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.

Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" from an associated MRF model. Herding differs from maximum likelihood estimation in that the sequence of parameters does not converge to a fixed point and differs from an MCMC posterior sampling approach in that the sequence of states is generated deterministically. Herding may be interpreted as a"perturb and map" method where the parameter perturbations are generated using a deterministic nonlinear dynamical system rather than randomly from a Gumbel distribution. This chapter studies the distinct statistical characteristics of the herding algorithm and shows that the fast convergence rate of the controlled moments may be attributed to edge of chaos dynamics. The herding algorithm can also be generalized to models with latent variables and to a discriminative learning setting. The perceptron cycling theorem ensures that the fast moment matching property is preserved in the more general framework.

Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40%. In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25% relative gains on the softmax classifier and 25-50% on triplet loss in these tasks.

Representation learning systems typically rely on massive amounts of labeled data in order to be trained to high accuracy. Recently, high-dimensional parametric models like neural networks have succeeded in building rich representations using either compressive, reconstructive or supervised criteria. However, the semantic structure inherent in observations is oftentimes lost in the process. Human perception excels at understanding semantics but cannot always be expressed in terms of labels. Thus, \emph{oracles} or \emph{human-in-the-loop systems}, for example crowdsourcing, are often employed to generate similarity constraints using an implicit similarity function encoded in human perception. In this work we propose to combine \emph{generative unsupervised feature learning} with a \emph{probabilistic treatment of oracle information like triplets} in order to transfer implicit privileged oracle knowledge into explicit nonlinear Bayesian latent factor models of the observations. We use a fast variational algorithm to learn the joint model and demonstrate applicability to a well-known image dataset. We show how implicit triplet information can provide rich information to learn representations that outperform previous metric learning approaches as well as generative models without this side-information in a variety of predictive tasks. In addition, we illustrate that the proposed approach compartmentalizes the latent spaces semantically which allows interpretation of the latent variables.

We propose a new algorithmic framework for sequential hypothesis testing with i.i.d. data, which includes A/B testing, nonparametric two-sample testing, and independence testing as special cases. It is novel in several ways: (a) it takes linear time and constant space to compute on the fly, (b) it has the same power guarantee as a non-sequential version of the test with the same computational constraints up to a small factor, and (c) it accesses only as many samples as are required - its stopping time adapts to the unknown difficulty of the problem. All our test statistics are constructed to be zero-mean martingales under the null hypothesis, and the rejection threshold is governed by a uniform non-asymptotic law of the iterated logarithm (LIL). For the case of nonparametric two-sample mean testing, we also provide a finite sample power analysis, and the first non-asymptotic stopping time calculations for this class of problems. We verify our predictions for type I and II errors and stopping times using simulations.

As an emerging research direction, online streaming feature selection deals with sequentially added dimensions in a feature space while the number of data instances is fixed. Online streaming feature selection provides a new, complementary algorithmic methodology to enrich online feature selection, especially targets to high dimensionality in big data analytics. This paper introduces the first comprehensive open-source library for use in MATLAB that implements the state-of-the-art algorithms of online streaming feature selection. The library is designed to facilitate the development of new algorithms in this exciting research direction and make comparisons between the new methods and existing ones available.

Module extraction is the task of computing a (preferably small) fragment M of an ontology T that preserves a class of entailments over a signature of interest S. Extracting modules of minimal size is well-known to be computationally hard, and often algorithmically infeasible, especially for highly expressive ontology languages. Thus, practical techniques typically rely on approximations, where M provably captures the relevant entailments, but is not guaranteed to be minimal. Existing approximations ensure that M preserves all second-order entailments of T w.r.t. S, which is a stronger condition than is required in many applications, and may lead to unnecessarily large modules in practice. In this paper we propose a novel approach in which module extraction is reduced to a reasoning problem in datalog. Our approach generalises existing approximations in an elegant way. More importantly, it allows extraction of modules that are tailored to preserve only specific kinds of entailments, and thus are often significantly smaller. Our evaluation on a wide range of ontologies confirms the feasibility and benefits of our approach in practice.

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a wide matrix, with an elastic net penalty on the former and an $\ell_1$ penalty on the latter. The first matrix linearly transforms the predictors to a set of latent factors, and the second one regresses the responses on these factors. Our algorithm simultaneously performs dimension reduction and coefficient estimation and automatically estimates the number of latent factors from the data. Our formulation results in a non-convex optimization problem, which despite its flexibility to impose effective low-dimensional structure, is difficult, or even impossible, to solve exactly in a reasonable time. We specify an optimization algorithm based on alternating minimization with three different sets of updates to solve this non-convex problem and provide theoretical results on its convergence and optimality. Finally, we demonstrate the effectiveness of our algorithm via experiments on simulated and real data.

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are reparametrized through a multilayer perceptron. The key aspect of this reformulation is that it prevents the proliferation of variational parameters which otherwise grow linearly in proportion to the sample size. We derive a new formulation of the variational lower bound that allows us to distribute most of the computation in a way that enables to handle datasets of the size of mainstream deep learning tasks. We show the efficacy of the method on a variety of challenges including deep unsupervised learning and deep Bayesian optimization.

A BSTRACT Competing with top human players in the ancient game of Go has been a long-term goal of artificial intelligence. Go's high branching factor makes traditional search techniques ineffective, even on leading-edge hardware, and Go's evaluation function could change drastically with one stone change. Recent works [Maddi-son et al. (2015); Clark & Storkey (2015)] show that search is not strictly necessary for machine Go players. A pure pattern-matching approach, based on a Deep Convolutional Neural Network (DCNN) that predicts the next move, can perform as well as Monte Carlo Tree Search (MCTS)-based open source Go engines such as Pachi [Baudis & Gailly (2012)] if its search budget is limited. We extend this idea in our bot nameddarkforest, which relies on a DCNN designed for long-term predictions. Darkforest substantially improves the win rate for pattern-matching approaches against MCTS-based approaches, even with looser search budgets. Against human players, the newest versions, darkfores2, achieve a stable 3d level on KGS Go Server as a ranked bot, a substantial improvement upon the estimated 4k-5k ranks for DCNN reported in Clark & Storkey (2015) based on games against other machine players. Adding MCTS to darkfores2 creates a much stronger player named darkfmcts3: with 5000 rollouts, it beats Pachi with 10k rollouts in all 250 games; with 75k rollouts it achieves a stable 5d level in KGS server, on par with state-of-the-art Go AIs (e.g., Zen, DolBaram, CrazyStone) except for AlphaGo [Silver et al. (2016)]; with 110k rollouts, it won the 3rd place in January KGS Go Tournament. 1 I NTRODUCTION For a long time, computer Go is considered to be a grand challenge in artificial intelligence. Figure 1 shows a simple illustration of the game of Go. Black plays first on an empty board.