List of Figures 1.1 Discriminative modelling. Given data inX, predict labels inY. . 2 1.2 Data inXare observations governed by underlying world descriptors inW. ............................... 3 1.3 Directly predicting labels inY fromdata Xessentially sidesteps the world descriptors W, yet fromWit’s typically trivial to predict Y. ................................... 4 1.4 Latent variable modelling: the lower-dimensional latent space Z describes high-dimensional data inX. ............... 4 3.1 ELBO density distribution, ROC curves, and Precision-Recall curves for anomaly “edge erosion” on 3D-printed products, with a 64dimensionallatentspace. ...................... 33 3.2 Thefull3D-printedproduct. . . . . . . . . . . . . . . . . . . . . . 35 3.3 Examplesforeachdefectclass. . . . . . . . . . . . . . . . . . . . 36 3.4 Examples of samples in the dataset with their axial, coronal, and sagital perspective, for (a) 3 different healthy nodules and (b) 3 different nodules identified as anomalous (positive for cancer). . 37 3.5 Displaying 25 slices of 28×28 pixels, as a representation of the cube of 28×28×28 voxels used for training our models. . . . . . 38 3.6 VAE architecture for 3D-printed products. . . . . . . . . . . . . . 39 3.7 Trained 3D WGAN-GP architecture for the generator. . . . . . . . 40 3.8 3D VAE encoder architecture for NLST 3D nodules. . . . . . . . . 40
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