Soft Multivariate Truncated Normal Distribution (soft tMVN)
We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to sample from the soft tMVN distribution in high dimensions. We provide theoretical support to the approximation capability of the soft tMVN and provide further empirical evidence thereof. The soft tMVN distribution can be used to approximate simulations from a multivariate truncated normal distribution with linear constraints, or itself as a prior in shape-constrained problems. …

Kalman Gradient Descent
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical analysis of convergence in a non-convex setting and experimental results which demonstrate improved performance on a variety of machine learning areas including neural networks and black box variational inference. We also present a distributed version of our algorithm that enables large-dimensional optimization, and we extend our algorithm to SGD with momentum and RMSProp. …

NeurAll
Convolutional Neural Networks (CNNs) are successfully used for the important automotive visual perception tasks including object recognition, motion and depth estimation, visual SLAM, etc. However, these tasks are independently explored and modeled. In this paper, we propose a joint multi-task network design called NeurAll for learning all tasks simultaneously. Our main motivation is the computational efficiency achieved by sharing the expensive initial convolutional layers between all tasks. Indeed, the main bottleneck in automated driving systems is the limited processing power available on deployment hardware. There could be other benefits in improving accuracy for some tasks and it eases development effort. It also offers scalability to add more tasks leveraging existing features and achieving better generalization. We survey various CNN based solutions for visual perception tasks in automated driving. Then we propose a unified CNN model for the important tasks and discuss several advanced optimization and architecture design techniques to improve the baseline model. The paper is partly review and partly positional with demonstration of several preliminary results promising for future research. Firstly, we show that an efficient two-task model performing semantic segmentation and object detection achieves similar accuracies compared to separate models on various datasets with minimized runtime. We then illustrate that using depth regression as auxiliary task improves semantic segmentation and using multi-stream semantic segmentation outperforms one-stream semantic segmentation. The two-task network achieves 30 fps on an automotive grade low power SOC for 1280×384 image resolution …

Stochastic Gradient Coding (SGC)
We consider distributed gradient descent in the presence of stragglers. Recent work on \em gradient coding \em and \em approximate gradient coding \em have shown how to add redundancy in distributed gradient descent to guarantee convergence even if some workers are \em stragglers\em—that is, slow or non-responsive. In this work we propose an approximate gradient coding scheme called \em Stochastic Gradient Coding \em (SGC), which works when the stragglers are random. SGC distributes data points redundantly to workers according to a pair-wise balanced design, and then simply ignores the stragglers. We prove that the convergence rate of SGC mirrors that of batched Stochastic Gradient Descent (SGD) for the $\ell_2$ loss function, and show how the convergence rate can improve with the redundancy. We also provide bounds for more general convex loss functions. We show empirically that SGC requires a small amount of redundancy to handle a large number of stragglers and that it can outperform existing approximate gradient codes when the number of stragglers is large. …