In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: We introduce a new spatial data structure for high dimensional data called the approximate principal direction tree (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy similar to that of computationally-expensive PCA trees with similar time-complexity to that of loweraccuracy RP trees. APD trees use a small number of powermethod iterations to find splitting planes for recursively partitioning the data. As such they provide a natural trade-off between the running-time and accuracy achieved by RP and PCA trees. Our theoretical results establish a) strong performance guarantees regardless of the convergence rate of the powermethod and b) that O(log d) iterations suffice to establish the guarantee of PCA trees when the intrinsic dimension is d. We demonstrate this trade-off and the efficacy of our data structure on both the CPU and GPU.

Output: Approximate Principal Direction Trees


Input: Consider Input: Tissue segmentation is an important pre-requisite for efficient and accurate diagnostics in digital pathology. However, it is well known that whole-slide scanners can fail in detecting all tissue regions, for example due to the tissue type, or due to weak staining because their tissue detection algorithms are not robust enough. In this paper, we introduce two different convolutional neural network architectures for whole slide image segmentation to accurately identify the tissue sections. We also compare the algorithms to a published traditional method. We collected 54 whole slide images with differing stains and tissue types from three laboratories to validate our algorithms. We show that while the two methods do not differ significantly they outperform their traditional counterpart (Jaccard index of 0.937 and 0.929 vs. 0.870, p < 0.01).

Output: COMPARISON OF DIFFERENT METHODS FOR TISSUE SEGMENTATION IN HISTOPATHOLOGICAL WHOLE-SLIDE IMAGES


Input: Consider Input: Stochastic neurons can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic neurons, i.e., can we “back-propagate” through these stochastic neurons? We examine this question, existing approaches, and present two novel families of solutions, applicable in different settings. In particular, it is demonstrated that a simple biologically plausible formula gives rise to an an unbiased (but noisy) estimator of the gradient with respect to a binary stochastic neuron firing probability. Unlike other estimators which view the noise as a small perturbation in order to estimate gradients by finite differences, this estimator is unbiased even without assuming that the stochastic perturbation is small. This estimator is also interesting because it can be applied in very general settings which do not allow gradient back-propagation, including the estimation of the gradient with respect to future rewards, as required in reinforcement learning setups. We also propose an approach to approximating this unbiased but high-variance estimator by learning to predict it using a biased estimator. The second approach we propose assumes that an estimator of the gradient can be back-propagated and it provides an unbiased estimator of the gradient, but can only work with non-linearities unlike the hard threshold, but like the rectifier, that are not flat for all of their range. This is similar to traditional sigmoidal units but has the advantage that for many inputs, a hard decision (e.g., a 0 output) can be produced, which would be convenient for conditional computation and achieving sparse representations and sparse gradients.


Output: Estimating or Propagating Gradients Through Stochastic Neurons