Alexandre H. Thiéry

Alexandre H. Thiery, Fabian Braeu, Tin A. Tun et al.

Purpose: (1) To assess the performance of geometric deep learning (PointNet) in diagnosing glaucoma from a single optical coherence tomography (OCT) 3D scan of the optic nerve head (ONH); (2) To compare its performance to that obtained with a standard 3D convolutional neural network (CNN), and with a gold-standard glaucoma parameter, i.e. retinal nerve fiber layer (RNFL) thickness. Methods: 3D raster scans of the ONH were acquired with Spectralis OCT for 477 glaucoma and 2,296 non-glaucoma subjects at the Singapore National Eye Centre. All volumes were automatically segmented using deep learning to identify 7 major neural and connective tissues including the RNFL, the prelamina, and the lamina cribrosa (LC). Each ONH was then represented as a 3D point cloud with 1,000 points chosen randomly from all tissue boundaries. To simplify the problem, all ONH point clouds were aligned with respect to the plane and center of Bruch's membrane opening. Geometric deep learning (PointNet) was then used to provide a glaucoma diagnosis from a single OCT point cloud. The performance of our approach was compared to that obtained with a 3D CNN, and with RNFL thickness. Results: PointNet was able to provide a robust glaucoma diagnosis solely from the ONH represented as a 3D point cloud (AUC=95%). The performance of PointNet was superior to that obtained with a standard 3D CNN (AUC=87%) and with that obtained from RNFL thickness alone (AUC=80%). Discussion: We provide a proof-of-principle for the application of geometric deep learning in the field of glaucoma. Our technique requires significantly less information as input to perform better than a 3D CNN, and with an AUC superior to that obtained from RNFL thickness alone. Geometric deep learning may have wide applicability in the field of Ophthalmology.

Fabian A. Braeu, Alexandre H. Thiéry, Tin A. Tun et al.

Purpose: The optic nerve head (ONH) undergoes complex and deep 3D morphological changes during the development and progression of glaucoma. Optical coherence tomography (OCT) is the current gold standard to visualize and quantify these changes, however the resulting 3D deep-tissue information has not yet been fully exploited for the diagnosis and prognosis of glaucoma. To this end, we aimed: (1) To compare the performance of two relatively recent geometric deep learning techniques in diagnosing glaucoma from a single OCT scan of the ONH; and (2) To identify the 3D structural features of the ONH that are critical for the diagnosis of glaucoma. Methods: In this study, we included a total of 2,247 non-glaucoma and 2,259 glaucoma scans from 1,725 subjects. All subjects had their ONHs imaged in 3D with Spectralis OCT. All OCT scans were automatically segmented using deep learning to identify major neural and connective tissues. Each ONH was then represented as a 3D point cloud. We used PointNet and dynamic graph convolutional neural network (DGCNN) to diagnose glaucoma from such 3D ONH point clouds and to identify the critical 3D structural features of the ONH for glaucoma diagnosis. Results: Both the DGCNN (AUC: 0.97$\pm$0.01) and PointNet (AUC: 0.95$\pm$0.02) were able to accurately detect glaucoma from 3D ONH point clouds. The critical points formed an hourglass pattern with most of them located in the inferior and superior quadrant of the ONH. Discussion: The diagnostic accuracy of both geometric deep learning approaches was excellent. Moreover, we were able to identify the critical 3D structural features of the ONH for glaucoma diagnosis that tremendously improved the transparency and interpretability of our method. Consequently, our approach may have strong potential to be used in clinical applications for the diagnosis and prognosis of a wide range of ophthalmic disorders.

Fabian A. Braeu, Thanadet Chuangsuwanich, Tin A. Tun et al.

