Blaine Rister

Vignav Ramesh, Blaine Rister, Daniel L. Rubin

Chest X-rays of coronavirus disease 2019 (COVID-19) patients are frequently obtained to determine the extent of lung disease and are a valuable source of data for creating artificial intelligence models. Most work to date assessing disease severity on chest imaging has focused on segmenting computed tomography (CT) images; however, given that CTs are performed much less frequently than chest X-rays for COVID-19 patients, automated lung lesion segmentation on chest X-rays could be clinically valuable. There currently exists a universal shortage of chest X-rays with ground truth COVID-19 lung lesion annotations, and manually contouring lung opacities is a tedious, labor-intensive task. To accelerate severity detection and augment the amount of publicly available chest X-ray training data for supervised deep learning (DL) models, we leverage existing annotated CT images to generate frontal projection "chest X-ray" images for training COVID-19 chest X-ray models. In this paper, we propose an automated pipeline for segmentation of COVID-19 lung lesions on chest X-rays comprised of a Mask R-CNN trained on a mixed dataset of open-source chest X-rays and coronal X-ray projections computed from annotated volumetric CTs. On a test set containing 40 chest X-rays of COVID-19 positive patients, our model achieved IoU scores of 0.81 $\pm$ 0.03 and 0.79 $\pm$ 0.03 when trained on a dataset of 60 chest X-rays and on a mixed dataset of 10 chest X-rays and 50 projections from CTs, respectively. Our model far outperforms current baselines with limited supervised training and may assist in automated COVID-19 severity quantification on chest X-rays.

Blaine Rister, Daniel L. Rubin

Neuron death is a complex phenomenon with implications for model trainability: the deeper the network, the lower the probability of finding a valid initialization. In this work, we derive both upper and lower bounds on the probability that a ReLU network is initialized to a trainable point, as a function of model hyperparameters. We show that it is possible to increase the depth of a network indefinitely, so long as the width increases as well. Furthermore, our bounds are asymptotically tight under reasonable assumptions: first, the upper bound coincides with the true probability for a single-layer network with the largest possible input set. Second, the true probability converges to our lower bound as the input set shrinks to a single point, or as the network complexity grows under an assumption about the output variance. We confirm these results by numerical simulation, showing rapid convergence to the lower bound with increasing network depth. Then, motivated by the theory, we propose a practical sign flipping scheme which guarantees that the ratio of living data points in a $k$-layer network is at least $2^{-k}$. Finally, we show how these issues are mitigated by network design features currently seen in practice, such as batch normalization, residual connections, dense networks and skip connections. This suggests that neuron death may provide insight into the efficacy of various model architectures.

Blaine Rister, Darvin Yi, Kaushik Shivakumar et al.

Fully-convolutional neural networks have achieved superior performance in a variety of image segmentation tasks. However, their training requires laborious manual annotation of large datasets, as well as acceleration by parallel processors with high-bandwidth memory, such as GPUs. We show that simple models can achieve competitive accuracy for organ segmentation on CT images when trained with extensive data augmentation, which leverages existing graphics hardware to quickly apply geometric and photometric transformations to 3D image data. On 3 mm^3 CT volumes, our GPU implementation is 2.6-8X faster than a widely-used CPU version, including communication overhead. We also show how to automatically generate training labels using rudimentary morphological operations, which are efficiently computed by 3D Fourier transforms. We combined fully-automatic labels for the lungs and bone with semi-automatic ones for the liver, kidneys and bladder, to create a dataset of 130 labeled CT scans. To achieve the best results from data augmentation, our model uses the intersection-over-union (IOU) loss function, a close relative of the Dice loss. We discuss its mathematical properties and explain why it outperforms the usual weighted cross-entropy loss for unbalanced segmentation tasks. We conclude that there is no unique IOU loss function, as the naive one belongs to a broad family of functions with the same essential properties. When combining data augmentation with the IOU loss, our model achieves a Dice score of 78-92% for each organ. The trained model, code and dataset will be made publicly available, to further medical imaging research.

Blaine Rister, Daniel L Rubin

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. Firstly, that the network is piecewise convex as a function of the input data. Secondly, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Finally, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space.