Navy robots from Gecko Robotics will inspect U.S. warships in $71 million effort to reduce maintenance delays as only 60% of fleet remains operational amid China's naval expansion.

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, ``do two elements $u$ and $v$ belong to the same cluster?''. The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. To improve accuracy of clustering, a fruitful approach in recent years has been to ask a domain expert or crowd to obtain labeled data interactively.

Deep networks trained on large-scale data can learn transferable features to promote learning multiple tasks. Since deep features eventually transition from general to specific along deep networks, a fundamental problem of multi-task learning is how to exploit the task relatedness underlying parameter tensors and improve feature transferability in the multiple task-specific layers. This paper presents Multilinear Relationship Networks (MRN) that discover the task relationships based on novel tensor normal priors over parameter tensors of multiple task-specific layers in deep convolutional networks. By jointly learning transferable features and multilinear relationships of tasks and features, MRN is able to alleviate the dilemma of negative-transfer in the feature layers and under-transfer in the classifier layer. Experiments show that MRN yields state-of-the-art results on three multi-task learning datasets.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine whether $X \independent Y \vert Z$. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution $f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$ -- the joint distribution if and only if $X \independent Y \vert Z.$ -- when given access only to i.i.d.

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a Levy process. The resulting distribution has support for all stationary covariances---including the popular RBF, periodic, and Matern kernels---combined with inductive biases which enable automatic and data efficient learning, long-range extrapolation, and state of the art predictive performance. The proposed model also presents an approach to spectral regularization, as the Levy process introduces a sparsity-inducing prior over mixture components, allowing automatic selection over model order and pruning of extraneous components. We exploit the algebraic structure of the proposed process for O(n) training and O(1) predictions. We perform extrapolations having reasonable uncertainty estimates on several benchmarks, show that the proposed model can recover flexible ground truth covariances and that it is robust to errors in initialization.

Central to models of human visual attention is the saliency map. We propose a hierarchical visual architecture that operates on a saliency map and uses a novel attention mechanism to sequentially focus on salient regions and take additional glimpses within those regions. The architecture is motivated by human visual attention, and is used for multi-label image classification on a novel multiset task, demonstrating that it achieves high precision and recall while localizing objects with its attention. Unlike conventional multi-label image classification models, the model supports multiset prediction due to a reinforcement-learning based training process that allows for arbitrary label permutation and multiple instances per label.

We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to the problem solution. We prove that a proper choice of the tuning parameters allows Min-Sum Splitting to yield subdiffusive accelerated convergence rates, matching the rates obtained by shift-register methods. The acceleration scheme embodied by Min-Sum Splitting for the consensus problem bears similarities with lifted Markov chains techniques and with multi-step first order methods in convex optimization.

Few-shot learning refers to understanding new concepts from only a few examples. We propose an information retrieval-inspired approach for this problem that is motivated by the increased importance of maximally leveraging all the available information in this low-data regime. We define a training objective that aims to extract as much information as possible from each training batch by effectively optimizing over all relative orderings of the batch points simultaneously. In particular, we view each batch point as a `query' that ranks the remaining ones based on its predicted relevance to them and we define a model within the framework of structured prediction to optimize mean Average Precision over these rankings. Our method achieves impressive results on the standard few-shot classification benchmarks while is also capable of few-shot retrieval.

Affine policies (or control) are widely used as a solution approach in dynamic optimization where computing an optimal adjustable solution is usually intractable. While the worst case performance of affine policies can be significantly bad, the empirical performance is observed to be near-optimal for a large class of problem instances. For instance, in the two-stage dynamic robust optimization problem with linear covering constraints and uncertain right hand side, the worst-case approximation bound for affine policies is $O(\sqrt m)$ that is also tight (see Bertsimas and Goyal (2012)), whereas observed empirical performance is near-optimal. In this paper, we aim to address this stark-contrast between the worst-case and the empirical performance of affine policies. In particular, we show that affine policies give a good approximation for the two-stage adjustable robust optimization problem with high probability on random instances where the constraint coefficients are generated i.i.d.

Minimizing non-convex and high-dimensional objective functions is challenging, especially when training modern deep neural networks. In this paper, a novel approach is proposed which divides the training process into two consecutive phases to obtain better generalization performance: Bayesian sampling and stochastic optimization. The first phase is to explore the energy landscape and to capture the `fat'' modes; and the second one is to fine-tune the parameter learned from the first phase. In the Bayesian learning phase, we apply continuous tempering and stochastic approximation into the Langevin dynamics to create an efficient and effective sampler, in which the temperature is adjusted automatically according to the designed ``temperature dynamics''. These strategies can overcome the challenge of early trapping into bad local minima and have achieved remarkable improvements in various types of neural networks as shown in our theoretical analysis and empirical experiments.