Transfer learning assumes classifiers of similar tasks share certain parameter structures. Unfortunately, modern classifiers uses sophisticated feature representations with huge parameter spaces which lead to costly transfer. Under the impression that changes from one classifier to another should be ``simple'', an efficient transfer learning criteria that only learns the ``differences'' is proposed in this paper. We train a \emph{posterior ratio} which turns out to minimizes the upper-bound of the target learning risk. The model of posterior ratio does not have to share the same parameter space with the source classifier at all so it can be easily modelled and efficiently trained. The resulting classifier therefore is obtained by simply multiplying the existing probabilistic-classifier with the learned posterior ratio.

The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.

Clustering of high-dimensional signals, sequences or functional data is a common task that arises in many domains [18, 19]. Such data come up in diverse fields, as in speech analysis, genomics, mass spectrometry, MRI or EEG measurements, and many more. Clustering seeks to partition data into groups with high overall similarity between members (instances) of the same group and dissimilarity to members of other groups. For time-series signals, this means partitioning the instances into groups of similarly behaving functions over time, where the measure of similarity is crucial and often application-specific. In many real-world scenarios, signals are high-dimensional (such as in genomics), noisy (as in low-quality speech recordings), and exhibit non-stationary behavior: for example peaks and other non-smooth local patterns, or changes in frequency over time.

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.

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.

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.

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.

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.