaussian Mixture Model for Unsupervised Anomaly Detection. Please Let me know if there are any bugs in my code. Thank you! =)
I implemented this on Python 3.6 using PyTorch 0.4.0.
KDDCup99 http://kdd.ics.uci.edu/databases/kddcup99/
Paper's Reported Results (averaged over 20 runs) : Precision : 0.9297, Recall : 0.9442, F-score : 0.9369
My Implementation (only one run) : Precision : 0.9677, Recall : 0.9538, F-score : 0.9607
Below are code snippets of the two main components of the model. More specifically, computing the gmm parameters and sample energy.
def compute_gmm_params(self, z, gamma):
N = gamma.size(0)
# K
sum_gamma = torch.sum(gamma, dim=0)
# K
phi = (sum_gamma / N)
self.phi = phi.data
# K x D
mu = torch.sum(gamma.unsqueeze(-1) * z.unsqueeze(1), dim=0) / sum_gamma.unsqueeze(-1)
self.mu = mu.data
# z = N x D
# mu = K x D
# gamma N x K
# z_mu = N x K x D
z_mu = (z.unsqueeze(1)- mu.unsqueeze(0))
# z_mu_outer = N x K x D x D
z_mu_outer = z_mu.unsqueeze(-1) * z_mu.unsqueeze(-2)
# K x D x D
cov = torch.sum(gamma.unsqueeze(-1).unsqueeze(-1) * z_mu_outer, dim = 0) / sum_gamma.unsqueeze(-1).unsqueeze(-1)
self.cov = cov.data
return phi, mu, covI added some epsilon on the diagonals of the covariance matrix, otherwise I get nan values during training.
I tried using torch.potrf(cov_k).diag().prod()**2 to compute for the determinants, but for some reason I get errors after several epochs, so I used numpy's linalg to compute for the determinants instead.
def compute_energy(self, z, phi=None, mu=None, cov=None, size_average=True):
# Compute the energy based on the specified gmm params.
# If none are specified use the cached values.
if phi is None:
phi = to_var(self.phi)
if mu is None:
mu = to_var(self.mu)
if cov is None:
cov = to_var(self.cov)
k, D, _ = cov.size()
z_mu = (z.unsqueeze(1)- mu.unsqueeze(0))
cov_inverse = []
det_cov = []
cov_diag = 0
eps = 1e-12
for i in range(k):
# K x D x D
cov_k = cov[i] + to_var(torch.eye(D)*eps)
cov_inverse.append(torch.inverse(cov_k).unsqueeze(0))
det_cov.append(np.linalg.det(cov_k.data.cpu().numpy()* (2*np.pi)))
cov_diag = cov_diag + torch.sum(1 / cov_k.diag())
# K x D x D
cov_inverse = torch.cat(cov_inverse, dim=0)
# K
det_cov = to_var(torch.from_numpy(np.float32(np.array(det_cov))))
# N x K
exp_term_tmp = -0.5 * torch.sum(torch.sum(z_mu.unsqueeze(-1) * cov_inverse.unsqueeze(0), dim=-2) * z_mu, dim=-1)
# for stability (logsumexp)
max_val = torch.max((exp_term_tmp).clamp(min=0), dim=1, keepdim=True)[0]
exp_term = torch.exp(exp_term_tmp - max_val)
sample_energy = -max_val.squeeze() - torch.log(torch.sum(phi.unsqueeze(0) * exp_term / (torch.sqrt(det_cov)).unsqueeze(0), dim = 1) + eps)
if size_average:
sample_energy = torch.mean(sample_energy)
return sample_energy, cov_diag