It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to come up with notions of clusterability that distinguish realistically interesting input data from worst-case data sets. The hope is that there will be clustering algorithms that are provably efficient on such "clusterable" instances. This paper addresses the thesis that the computational hardness of clustering tasks goes away for inputs that one really cares about. In other words, that "Clustering is difficult only when it does not matter" (the \emph{CDNM thesis} for short). I wish to present a a critical bird's eye overview of the results published on this issue so far and to call attention to the gap between available and desirable results on this issue. A longer, more detailed version of this note is available as arXiv:1507.05307. I discuss which requirements should be met in order to provide formal support to the the CDNM thesis and then examine existing results in view of these requirements and list some significant unsolved research challenges in that direction.

Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is able to detect non-linear and non-monotonous signals, is designed to be immune to noise, and offers tunability in terms of computational complexity in its estimations. Furthermore, we show that, under specified conditions, the introduced measure can be regarded as an estimate of conditional mutual information (transfer entropy). The functionality of this measure is assessed using comparative simulations where it outperforms other existing methods. The paper is concluded with an application to climatological data.

Measuring the impact of scientific articles is important for evaluating the research output of individual scientists, academic institutions and journals. While citations are raw data for constructing impact measures, there exist biases and potential issues if factors affecting citation patterns are not properly accounted for. In this work, we address the problem of field variation and introduce an article level metric useful for evaluating individual articles' visibility. This measure derives from joint probabilistic modeling of the content in the articles and the citations amongst them using latent Dirichlet allocation (LDA) and the mixed membership stochastic blockmodel (MMSB). Our proposed model provides a visibility metric for individual articles adjusted for field variation in citation rates, a structural understanding of citation behavior in different fields, and article recommendations which take into account article visibility and citation patterns. We develop an efficient algorithm for model fitting using variational methods. To scale up to large networks, we develop an online variant using stochastic gradient methods and case-control likelihood approximation. We apply our methods to the benchmark KDD Cup 2003 dataset with approximately 30,000 high energy physics papers.

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investigate compressed least-squares problems and propose new models and algorithms that address the issue of error and noise introduced by compression. While maintaining computational efficiency, our models provide robust solutions that are more accurate--relative to solutions of uncompressed least-squares--than those of classical compressed variants. We introduce tools from robust optimization together with a form of partial compression to improve the error-time trade-offs of compressed least-squares solvers. We develop an efficient solution algorithm for our Robust Partially-Compressed (RPC) model based on a reduction to a one-dimensional search. We also derive the first approximation error bounds for Partially-Compressed least-squares solutions. Empirical results comparing numerous alternatives suggest that robust and partially compressed solutions are effectively insulated against aggressive randomized transforms.

While sparse coding-based clustering methods have shown to be successful, their bottlenecks in both efficiency and scalability limit the practical usage. In recent years, deep learning has been proved to be a highly effective, efficient and scalable feature learning tool. In this paper, we propose to emulate the sparse coding-based clustering pipeline in the context of deep learning, leading to a carefully crafted deep model benefiting from both. A feed-forward network structure, named TAGnet, is constructed based on a graph-regularized sparse coding algorithm. It is then trained with task-specific loss functions from end to end. We discover that connecting deep learning to sparse coding benefits not only the model performance, but also its initialization and interpretation. Moreover, by introducing auxiliary clustering tasks to the intermediate feature hierarchy, we formulate DTAGnet and obtain a further performance boost. Extensive experiments demonstrate that the proposed model gains remarkable margins over several state-of-the-art methods.

An active learner is given a hypothesis class, a large set of unlabeled examples and the ability to interactively query labels to an oracle of a subset of these examples; the goal of the learner is to learn a hypothesis in the class that fits the data well by making as few label queries as possible. This work addresses active learning with labels obtained from strong and weak labelers, where in addition to the standard active learning setting, we have an extra weak labeler which may occasionally provide incorrect labels. An example is learning to classify medical images where either expensive labels may be obtained from a physician (oracle or strong labeler), or cheaper but occasionally incorrect labels may be obtained from a medical resident (weak labeler). Our goal is to learn a classifier with low error on data labeled by the oracle, while using the weak labeler to reduce the number of label queries made to this labeler. We provide an active learning algorithm for this setting, establish its statistical consistency, and analyze its label complexity to characterize when it can provide label savings over using the strong labeler alone.

