README.md

Deep Autoencoding Gaussian Mixture Model for Unsupervised Anomaly Detection in PyTorch

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.

Dataset

KDDCup99 http://kdd.ics.uci.edu/databases/kddcup99/

Some Test Results

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

Visualizing the z-space:

Some Implementation Details

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, cov

I 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