$\mathbf{Purpose}$: To use artificial intelligence (AI) to: (1) exploit biomechanical knowledge of the optic nerve head (ONH) from a relatively large population; (2) assess ONH robustness from a single optical coherence tomography (OCT) scan of the ONH; (3) identify what critical three-dimensional (3D) structural features make a given ONH robust. $\mathbf{Design}$: Retrospective cross-sectional study. $\mathbf{Methods}$: 316 subjects had their ONHs imaged with OCT before and after acute intraocular pressure (IOP) elevation through ophthalmo-dynamometry. IOP-induced lamina-cribrosa deformations were then mapped in 3D and used to classify ONHs. Those with LC deformations superior to 4% were considered fragile, while those with deformations inferior to 4% robust. Learning from these data, we compared three AI algorithms to predict ONH robustness strictly from a baseline (undeformed) OCT volume: (1) a random forest classifier; (2) an autoencoder; and (3) a dynamic graph CNN (DGCNN). The latter algorithm also allowed us to identify what critical 3D structural features make a given ONH robust. $\mathbf{Results}$: All 3 methods were able to predict ONH robustness from 3D structural information alone and without the need to perform biomechanical testing. The DGCNN (area under the receiver operating curve [AUC]: 0.76 $\pm$ 0.08) outperformed the autoencoder (AUC: 0.70 $\pm$ 0.07) and the random forest classifier (AUC: 0.69 $\pm$ 0.05). Interestingly, to assess ONH robustness, the DGCNN mainly used information from the scleral canal and the LC insertion sites. $\mathbf{Conclusions}$: We propose an AI-driven approach that can assess the robustness of a given ONH solely from a single OCT scan of the ONH, and without the need to perform biomechanical testing. Longitudinal studies should establish whether ONH robustness could help us identify fast visual field loss progressors.

Fabian A. Braeu, Thanadet Chuangsuwanich, Tin A. Tun et al.

$\bf{Purpose}$: To describe the 3D structural changes in both connective and neural tissues of the optic nerve head (ONH) that occur concurrently at different stages of glaucoma using traditional and AI-driven approaches. $\bf{Methods}$: We included 213 normal, 204 mild glaucoma (mean deviation [MD] $\ge$ -6.00 dB), 118 moderate glaucoma (MD of -6.01 to -12.00 dB), and 118 advanced glaucoma patients (MD < -12.00 dB). All subjects had their ONHs imaged in 3D with Spectralis optical coherence tomography. To describe the 3D structural phenotype of glaucoma as a function of severity, we used two different approaches: (1) We extracted human-defined 3D structural parameters of the ONH including retinal nerve fiber layer (RNFL) thickness, lamina cribrosa (LC) shape and depth at different stages of glaucoma; (2) we also employed a geometric deep learning method (i.e. PointNet) to identify the most important 3D structural features that differentiate ONHs from different glaucoma severity groups without any human input. $\bf{Results}$: We observed that the majority of ONH structural changes occurred in the early glaucoma stage, followed by a plateau effect in the later stages. Using PointNet, we also found that 3D ONH structural changes were present in both neural and connective tissues. In both approaches, we observed that structural changes were more prominent in the superior and inferior quadrant of the ONH, particularly in the RNFL, the prelamina, and the LC. As the severity of glaucoma increased, these changes became more diffuse (i.e. widespread), particularly in the LC. $\bf{Conclusions}$: In this study, we were able to uncover complex 3D structural changes of the ONH in both neural and connective tissues as a function of glaucoma severity. We hope to provide new insights into the complex pathophysiology of glaucoma that might help clinicians in their daily clinical care.

Se-In Jang, Michael J. A. Girard, Alexandre H. Thiery

In this paper, we propose an explainable and interpretable diabetic retinopathy (ExplainDR) classification model based on neural-symbolic learning. To gain explainability, a highlevel symbolic representation should be considered in decision making. Specifically, we introduce a human-readable symbolic representation, which follows a taxonomy style of diabetic retinopathy characteristics related to eye health conditions to achieve explainability. We then include humanreadable features obtained from the symbolic representation in the disease prediction. Experimental results on a diabetic retinopathy classification dataset show that our proposed ExplainDR method exhibits promising performance when compared to that from state-of-the-art methods applied to the IDRiD dataset, while also providing interpretability and explainability.

Charis Y. N. Chiang, Fabian Braeu, Thanadet Chuangsuwanich et al.

