We consider the stochastic multi-armed bandit problem and the contextual bandit problem with historical observations and pre-clustered arms. The historical observations can contain any number of instances for each arm, and the pre-clustering information is a fixed clustering of arms provided as part of the input. We develop a variety of algorithms which incorporate this offline information effectively during the online exploration phase and derive their regret bounds. In particular, we develop the META algorithm which effectively hedges between two other algorithms: one which uses both historical observations and clustering, and another which uses only the historical observations. The former outperforms the latter when the clustering quality is good, and vice-versa. Extensive experiments on synthetic and real world datasets on Warafin drug dosage and web server selection for latency minimization validate our theoretical insights and demonstrate that META is a robust strategy for optimally exploiting the pre-clustering information.

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to spatial point processes. While the original embedding is infinite-dimensional and implicit, our approximate embedding is finite-dimensional and comes with explicit closed-form formulas. With its help we reduce the pattern comparison problem to the comparison of means in the Euclidean space. Hypothesis testing is based on conducting $t$-tests on each dimension of the embedding and combining the resulting $p$-values using the harmonic mean $p$-value combination technique. The main advantages of the proposed approach are that it can be applied to both single and replicated pattern comparisons, and that neither bootstrap nor permutation procedures are needed to obtain or calibrate the $p$-values. Our experiments show that the resulting tests are powerful and the $p$-values are well-calibrated; two applications to real world data are presented.

Automatic estimation of relative difficulty of a pair of questions is an important and challenging problem in community question answering (CQA) services. There are limited studies which addressed this problem. Past studies mostly leveraged expertise of users answering the questions and barely considered other properties of CQA services such as metadata of users and posts, temporal information and textual content. In this paper, we propose DiffQue, a novel system that maps this problem to a network-aided edge directionality prediction problem. DiffQue starts by constructing a novel network structure that captures different notions of difficulties among a pair of questions. It then measures the relative difficulty of two questions by predicting the direction of a (virtual) edge connecting these two questions in the network. It leverages features extracted from the network structure, metadata of users/posts and textual description of questions and answers. Experiments on datasets obtained from two CQA sites (further divided into four datasets) with human annotated ground-truth show that DiffQue outperforms four state-of-the-art methods by a significant margin (28.77% higher F1 score and 28.72% higher AUC than the best baseline). As opposed to the other baselines, (i) DiffQue appropriately responds to the training noise, (ii) DiffQue is capable of adapting multiple domains (CQA datasets), and (iii) DiffQue can efficiently handle 'cold start' problem which may arise due to the lack of information for newly posted questions or newly arrived users.

Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the underlying relation between entities is pre-determined. However, the explicit graph structure (relation) does not necessarily reflect the true dependency and genuine relation may be missing due to the incomplete connections in the data. Furthermore, existing methods are ineffective to capture the temporal trends as the RNNs or CNNs employed in these methods cannot capture long-range temporal sequences. To overcome these limitations, we propose in this paper a novel graph neural network architecture, Graph WaveNet, for spatial-temporal graph modeling. By developing a novel adaptive dependency matrix and learn it through node embedding, our model can precisely capture the hidden spatial dependency in the data. With a stacked dilated 1D convolution component whose receptive field grows exponentially as the number of layers increases, Graph WaveNet is able to handle very long sequences. These two components are integrated seamlessly in a unified framework and the whole framework is learned in an end-to-end manner. Experimental results on two public traffic network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of our algorithm.

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its robust and effective performance. Tremendous research efforts have been made to thrive this domain in terms of algorithms and applications. Although there are some survey papers to summarize the existing literature, they neglect to explore the underlying connection among different categories. Differently, in this paper we aim to provide an embedding prospective to illustrate the consensus mechanism, which transfers categorical basic partitions to other representations (e.g., binary coding, spectral embedding, etc) for the clustering purpose. To this end, we not only unify two major categories of consensus clustering, but also build an intuitive connection between consensus clustering and graph embedding. Moreover, we elaborate several extensions of classical consensus clustering from different settings and problems. Beyond this, we demonstrate how to leverage consensus clustering to address other tasks, such as constrained clustering, domain adaptation, feature selection, and outlier detection. Finally, we conclude this survey with future work in terms of interpretability, learnability and theoretical analysis.

Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. If the problem has a statistical maximum likelihood formulation, a local test of global optimality can be constructed. In this paper, we develop an improved test, based on a global maximum validation function proposed by Biernacki, under the assumption that the statistical distribution is in the generalized location family, a condition often satisfied in imaging problems. In addition, a new reparameterization and embedding procedure is presented that exploits knowledge about the forward operator to improve the global maximum validation function. Finally, the reparameterized embedding technique is applied to a physically-motivated joint-inverse problem arising in camera blur estimation. The advantages of the proposed global optimum testing techniques are numerically demonstrated in terms of increased detection accuracy and reduced computation.

As deep learning applications continue to become more diverse, an interesting question arises: Can general problem solving arise from jointly learning several such diverse tasks? To approach this question, deep multi-task learning is extended in this paper to the setting where there is no obvious overlap between task architectures. The idea is that any set of (architecture,task) pairs can be decomposed into a set of potentially related subproblems, whose sharing is optimized by an efficient stochastic algorithm. The approach is first validated in a classic synthetic multi-task learning benchmark, and then applied to sharing across disparate architectures for vision, NLP, and genomics tasks. It discovers regularities across these domains, encodes them into sharable modules, and combines these modules systematically to improve performance in the individual tasks. The results confirm that sharing learned functionality across diverse domains and architectures is indeed beneficial, thus establishing a key ingredient for general problem solving in the future.

In this article, we investigate a family of classification algorithms defined by the principle of empirical risk minimization, in the high dimensional regime where the feature dimension $p$ and data number $n$ are both large and comparable. Based on recent advances in high dimensional statistics and random matrix theory, we provide under mixture data model a unified stochastic characterization of classifiers learned with different loss functions. Our results are instrumental to an in-depth understanding as well as practical improvements on this fundamental classification approach. As the main outcome, we demonstrate the existence of a universally optimal loss function which yields the best high dimensional performance at any given $n/p$ ratio.

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of models. An attractive feature of these models is that they can admit analytic predictive means even when the likelihood is non-linear and the predictive distributions are non-Gaussian. We validate the modeling potential of these models in a variety of experiments in both the supervised and unsupervised setting. We demonstrate that the flexibility of these `neural' likelihoods can improve prediction quality as compared to simpler Gaussian process models and that neural likelihoods can be readily combined with a variety of underlying Gaussian process models, including deep Gaussian processes.

In the context of the Gaussian regression model, RKHSMetaMod estimates a meta model by solving the Ridge Group Sparse Optimization Problem based on the Reproducing Kernel Hilbert Spaces (RKHS). The estimated meta model is an additive model that satisfies the properties of the Hoeffding decomposition, and its terms estimate the terms in the Hoeffding decomposition of the unkwown regression function. This package provides an interface from R statistical computing environment to the C++ libraries Eigen and GSL. It uses the efficient C++ functions through RcppEigen and RcppGSL packages to speed up the execution time and the R environment in order to propose an user friendly package.