We develop a parallel variational inference (VI) procedure for use in data-distributed settings, where each machine only has access to a subset of data and runs VI independently, without communicating with other machines. This type of "embarrassingly parallel" procedure has recently been developed for MCMC inference algorithms; however, in many cases it is not possible to directly extend this procedure to VI methods without requiring certain restrictive exponential family conditions on the form of the model. Furthermore, most existing (nonparallel) VI methods are restricted to use on conditionally conjugate models, which limits their applicability. To combat these issues, we make use of the recently proposed nonparametric VI to facilitate an embarrassingly parallel VI procedure that can be applied to a wider scope of models, including to nonconjugate models. We derive our embarrassingly parallel VI algorithm, analyze our method theoretically, and demonstrate our method empirically on a few nonconjugate models.

In order to identify important variables that are involved in making optimal treatment decision, Lu et al. (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against the misspecification of the conditional mean model. Two problems arise: (i) in a world of explosively big data, effective methods are needed to handle ultra-high dimensional data set, for example, with the dimension of predictors is of the non-polynomial (NP) order of the sample size; (ii) both the propensity score and conditional mean models need to be estimated from data under NP dimensionality. In this paper, we propose a two-step estimation procedure for deriving the optimal treatment regime under NP dimensionality. In both steps, penalized regressions are employed with the non-concave penalty function, where the conditional mean model of the response given predictors may be misspecified. The asymptotic properties, such as weak oracle properties, selection consistency and oracle distributions, of the proposed estimators are investigated. In addition, we study the limiting distribution of the estimated value function for the obtained optimal treatment regime. The empirical performance of the proposed estimation method is evaluated by simulations and an application to a depression dataset from the STAR*D study.

The EM training algorithm of the classical i-vector extractor is often incorrectly described as a maximum-likelihood method. The i-vector model is however intractable: the likelihood itself and the hidden-variable posteriors needed for the EM algorithm cannot be computed in closed form. We show here that the classical i-vector extractor recipe is actually a mean-field variational Bayes (VB) recipe. This theoretical VB interpretation turns out to be of further use, because it also offers an interpretation of the newer phonetic i-vector extractor recipe, thereby unifying the two flavours of extractor. More importantly, the VB interpretation is also practically useful: it suggests ways of modifying existing i-vector extractors to make them more accurate. In particular, in existing methods, the approximate VB posterior for the GMM states is fixed, while only the parameters of the generative model are adapted. Here we explore the possibility of also mildly adjusting (calibrating) those posteriors, so that they better fit the generative model.

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time. This premise has recently guided the research to the innovative and meaningful idea of imposing multiple constraints on the parameters involved in the problem under study. For instance, when dealing with problems whose parameters form sparse and low-rank matrices, the adoption of suitably combined constraints imposing sparsity and low-rankness, is expected to yield substantially enhanced estimation results. In this paper, we address the spectral unmixing problem in hyperspectral images. Specifically, two novel unmixing algorithms are introduced, in an attempt to exploit both spatial correlation and sparse representation of pixels lying in homogeneous regions of hyperspectral images. To this end, a novel convex mixed penalty term is first defined consisting of the sum of the weighted $\ell_1$ and the weighted nuclear norm of the abundance matrix corresponding to a small area of the image determined by a sliding square window. This penalty term is then used to regularize a conventional quadratic cost function and impose simultaneously sparsity and row-rankness on the abundance matrix. The resulting regularized cost function is minimized by a) an incremental proximal sparse and low-rank unmixing algorithm and b) an algorithm based on the alternating minimization method of multipliers (ADMM). The effectiveness of the proposed algorithms is illustrated in experiments conducted both on simulated and real data.