Purpose: (1) To develop a deep learning algorithm to automatically segment structures of the optic nerve head (ONH) and macula in 3D wide-field optical coherence tomography (OCT) scans; (2) To assess whether 3D macula or ONH structures (or the combination of both) provide the best diagnostic power for glaucoma. Methods: A cross-sectional comparative study was performed which included wide-field swept-source OCT scans from 319 glaucoma subjects and 298 non-glaucoma subjects. All scans were compensated to improve deep-tissue visibility. We developed a deep learning algorithm to automatically label all major ONH tissue structures by using 270 manually annotated B-scans for training. The performance of our algorithm was assessed using the Dice coefficient (DC). A glaucoma classification algorithm (3D CNN) was then designed using a combination of 500 OCT volumes and their corresponding automatically segmented masks. This algorithm was trained and tested on 3 datasets: OCT scans cropped to contain the macular tissues only, those to contain the ONH tissues only, and the full wide-field OCT scans. The classification performance for each dataset was reported using the AUC. Results: Our segmentation algorithm was able to segment ONH and macular tissues with a DC of 0.94 $\pm$ 0.003. The classification algorithm was best able to diagnose glaucoma using wide-field 3D-OCT volumes with an AUC of 0.99 $\pm$ 0.01, followed by ONH volumes with an AUC of 0.93 $\pm$ 0.06, and finally macular volumes with an AUC of 0.91 $\pm$ 0.11. Conclusions: this study showed that using wide-field OCT as compared to the typical OCT images containing just the ONH or macular may allow for a significantly improved glaucoma diagnosis. This may encourage the mainstream adoption of 3D wide-field OCT scans. For clinical AI studies that use traditional machines, we would recommend the use of ONH scans as opposed to macula scans.

Rahul Rahaman, Dipika Singhania, Alexandre Thiery et al.

In temporal action segmentation, Timestamp supervision requires only a handful of labelled frames per video sequence. For unlabelled frames, previous works rely on assigning hard labels, and performance rapidly collapses under subtle violations of the annotation assumptions. We propose a novel Expectation-Maximization (EM) based approach that leverages the label uncertainty of unlabelled frames and is robust enough to accommodate possible annotation errors. With accurate timestamp annotations, our proposed method produces SOTA results and even exceeds the fully-supervised setup in several metrics and datasets. When applied to timestamp annotations with missing action segments, our method presents stable performance. To further test our formulation's robustness, we introduce the new challenging annotation setup of Skip-tag supervision. This setup relaxes constraints and requires annotations of any fixed number of random frames in a video, making it more flexible than Timestamp supervision while remaining competitive.

Nicolas Chopin, Andras Fulop, Jeremy Heng et al.

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.

Alvin Heng, Alexandre H. Thiery, Harold Soh

Out-of-distribution (OOD) detection is a critical task in machine learning that seeks to identify abnormal samples. Traditionally, unsupervised methods utilize a deep generative model for OOD detection. However, such approaches require a new model to be trained for each inlier dataset. This paper explores whether a single model can perform OOD detection across diverse tasks. To that end, we introduce Diffusion Paths (DiffPath), which uses a single diffusion model originally trained to perform unconditional generation for OOD detection. We introduce a novel technique of measuring the rate-of-change and curvature of the diffusion paths connecting samples to the standard normal. Extensive experiments show that with a single model, DiffPath is competitive with prior work using individual models on a variety of OOD tasks involving different distributions. Our code is publicly available at https://github.com/clear-nus/diffpath.

Zhidi Lin, Ying Li, Feng Yin et al.

Gaussian process state-space models (GPSSMs) offer a principled framework for learning and inference in nonlinear dynamical systems with uncertainty quantification. However, existing GPSSMs are limited by the use of multiple independent stationary Gaussian processes (GPs), leading to prohibitive computational and parametric complexity in high-dimensional settings and restricted modeling capacity for non-stationary dynamics. To address these challenges, we propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems. Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics while significantly reducing model complexity. For the inference of the implicit process, we develop a variational inference algorithm that jointly approximates the posterior over the underlying GP and the neural network parameters defining the normalizing flows. To avoid explicit variational parameterization of the latent states, we further incorporate the ensemble Kalman filter (EnKF) into the variational framework, enabling accurate and efficient state estimation. Extensive empirical evaluations on synthetic and real-world datasets demonstrate the superior performance of our ETGPSSM in system dynamics learning, high-dimensional state estimation, and time-series forecasting, outperforming existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.

