Kernel methods provide a principled approach for detecting nonlinear relations using well understood linear algorithms. In exploratory data analyses when the underlying structure of the data's probability space is unclear, the choice of kernel is often arbitrary. Here, we present a novel kernel, Semblance, on a probability feature space. The advantage of Semblance lies in its distribution free formulation and its ability to detect niche features by placing greater emphasis on similarity between observation pairs that fall at the tail ends of a distribution, as opposed to those that fall towards the mean. We prove that Semblance is a valid Mercer kernel and illustrate its applicability through simulations and real world examples.

We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a hierarchical manner using a simple reparameterizable distribution whose variational parameters are defined by arbitrarily flexible deep neural networks. Unlike previous works, UIVI directly optimizes the evidence lower bound (ELBO) rather than an approximation to the ELBO. We demonstrate UIVI on several models, including Bayesian multinomial logistic regression and variational autoencoders, and show that UIVI achieves both tighter ELBO and better predictive performance than existing approaches at a similar computational cost.

In this paper we study a family of variance reduction methods with randomized batch size---at each step, the algorithm first randomly chooses the batch size and then selects a batch of samples to conduct a variance-reduced stochastic update. We give the linear convergence rate for this framework for composite functions, and show that the optimal strategy to achieve the optimal convergence rate per data access is to always choose batch size of 1, which is equivalent to the SAGA algorithm. However, due to the presence of cache/disk IO effect in computer architecture, the number of data access cannot reflect the running time because of 1) random memory access is much slower than sequential access, 2) when data is too big to fit into memory, disk seeking takes even longer time. After taking these into account, choosing batch size of $1$ is no longer optimal, so we propose a new algorithm called SAGA++ and show how to calculate the optimal average batch size theoretically. Our algorithm outperforms SAGA and other existing batched and stochastic solvers on real datasets. In addition, we also conduct a precise analysis to compare different update rules for variance reduction methods, showing that SAGA++ converges faster than SVRG in theory.

As convolutional neural networks (CNNs) enable state-of-the-art computer vision applications, their high energy consumption has emerged as a key impediment to their deployment on embedded and mobile devices. Towards efficient image classification under hardware constraints, prior work has proposed adaptive CNNs, i.e., systems of networks with different accuracy and computation characteristics, where a selection scheme adaptively selects the network to be evaluated for each input image. While previous efforts have investigated different network selection schemes, we find that they do not necessarily result in energy savings when deployed on mobile systems. The key limitation of existing methods is that they learn only how data should be processed among the CNNs and not the network architectures, with each network being treated as a blackbox. To address this limitation, we pursue a more powerful design paradigm where the architecture settings of the CNNs are treated as hyper-parameters to be globally optimized. We cast the design of adaptive CNNs as a hyper-parameter optimization problem with respect to energy, accuracy, and communication constraints imposed by the mobile device. To efficiently solve this problem, we adapt Bayesian optimization to the properties of the design space, reaching near-optimal configurations in few tens of function evaluations. Our method reduces the energy consumed for image classification on a mobile device by up to 6x, compared to the best previously published work that uses CNNs as blackboxes. Finally, we evaluate two image classification practices, i.e., classifying all images locally versus over the cloud under energy and communication constraints.

In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objective. We consider the problem of estimating CVaR from i.i.d. samples of an unbounded random variable, which is either sub-Gaussian or sub-exponential. We derive a novel one-sided concentration bound for a natural sample-based CVaR estimator in this setting. Our bound relies on a concentration result for a quantile-based estimator for Value-at-Risk (VaR), which may be of independent interest.

We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is related to the spectral properties of the Markov chain. We show that there exists a wide statistical window, in terms of sample complexity for hypothesis testing between different pairs of initial distributions. We illustrate these results in several concrete examples.

We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic MDPs with $S$ states, $A$ actions, and mixing time parameter $t_{\rm mix}$. These bounds are the first regret bounds in the general, non-episodic setting with an optimal dependence on all given parameters. They could only be improved by using an alternative mixing time parameter.

Training deep recurrent neural network (RNN) architectures is complicated due to the increased network complexity. This disrupts the learning of higher order abstracts using deep RNN. In case of feed-forward networks training deep structures is simple and faster while learning long-term temporal information is not possible. In this paper we propose a residual memory neural network (RMN) architecture to model short-time dependencies using deep feed-forward layers having residual and time delayed connections. The residual connection paves way to construct deeper networks by enabling unhindered flow of gradients and the time delay units capture temporal information with shared weights. The number of layers in RMN signifies both the hierarchical processing depth and temporal depth. The computational complexity in training RMN is significantly less when compared to deep recurrent networks. RMN is further extended as bi-directional RMN (BRMN) to capture both past and future information. Experimental analysis is done on AMI corpus to substantiate the capability of RMN in learning long-term information and hierarchical information. Recognition performance of RMN trained with 300 hours of Switchboard corpus is compared with various state-of-the-art LVCSR systems. The results indicate that RMN and BRMN gains 6 % and 3.8 % relative improvement over LSTM and BLSTM networks.

The NIPS 2018 Adversarial Vision Challenge is a competition to facilitate measurable progress towards robust machine vision models and more generally applicable adversarial attacks. This document is an updated version of our competition proposal that was accepted in the competition track of 32nd Conference on Neural Information Processing Systems (NIPS 2018).

Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, and thus there is a need of its fully automatic segmentation from clinical images. In this work we present an architecture based in 3D-convolution kernels, a Volumetric Fully Convolution Neural Network (V-FCNN), able to segment the entire volume in one-shot, and consequently integrate the implicit spatial redundancy present in high resolution images. A loss function based on the mixture of both Mean Square Error (MSE) and Dice Loss (DL) is used, in an attempt to combine the ability to capture the bulk shape and the reduction of local errors products by over segmentation. Results demonstrate a reasonable performance in the middle region of the atria, and the impact of the challenges of capturing the variability of the pulmonary veins or the identification of the valve plane that separates the atria to the ventricle.