Joint Segmentation and Uncertainty Visualization of Retinal Layers in Optical Coherence Tomography Images using Bayesian Deep Learning

Optical coherence tomography (OCT) is commonly used to analyze retinal layers for assessment of ocular diseases. In this paper, we propose a method for retinal layer segmentation and quantification of uncertainty based on Bayesian deep learning. Our method not only performs end-to-end segmentation of retinal layers, but also gives the pixel wise uncertainty measure of the segmentation output. The generated uncertainty map can be used to identify erroneously segmented image regions which is useful in downstream analysis. We have validated our method on a dataset of 1487 images obtained from 15 subjects (OCT volumes) and compared it against the state-of-the-art segmentation algorithms that does not take uncertainty into account. The proposed uncertainty based segmentation method results in comparable or improved performance, and most importantly is more robust against noise

Biomass and nutrient cycling of a highly productive Corsican pine stand on former heathland in northern Belgium

Biomass and nutrient cycling were examined in a 62-year-old highly productive Corsican pine stand (Pinus nigra Arn. ssp. laricio Poiret) growing on a coarse and dry sandy soil with low exchangeable nutrient pools. Total aboveground biomass was estimated at 240 tons dry weight per hectare of which 201 tons concerned boles. The belowground biomass amounted to 46 t ha -1 (16 % of total standing biomass). The current annual volume increment was estimated at 20.6 m 3 ha-1 year-1. Root study emphasized the role of the rooting depth as an important growth factor. Calculated uptake rates for N, P, K, Ca and Mg were respectively 50.5, 1.9, 38.2, 15.6 and 3.3 kg ha-1 year-1. Despite an abundant nitrogen deposition (46 kg inorg. N ha-1 year-1) between 23 and 35 % of the nitrogen demand was supplied by internal transfers. Retranslocation of phosphorus fulfilled 64 % of the annual requirement. The root uptake of potassium, calcium and magnesium were better coupled with the tree requirements. The uptake rates of Ca and Mg could be met by atmospheric deposition. The canopy leaching of potassium accounted for 70 % of the root uptake. The low uptake rates of P, Ca and Mg were inconsistent with the vigorous growth of the stand, which could only be maintained by a high nutrient use efficiency. The monitoring of the nutrient status between 1988 and 1995 revealed an obvious decline in the concentrations of Ca, Mg, K and P due to growth dilution. (© Inra/Elsevier, Paris.)La biomasse et le cycle des éléments minéraux d'un peuplement de pin laricio de Corse de forte production sur un sol sableux. La biomasse et le cycle des éléments minéraux ont été étudiés dans un peuplement de pin laricio de Corse (Pinus nigra Am. ssp. laricio Poiret) de 62 ans, de forte productivité, sur un sol sableux et sec, aux réserves d'éléments disponibles limitées. La biomasse épigée s'élévait à 240 tonnes de matière sèche par hectare dont 201 tonnes étaient incluses dans les troncs. La biomasse des racines était de 46 tonnes ha-1 (16 % de la biomasse totale). L'accroissement courant annuel atteignait 20,6 m3 ha-1 an-1. L'étude des racines a mis en évidence la profondeur de l'enracinement comme facteur de croissance important. Les prélèvements réels de N, P, K, Ca et Mg s'élévaient à respectivement 50,5, 1,9, 38,2, 15,6 et 3,3 kg ha-1 an-1. Malgré un apport abondant d'azote (46 kg N inorganique ha-1), entre 23 % et 35 % de la demande azotée était soutenue par le transfert interne. Les transferts internes de phosphore contribuaient pour 64 % à la masse minérale nécessaire pour la formation des tissus nouveaux. Les prélèvements réels de potassium, calcium et magnésium correspondaient mieux à leurs prélèvements apparents. Les prélèvements de Ca et Mg pouvaient être suppléés par des apports atmosphériques. Il ressort que le pluviolessivage de potassium constituait 70 % de l'absorption racinaire. Les prélèvements réels de Ca, Mg et P étaient en opposition avec la forte productivité qui ne pouvait qu'être soutenue par un usage efficace des nutrients. L'évolution de la nutrition foliaire décelait une baisse nette en teneurs de Ca, Mg, K et P engendrée par la discordance entre leurs réserves limitées et la forte croissance du peuplement. (© Inra/Elsevier, Paris.

Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets

Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by extrapolating to the full dataset. We construct a Bayesian optimization procedure, dubbed Fabolas, which models loss and training time as a function of dataset size and automatically trades off high information gain about the global optimum against computational cost. Experiments optimizing support vector machines and deep neural networks show that Fabolas often finds high-quality solutions 10 to 100 times faster than other state-of-the-art Bayesian optimization methods or the recently proposed bandit strategy Hyperband

Practical Bayesian optimization in the presence of outliers

Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This allows outstanding sample efficiency because the probabilistic machinery provides a memory of the whole optimization process. However, that virtue becomes a disadvantage when the memory is populated with outliers, inducing bias in the estimation. In this paper, we present an empirical evaluation of Bayesian optimization methods in the presence of outliers. The empirical evidence shows that Bayesian optimization with robust regression often produces suboptimal results. We then propose a new algorithm which combines robust regression (a Gaussian process with Student-t likelihood) with outlier diagnostics to classify data points as outliers or inliers. By using an scheduler for the classification of outliers, our method is more efficient and has better convergence over the standard robust regression. Furthermore, we show that even in controlled situations with no expected outliers, our method is able to produce better results.Comment: 10 pages (2 of references), 6 figures, 1 algorith