Thanadet Chuangsuwanich, Monisha E. Nongpiur, Fabian A. Braeu et al.

Objective. (1) To assess whether neural tissue structure and biomechanics could predict functional loss in glaucoma; (2) To evaluate the importance of biomechanics in making such predictions. Design, Setting and Participants. We recruited 238 glaucoma subjects. For one eye of each subject, we imaged the optic nerve head (ONH) using spectral-domain OCT under the following conditions: (1) primary gaze and (2) primary gaze with acute IOP elevation. Main Outcomes: We utilized automatic segmentation of optic nerve head (ONH) tissues and digital volume correlation (DVC) analysis to compute intraocular pressure (IOP)-induced neural tissue strains. A robust geometric deep learning approach, known as Point-Net, was employed to predict the full Humphrey 24-2 pattern standard deviation (PSD) maps from ONH structural and biomechanical information. For each point in each PSD map, we predicted whether it exhibited no defect or a PSD value of less than 5%. Predictive performance was evaluated using 5-fold cross-validation and the F1-score. We compared the model's performance with and without the inclusion of IOP-induced strains to assess the impact of biomechanics on prediction accuracy. Results: Integrating biomechanical (IOP-induced neural tissue strains) and structural (tissue morphology and neural tissues thickness) information yielded a significantly better predictive model (F1-score: 0.76+-0.02) across validation subjects, as opposed to relying only on structural information, which resulted in a significantly lower F1-score of 0.71+-0.02 (p < 0.05). Conclusion: Our study has shown that the integration of biomechanical data can significantly improve the accuracy of visual field loss predictions. This highlights the importance of the biomechanics-function relationship in glaucoma, and suggests that biomechanics may serve as a crucial indicator for the development and progression of glaucoma.

Zhidi Lin, Yiyong Sun, Feng Yin et al.

The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational inference approaches, particularly under the more realistic non-mean-field (NMF) assumption, including extensive training effort, compromised inference accuracy, and infeasibility for online applications, among others. In this paper, we tackle these challenges by incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the NMF variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO). Moreover, owing to the streamlined parameterization via the EnKF, the new GPSSM model can be easily accommodated in online learning applications. We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting. We also provide detailed analysis and fresh insights for the proposed algorithms. Comprehensive evaluation across diverse real and synthetic datasets corroborates the superior learning and inference performance of our EnKF-aided variational inference algorithms compared to existing methods.

Chao Wang, Alexandre Hoang Thiery

This article introduces GIT-Net, a deep neural network architecture for approximating Partial Differential Equation (PDE) operators, inspired by integral transform operators. GIT-NET harnesses the fact that differential operators commonly used for defining PDEs can often be represented parsimoniously when expressed in specialized functional bases (e.g., Fourier basis). Unlike rigid integral transforms, GIT-Net parametrizes adaptive generalized integral transforms with deep neural networks. When compared to several recently proposed alternatives, GIT-Net's computational and memory requirements scale gracefully with mesh discretizations, facilitating its application to PDE problems on complex geometries. Numerical experiments demonstrate that GIT-Net is a competitive neural network operator, exhibiting small test errors and low evaluations across a range of PDE problems. This stands in contrast to existing neural network operators, which typically excel in just one of these areas.

Michaël J. A. Girard, Satish K. Panda, Tin Aung Tun et al.

Purpose: (1) To develop a deep learning algorithm to identify major tissue structures of the optic nerve head (ONH) in 3D optical coherence tomography (OCT) scans; (2) to exploit such information to robustly differentiate among healthy, optic disc drusen (ODD), and papilledema ONHs. It was a cross-sectional comparative study with confirmed ODD (105 eyes), papilledema due to high intracranial pressure (51 eyes), and healthy controls (100 eyes). 3D scans of the ONHs were acquired using OCT, then processed to improve deep-tissue visibility. At first, a deep learning algorithm was developed using 984 B-scans (from 130 eyes) in order to identify: major neural/connective tissues, and ODD regions. The performance of our algorithm was assessed using the Dice coefficient (DC). In a 2nd step, a classification algorithm (random forest) was designed using 150 OCT volumes to perform 3-class classifications (1: ODD, 2: papilledema, 3: healthy) strictly from their drusen and prelamina swelling scores (derived from the segmentations). To assess performance, we reported the area under the receiver operating characteristic curves (AUCs) for each class. Our segmentation algorithm was able to isolate neural and connective tissues, and ODD regions whenever present. This was confirmed by an average DC of 0.93$\pm$0.03 on the test set, corresponding to good performance. Classification was achieved with high AUCs, i.e. 0.99$\pm$0.01 for the detection of ODD, 0.99 $\pm$ 0.01 for the detection of papilledema, and 0.98$\pm$0.02 for the detection of healthy ONHs. Our AI approach accurately discriminated ODD from papilledema, using a single OCT scan. Our classification performance was excellent, with the caveat that validation in a much larger population is warranted. Our approach may have the potential to establish OCT as the mainstay of diagnostic imaging in neuro-ophthalmology.

