We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections, we show a range of numerical experiments for simulated and real-world problems.

Extracting the underlying low-dimensional space where high-dimensional signals often reside has long been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. At the same time, working with incomplete (partly observed) large scale datasets has recently been commonplace for diverse reasons. This so called {\it big data era} we are currently living calls for devising online subspace learning algorithms that can suitably handle incomplete data. Their envisaged objective is to {\it recursively} estimate the unknown subspace by processing streaming data sequentially, thus reducing computational complexity, while obviating the need for storing the whole dataset in memory. In this paper, an online variational Bayes subspace learning algorithm from partial observations is presented. To account for the unawareness of the true rank of the subspace, commonly met in practice, low-rankness is explicitly imposed on the sought subspace data matrix by exploiting sparse Bayesian learning principles. Moreover, sparsity, {\it simultaneously} to low-rankness, is favored on the subspace matrix by the sophisticated hierarchical Bayesian scheme that is adopted. In doing so, the proposed algorithm becomes adept in dealing with applications whereby the underlying subspace may be also sparse, as, e.g., in sparse dictionary learning problems. As shown, the new subspace tracking scheme outperforms its state-of-the-art counterparts in terms of estimation accuracy, in a variety of experiments conducted on simulated and real data.

Peer grading is the process of students reviewing each others' work, such as homework submissions, and has lately become a popular mechanism used in massive open online courses (MOOCs). Intrigued by this idea, we used it in a course on algorithms and data structures at the University of Hamburg. Throughout the whole semester, students repeatedly handed in submissions to exercises, which were then evaluated both by teaching assistants and by a peer grading mechanism, yielding a large dataset of teacher and peer grades. We applied different statistical and machine learning methods to aggregate the peer grades in order to come up with accurate final grades for the submissions (supervised and unsupervised, methods based on numeric scores and ordinal rankings). Surprisingly, none of them improves over the baseline of using the mean peer grade as the final grade. We discuss a number of possible explanations for these results and present a thorough analysis of the generated dataset.

ABSTRACT We present a method for fast resting-state fMRI spatial decompositions of very large datasets, based on the reduction of the temporal dimension before applying dictionary learning on concatenated individual records from groups of subjects. Introducing a measure of correspondence between spatial decompositions of rest fMRI, we demonstrates that time-reduced dictionary learning produces result as reliable as non-reduced decompositions. We also show that this reduction significantly improves computational scalability. Index Terms-- resting-state fMRI, sparse decomposition, dictionary learning, online learning, rangefinder 1. INTRODUCTION Resting-state fMRI data analysis traditionally implies, as an initial step, to decompose a set of raw 4D records (time-series sampled in a volumic voxel grid) into a sum of spatially located functional networks that isolate a part of the brain signals. Functional networks, that can be seen as a set of brain activation maps, form a relevant basis for the experiment signals that captures its essence in a low-dimensional space.

A successful class of image denoising methods is based on Bayesian approaches working in wavelet representations. However, analytical estimates can be obtained only for particular combinations of analytical models of signal and noise, thus precluding its straightforward extension to deal with other arbitrary noise sources. In this paper, we propose an alternative non-explicit way to take into account the relations among natural image wavelet coefficients for denoising: we use support vector regression (SVR) in the wavelet domain to enforce these relations in the estimated signal. Since relations among the coefficients are specific to the signal, the regularization property of SVR is exploited to remove the noise, which does not share this feature. The specific signal relations are encoded in an anisotropic kernel obtained from mutual information measures computed on a representative image database. Training considers minimizing the Kullback-Leibler divergence (KLD) between the estimated and actual probability functions of signal and noise in order to enforce similarity. Due to its non-parametric nature, the method can eventually cope with different noise sources without the need of an explicit re-formulation, as it is strictly necessary under parametric Bayesian formalisms. Results under several noise levels and noise sources show that: (1) the proposed method outperforms conventional wavelet methods that assume coefficient independence, (2) it is similar to state-of-the-art methods that do explicitly include these relations when the noise source is Gaussian, and (3) it gives better numerical and visual performance when more complex, realistic noise sources are considered. Therefore, the proposed machine learning approach can be seen as a more flexible (model-free) alternative to the explicit description of wavelet coefficient relations for image denoising.

This book provides a tutorial introduction to modern techniques for representing and reasoning about qualitative preferences with respect to a set of alternatives. The syntax and semantics of several languages for representing preference languages, including CP-nets, TCP-nets, CI-nets, and CP-theories, are reviewed. Some key problems in reasoning about preferences are introduced, including determining whether one alternative is preferred to another, or whether they are equivalent, with respect to a given set of preferences. These tasks can be reduced to model checking in temporal logic. Specifically, an induced preference graph that represents a given set of preferences can be efficiently encoded using a Kripke Structure for Computational Tree Logic (CTL).

For the vast majority of queries (for example, navigation, simple fact lookup, and others), search engines do extremely well. Their ability to quickly provide answers to queries is a remarkable testament to the power of many of the fundamental methods of AI. They also highlight many of the issues that are common to sophisticated AI question-answering systems. It has become clear that people think of search programs in ways that are very different from traditional information sources. Rapid and ready-at-hand access, depth of processing, and the way they enable people to offload some ordinary memory tasks suggest that search engines have become more of a cognitive amplifier than a simple repository or front-end to the Internet. Like all sophisticated tools, people still need to learn how to use them. Although search engines are superb at finding and presenting information—up to and including extracting complex relations and making simple inferences—knowing how to frame questions and evaluate their results for accuracy and credibility remains an ongoing challenge. Some questions are still deep and complex, and still require knowledge on the part of the search user to work through to a successful answer. And the fact that the underlying information content, user interfaces, and capabilities are all in a continual state of change means that searchers need to continually update their knowledge of what these programs can (and cannot) do.

This article is aimed at helping AI researchers and practitioners imagine roles intelligent technologies might play in the many different and varied ecosystems in which people learn. My observations are based on learning sciences research of the past several decades, the possibilities of new technologies of the past few years, and my experience as program officer for the National Science Foundation’s Cyberlearning and Future Learning Technologies program. My thesis is that new technologies have potential to transform possibilities for fostering learning in both formal and informal learning environments by making it possible and manageable for learners to engage in the kinds of project work that professionals engage in and learn important content, skills, practices, habits, and dispositions from those experiences. The expertise of AI researchers and practitioners is critical to that vision, but it will require teaming up with others — for example, technology imagineers, educators, and learning scientists.

This introduction focuses on how human-centered computing (HCC) is changing the way that people think about information technology. The AI perspective views this HCC framework as embodying a systems view, in which human thought and action are linked and equally important in terms of analysis, design, and evaluation. This emerging technology provides a new research outlook for AI applications, with new research goals and agendas.

We present a scalable Bayesian multi-label learning model based on learning low-dimensional label embeddings. Our model assumes that each label vector is generated as a weighted combination of a set of topics (each topic being a distribution over labels), where the combination weights (i.e., the embeddings) for each label vector are conditioned on the observed feature vector. This construction, coupled with a Bernoulli-Poisson link function for each label of the binary label vector, leads to a model with a computational cost that scales in the number of positive labels in the label matrix. This makes the model particularly appealing for real-world multi-label learning problems where the label matrix is usually very massive but highly sparse. Using a data-augmentation strategy leads to full local conjugacy in our model, facilitating simple and very efficient Gibbs sampling, as well as an Expectation Maximization algorithm for inference. Also, predicting the label vector at test time does not require doing an inference for the label embeddings and can be done in closed form. We report results on several benchmark data sets, comparing our model with various state-of-the art methods.