No-U-Turn (NUTS)
Algorithm by Hoffman and Gelman (2014): Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order gradient information. These features allow it to converge to high-dimensional target distributions much more quickly than simpler methods such as random walk Metropolis or Gibbs sampling. However, HMC’s performance is highly sensitive to two user-specified parameters: a step size ϵϵ and a desired number of steps LL. In particular, if LL is too small then the algorithm exhibits undesirable random walk behavior, while if LL is too large the algorithm wastes computation. We introduce the No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps LL. NUTS uses a recursive algorithm to build a set of likely candidate points that spans a wide swath of the target distribution, stopping automatically when it starts to double back and retrace its steps. Empirically, NUTS performs at least as efficiently as (and sometimes more efficiently than) a well tuned standard HMC method, without requiring user intervention or costly tuning runs. We also derive a method for adapting the step size parameter ϵϵ on the fly based on primal-dual averaging. NUTS can thus be used with no hand-tuning at all, making it suitable for applications such as BUGS-style automatic inference engines that require efficient ‘turnkey’ samplers. …

Monte Carlo Fusion
This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem arises in many settings (for instance, expert elicitation, multi-view learning, distributed ‘big data’ problems etc.), but to-date the framework and methodology proposed in this paper (Monte Carlo Fusion) is the first general approach which avoids any form of approximation error in obtaining the unified inference. In this paper we focus on the key theoretical underpinnings of this new methodology, and simple (direct) Monte Carlo interpretations of the theory. There is considerable scope to tailor the theory introduced in this paper to particular application settings (such as the big data setting), construct efficient parallelised schemes, understand the approximation and computational efficiencies of other such unification paradigms, and explore new theoretical and methodological directions. …

Functional Average Variance Estimation (FAVE)
We propose an estimation method that we call functional average variance estimation (FAVE), for estimating the EDR space in functional semiparametric regression model, based on kernel estimates of density and regression. Consistency results are then established for the estimator of the interest operator, and for the directions of EDR space. A simulation study that shows that the proposed approach performs as well as traditional ones is presented. …

ESPNetv2
We introduce a light-weight, power efficient, and general purpose convolutional neural network, ESPNetv2, for modeling visual and sequential data. Our network uses group point-wise and depth-wise dilated separable convolutions to learn representations from a large effective receptive field with fewer FLOPs and parameters. The performance of our network is evaluated on three different tasks: (1) object classification, (2) semantic segmentation, and (3) language modeling. Experiments on these tasks, including image classification on the ImageNet and language modeling on the PenTree bank dataset, demonstrate the superior performance of our method over the state-of-the-art methods. Our network has better generalization properties than ShuffleNetv2 when tested on the MSCOCO multi-object classification task and the Cityscapes urban scene semantic segmentation task. Our experiments show that ESPNetv2 is much more power efficient than existing state-of-the-art efficient methods including ShuffleNets and MobileNets. Our code is open-source and available at \url{https://…/ESPNetv2} …