Satish K. Panda, Haris Cheong, Tin A. Tun et al.

Purpose: To assess whether the three-dimensional (3D) structural configuration of the central retinal vessel trunk and its branches (CRVT&B) could be used as a diagnostic marker for glaucoma. Method: We trained a deep learning network to automatically segment the CRVT&B from the B-scans of the optical coherence tomography (OCT) volume of the optic nerve head (ONH). Subsequently, two different approaches were used for glaucoma diagnosis using the structural configuration of the CRVT&B as extracted from the OCT volumes. In the first approach, we aimed to provide a diagnosis using only 3D CNN and the 3D structure of the CRVT&B. For the second approach, we projected the 3D structure of the CRVT&B orthographically onto three planes to obtain 2D images, and then a 2D CNN was used for diagnosis. The segmentation accuracy was evaluated using the Dice coefficient, whereas the diagnostic accuracy was assessed using the area under the receiver operating characteristic curves (AUC). The diagnostic performance of the CRVT&B was also compared with that of retinal nerve fiber layer (RNFL) thickness. Results: Our segmentation network was able to efficiently segment retinal blood vessels from OCT scans. On a test set, we achieved a Dice coefficient of 0.81\pm0.07. The 3D and 2D diagnostic networks were able to differentiate glaucoma from non-glaucoma subjects with accuracies of 82.7% and 83.3%, respectively. The corresponding AUCs for CRVT&B were 0.89 and 0.90, higher than those obtained with RNFL thickness alone. Conclusions: Our work demonstrated that the diagnostic power of the CRVT&B is superior to that of a gold-standard glaucoma parameter, i.e., RNFL thickness. Our work also suggested that the major retinal blood vessels form a skeleton -- the configuration of which may be representative of major ONH structural changes as typically observed with the development and progression of glaucoma.

Rahul Rahaman, Atin Ghosh, Alexandre H. Thiery

Locating semantically meaningful landmark points is a crucial component of a large number of computer vision pipelines. Because of the small number of available datasets with ground truth landmark annotations, it is important to design robust unsupervised and semi-supervised methods for landmark detection. Many of the recent unsupervised learning methods rely on the equivariance properties of landmarks to synthetic image deformations. Our work focuses on such widely used methods and sheds light on its core problem, its inability to produce equivariant intermediate convolutional features. This finding leads us to formulate a two-step unsupervised approach that overcomes this challenge by first learning powerful pixel-based features and then use the pre-trained features to learn a landmark detector by the traditional equivariance method. Our method produces state-of-the-art results in several challenging landmark detection datasets such as the BBC Pose dataset and the Cat-Head dataset. It performs comparably on a range of other benchmarks.

Atin Ghosh, Alexandre H. Thiery

Recently proposed consistency-based Semi-Supervised Learning (SSL) methods such as the $Π$-model, temporal ensembling, the mean teacher, or the virtual adversarial training, have advanced the state of the art in several SSL tasks. These methods can typically reach performances that are comparable to their fully supervised counterparts while using only a fraction of labelled examples. Despite these methodological advances, the understanding of these methods is still relatively limited. In this text, we analyse (variations of) the $Π$-model in settings where analytically tractable results can be obtained. We establish links with Manifold Tangent Classifiers and demonstrate that the quality of the perturbations is key to obtaining reasonable SSL performances. Importantly, we propose a simple extension of the Hidden Manifold Model that naturally incorporates data-augmentation schemes and offers a framework for understanding and experimenting with SSL methods.

