This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies---the pathwise, score function, and measure-valued gradient estimators---exploring their historical development, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.

Tensor Train decomposition is used across many branches of machine learning. We present T3F—a library for Tensor Train decomposition based on TensorFlow. T3F supports GPU execution, batch processing, automatic differentiation, and versatile functionality for the Riemannian optimization framework, which takes into account the underlying manifold structure to construct efficient optimization methods. The library makes it easier to implement machine learning papers that rely on the Tensor Train decomposition. T3F includes documentation, examples and 94% test coverage.

By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an alternative approach to computing reparameterization gradients based on implicit differentiation and demonstrate its broader applicability by applying it to Gamma, Beta, Dirichlet, and von Mises distributions, which cannot be used with the classic reparameterization trick. Our experiments show that the proposed approach is faster and more accurate than the existing gradient estimators for these distributions.

This paper proposes a deep learning architecture based on Residual Network that dynamically adjusts the number of executed layers for the regions of the image. This architecture is end-to-end trainable, deterministic and problem-agnostic. It is therefore applicable without any modifications to a wide range of computer vision problems such as image classification, object detection and image segmentation. We present experimental results showing that this model improves the computational efficiency of Residual Networks on the challenging ImageNet classification and COCO object detection datasets. Additionally, we evaluate the computation time maps on the visual saliency dataset cat2000 and find that they correlate surprisingly well with human eye fixation positions.

We propose a novel approach to reduce the computational cost of evaluation of convolutional neural networks, a factor that has hindered their deployment in low-power devices such as mobile phones. Inspired by the loop perforation technique from source code optimization, we speed up the bottleneck convolutional layers by skipping their evaluation in some of the spatial positions. We propose and analyze several strategies of choosing these positions. We demonstrate that perforation can accelerate modern convolutional networks such as AlexNet and VGG-16 by a factor of 2x - 4x. Additionally, we show that perforation is complementary to the recently proposed acceleration method of Zhang et al.