xii CONTENTS 3 Anomaly Detection with Variational Autoencoders 25 3.1 Introduction.............................. 26 3.2 RelatedWork ............................. 27 3.3 Anomaly Detection with Generative Models . . . . . . . . . . . . 28 3.3.1 Likelihood Estimation with VAEs . . . . . . . . . . . . . . 29 3.3.2 Likelihood Estimation with GANs . . . . . . . . . . . . . . 30 3.3.3 Thresholds for Likelihood Scores . . . . . . . . . . . . . . 32 3.3.4 Localising Anomalies with Reconstructions . . . . . . . . . 33 3.4 ExperimentalSetup.......................... 34 3.4.1 Datasets............................ 34 3.4.2 Architectures and Hyperparameters . . . . . . . . . . . . . 37 3.5 Results................................. 41 3.5.1 MNIST............................. 41 3.5.2 3D-PrintedProducts ..................... 43 3.5.3 NLST3Dnodules....................... 45 3.6 Conclusion .............................. 48 4 Quantifying and Learning Linear Symmetry-Based Disentanglement (LSBD) 51 4.1 Introduction.............................. 52 4.2 LSBDDefinition............................ 53 4.3 RelatedWork ............................. 57 4.4 DLSBD:QuantifyingLSBD...................... 61 4.4.1 Intuition: Measuring Equivariance with Dispersion . . . . 61 4.4.2 DLSBD:AMetricforLSBD.................. 62 4.4.3 Practical Computation of DLSBD .............. 66 4.5 LSBD-VAE: Learning LSBD Representations . . . . . . . . . . . . . 68 4.5.1 Assumptions ......................... 68 4.5.2 Unsupervised Learning on a Latent Manifold with∆VAE . 69 4.5.3 Semi-Supervised Learning with Transformation Labels . . 70 4.6 ExperimentalSetup.......................... 72 4.6.1 Datasets............................ 72 4.6.2 LSBD-VAE with Semi-supervised Labelled Pairs . . . . . . 74 4.6.3 LSBD-VAE with Paths of Consecutive Observations . . . . 75 4.6.4 Other Disentanglement Methods . . . . . . . . . . . . . . 75 4.6.5 Disentanglement Metrics . . . . . . . . . . . . . . . . . . . 77 4.6.6 Further Experimental Details . . . . . . . . . . . . . . . . 77 4.7 Results: Evaluating LSBD withDLSBD ............... 80
RkJQdWJsaXNoZXIy MjY0ODMw