Satish K. Panda, Haris Cheong, Tin A. Tun et al.

The optic nerve head (ONH) typically experiences complex neural- and connective-tissue structural changes with the development and progression of glaucoma, and monitoring these changes could be critical for improved diagnosis and prognosis in the glaucoma clinic. The gold-standard technique to assess structural changes of the ONH clinically is optical coherence tomography (OCT). However, OCT is limited to the measurement of a few hand-engineered parameters, such as the thickness of the retinal nerve fiber layer (RNFL), and has not yet been qualified as a stand-alone device for glaucoma diagnosis and prognosis applications. We argue this is because the vast amount of information available in a 3D OCT scan of the ONH has not been fully exploited. In this study we propose a deep learning approach that can: \textbf{(1)} fully exploit information from an OCT scan of the ONH; \textbf{(2)} describe the structural phenotype of the glaucomatous ONH; and that can \textbf{(3)} be used as a robust glaucoma diagnosis tool. Specifically, the structural features identified by our algorithm were found to be related to clinical observations of glaucoma. The diagnostic accuracy from these structural features was $92.0 \pm 2.3 \%$ with a sensitivity of $90.0 \pm 2.4 \% $ (at $95 \%$ specificity). By changing their magnitudes in steps, we were able to reveal how the morphology of the ONH changes as one transitions from a `non-glaucoma' to a `glaucoma' condition. We believe our work may have strong clinical implication for our understanding of glaucoma pathogenesis, and could be improved in the future to also predict future loss of vision.

Haris Cheong, Sripad Krishna Devalla, Thanadet Chuangsuwanich et al.

Speckle noise and retinal shadows within OCT B-scans occlude important edges, fine textures and deep tissues, preventing accurate and robust diagnosis by algorithms and clinicians. We developed a single process that successfully removed both noise and retinal shadows from unseen single-frame B-scans within 10.4ms. Mean average gradient magnitude (AGM) for the proposed algorithm was 57.2% higher than current state-of-the-art, while mean peak signal to noise ratio (PSNR), contrast to noise ratio (CNR), and structural similarity index metric (SSIM) increased by 11.1%, 154% and 187% respectively compared to single-frame B-scans. Mean intralayer contrast (ILC) improvement for the retinal nerve fiber layer (RNFL), photoreceptor layer (PR) and retinal pigment epithelium (RPE) layers decreased from 0.362 \pm 0.133 to 0.142 \pm 0.102, 0.449 \pm 0.116 to 0.0904 \pm 0.0769, 0.381 \pm 0.100 to 0.0590 \pm 0.0451 respectively. The proposed algorithm reduces the necessity for long image acquisition times, minimizes expensive hardware requirements and reduces motion artifacts in OCT images.

Rahul Rahaman, Alexandre H. Thiery

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. This text examines the interplay between three of the most simple and commonly used approaches to leverage deep learning when data is scarce: data-augmentation, ensembling, and post-processing calibration methods. Although standard ensembling techniques certainly help boost accuracy, we demonstrate that the calibration of deep ensembles relies on subtle trade-offs. We also find that calibration methods such as temperature scaling need to be slightly tweaked when used with deep-ensembles and, crucially, need to be executed after the averaging process. Our simulations indicate that this simple strategy can halve the Expected Calibration Error (ECE) on a range of benchmark classification problems compared to standard deep-ensembles in the low data regime.

Haris Cheong, Sripad Krishna Devalla, Tan Hung Pham et al.

Purpose: To remove retinal shadows from optical coherence tomography (OCT) images of the optic nerve head(ONH). Methods:2328 OCT images acquired through the center of the ONH using a Spectralis OCT machine for both eyes of 13 subjects were used to train a generative adversarial network (GAN) using a custom loss function. Image quality was assessed qualitatively (for artifacts) and quantitatively using the intralayer contrast: a measure of shadow visibility ranging from 0 (shadow-free) to 1 (strong shadow) and compared to compensated images. This was computed in the Retinal Nerve Fiber Layer (RNFL), the Inner Plexiform Layer (IPL), the Photoreceptor layer (PR) and the Retinal Pigment Epithelium (RPE) layers. Results: Output images had improved intralayer contrast in all ONH tissue layers. On average the intralayer contrast decreased by 33.7$\pm$6.81%, 28.8$\pm$10.4%, 35.9$\pm$13.0%, and43.0$\pm$19.5%for the RNFL, IPL, PR, and RPE layers respectively, indicating successful shadow removal across all depths. This compared to 70.3$\pm$22.7%, 33.9$\pm$11.5%, 47.0$\pm$11.2%, 26.7$\pm$19.0%for compensation. Output images were also free from artifacts commonly observed with compensation. Conclusions: DeshadowGAN significantly corrected blood vessel shadows in OCT images of the ONH. Our algorithm may be considered as a pre-processing step to improve the performance of a wide range of algorithms including those currently being used for OCT image segmentation, denoising, and classification. Translational Relevance: DeshadowGAN could be integrated to existing OCT devices to improve the diagnosis and prognosis of ocular pathologies.

Tan Hung Pham, Sripad Krishna Devalla, Aloysius Ang et al.

Accurate isolation and quantification of intraocular dimensions in the anterior segment (AS) of the eye using optical coherence tomography (OCT) images is important in the diagnosis and treatment of many eye diseases, especially angle closure glaucoma. In this study, we developed a deep convolutional neural network (DCNN) for the localization of the scleral spur, and the segmentation of anterior segment structures (iris, corneo-sclera shell, anterior chamber). With limited training data, the DCNN was able to detect the scleral spur on unseen ASOCT images as accurately as an experienced ophthalmologist; and simultaneously isolated the anterior segment structures with a Dice coefficient of 95.7%. We then automatically extracted eight clinically relevant ASOCT parameters and proposed an automated quality check process that asserts the reliability of these parameters. When combined with an OCT machine capable of imaging multiple radial sections, the algorithms can provide a more complete objective assessment. This is an essential step toward providing a robust automated framework for reliable quantification of ASOCT scans, for applications in the diagnosis and management of angle closure glaucoma.

Axel Finke, Alexandre H. Thiery

The importance weighted autoencoder (IWAE) (Burda et al., 2016) is a popular variational-inference method which achieves a tighter evidence bound (and hence a lower bias) than standard variational autoencoders by optimising a multi-sample objective, i.e. an objective that is expressible as an integral over $K > 1$ Monte Carlo samples. Unfortunately, IWAE crucially relies on the availability of reparametrisations and even if these exist, the multi-sample objective leads to inference-network gradients which break down as $K$ is increased (Rainforth et al., 2018). This breakdown can only be circumvented by removing high-variance score-function terms, either by heuristically ignoring them (which yields the 'sticking-the-landing' IWAE (IWAE-STL) gradient from Roeder et al. (2017)) or through an identity from Tucker et al. (2019) (which yields the 'doubly-reparametrised' IWAE (IWAE-DREG) gradient). In this work, we argue that directly optimising the proposal distribution in importance sampling as in the reweighted wake-sleep (RWS) algorithm from Bornschein & Bengio (2015) is preferable to optimising IWAE-type multi-sample objectives. To formalise this argument, we introduce an adaptive-importance sampling framework termed adaptive importance sampling for learning (AISLE) which slightly generalises the RWS algorithm. We then show that AISLE admits IWAE-STL and IWAE-DREG (i.e. the IWAE-gradients which avoid breakdown) as special cases.

Sripad Krishna Devalla, Giridhar Subramanian, Tan Hung Pham et al.

Purpose: To develop a deep learning approach to de-noise optical coherence tomography (OCT) B-scans of the optic nerve head (ONH). Methods: Volume scans consisting of 97 horizontal B-scans were acquired through the center of the ONH using a commercial OCT device (Spectralis) for both eyes of 20 subjects. For each eye, single-frame (without signal averaging), and multi-frame (75x signal averaging) volume scans were obtained. A custom deep learning network was then designed and trained with 2,328 "clean B-scans" (multi-frame B-scans), and their corresponding "noisy B-scans" (clean B-scans + gaussian noise) to de-noise the single-frame B-scans. The performance of the de-noising algorithm was assessed qualitatively, and quantitatively on 1,552 B-scans using the signal to noise ratio (SNR), contrast to noise ratio (CNR), and mean structural similarity index metrics (MSSIM). Results: The proposed algorithm successfully denoised unseen single-frame OCT B-scans. The denoised B-scans were qualitatively similar to their corresponding multi-frame B-scans, with enhanced visibility of the ONH tissues. The mean SNR increased from $4.02 \pm 0.68$ dB (single-frame) to $8.14 \pm 1.03$ dB (denoised). For all the ONH tissues, the mean CNR increased from $3.50 \pm 0.56$ (single-frame) to $7.63 \pm 1.81$ (denoised). The MSSIM increased from $0.13 \pm 0.02$ (single frame) to $0.65 \pm 0.03$ (denoised) when compared with the corresponding multi-frame B-scans. Conclusions: Our deep learning algorithm can denoise a single-frame OCT B-scan of the ONH in under 20 ms, thus offering a framework to obtain superior quality OCT B-scans with reduced scanning times and minimal patient discomfort.

Sripad Krishna Devalla, Prajwal K. Renukanand, Bharathwaj K. Sreedhar et al.

Given that the neural and connective tissues of the optic nerve head (ONH) exhibit complex morphological changes with the development and progression of glaucoma, their simultaneous isolation from optical coherence tomography (OCT) images may be of great interest for the clinical diagnosis and management of this pathology. A deep learning algorithm was designed and trained to digitally stain (i.e. highlight) 6 ONH tissue layers by capturing both the local (tissue texture) and contextual information (spatial arrangement of tissues). The overall dice coefficient (mean of all tissues) was $0.91 \pm 0.05$ when assessed against manual segmentations performed by an expert observer. We offer here a robust segmentation framework that could be extended for the automated parametric study of the ONH tissues.

Sripad Krishna Devalla, Jean-Martial Mari, Tin A. Tun et al.

Purpose: To develop a deep learning approach to digitally-stain optical coherence tomography (OCT) images of the optic nerve head (ONH). Methods: A horizontal B-scan was acquired through the center of the ONH using OCT (Spectralis) for 1 eye of each of 100 subjects (40 normal & 60 glaucoma). All images were enhanced using adaptive compensation. A custom deep learning network was then designed and trained with the compensated images to digitally stain (i.e. highlight) 6 tissue layers of the ONH. The accuracy of our algorithm was assessed (against manual segmentations) using the Dice coefficient, sensitivity, and specificity. We further studied how compensation and the number of training images affected the performance of our algorithm. Results: For images it had not yet assessed, our algorithm was able to digitally stain the retinal nerve fiber layer + prelamina, the retinal pigment epithelium, all other retinal layers, the choroid, and the peripapillary sclera and lamina cribrosa. For all tissues, the mean dice coefficient was $0.84 \pm 0.03$, the mean sensitivity $0.92 \pm 0.03$, and the mean specificity $0.99 \pm 0.00$. Our algorithm performed significantly better when compensated images were used for training. Increasing the number of images (from 10 to 40) to train our algorithm did not significantly improve performance, except for the RPE. Conclusion. Our deep learning algorithm can simultaneously stain neural and connective tissues in ONH images. Our approach offers a framework to automatically measure multiple key structural parameters of the ONH that may be critical to improve glaucoma management.

Yee Whye Teh, Alexandre Thiéry, Sebastian Vollmer

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the whole data set. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem by generating proposals which are only based on a subset of the data, by skipping the accept-reject step and by using decreasing step-sizes sequence $(δ_m)_{m \geq 0}$. %Under appropriate Lyapunov conditions, We provide in this article a rigorous mathematical framework for analysing this algorithm. We prove that, under verifiable assumptions, the algorithm is consistent, satisfies a central limit theorem (CLT) and its asymptotic bias-variance decomposition can be characterized by an explicit functional of the step-sizes sequence $(δ_m)_{m \geq 0}$. We leverage this analysis to give practical recommendations for the notoriously difficult tuning of this algorithm: it is asymptotically optimal to use a step-size sequence of the type $δ_m \asymp m^{-1/3}$, leading to an algorithm whose mean squared error (MSE) decreases at rate $\mathcal{O}(m^{-1/3})$