We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret bound is achievable we establish a connection to the theory of decoupling inequalities for martingales in Banach spaces. When the hypothesis class is a set of linear functions bounded in some norm, such a regret bound is achievable if and only if the norm satisfies certain decoupling inequalities for martingales. Donald Burkholder's celebrated geometric characterization of decoupling inequalities (1984) states that such an inequality holds if and only if there exists a special function called a Burkholder function satisfying certain restricted concavity properties. Our online learning algorithms are efficient in terms of queries to this function. We realize our general theory by giving novel efficient algorithms for classes including lp norms, Schatten p-norms, group norms, and reproducing kernel Hilbert spaces. The empirical Rademacher complexity regret bound implies --- when used in the i.i.d. setting --- a data-dependent complexity bound for excess risk after online-to-batch conversion. To showcase the power of the empirical Rademacher complexity regret bound, we derive improved rates for a supervised learning generalization of the online learning with low rank experts task and for the online matrix prediction task. In addition to obtaining tight data-dependent regret bounds, our algorithms enjoy improved efficiency over previous techniques based on Rademacher complexity, automatically work in the infinite horizon setting, and are scale-free. To obtain such adaptive methods, we introduce novel machinery, and the resulting algorithms are not based on the standard tools of online convex optimization.

The resulting graph structure can then be used to design procedures for data clustering (unsupervised learning), data classification (supervised learning) and dimensionality reduction. For all of these graph-based procedures, it is important (as with any procedure in statistics) to study their consistency and to quantify how accurately they reveal features from the ground-truth distribution. Many of the graph-based procedures for which there are consistency results available are really optimization problems whose objective functionals incorporate the graph structure in one way or the other. This is the case for procedures like spectral clustering and total variation clustering, where the notions of graph Laplacian and graph perimeter are fundamental in the definition of the algorithms. Operators and functionals in the cloud are defined in close resemblance to operators and functionals in the continuum and it is often the case that this resemblance is the starting point for establishing consistency results.

In this paper, we consider a new low-quality label learning problem: learning time series detection models from temporally imprecise labels. In this problem, the data consist of a set of input time series, and supervision is provided by a sequence of noisy time stamps corresponding to the occurrence of positive class events. Such temporally imprecise labels commonly occur in areas like mobile health research where human annotators are tasked with labeling the occurrence of very short duration events. We propose a general learning framework for this problem that can accommodate different base classifiers and noise models. We present results on real mobile health data showing that the proposed framework significantly outperforms a number of alternatives including assuming that the label time stamps are noise-free, transforming the problem into the multiple instance learning framework, and learning on labels that were manually re-aligned.

Boosting combines weak (biased) learners to obtain effective learning algorithms for classification and prediction. In this paper, we show a connection between boosting and kernel-based methods, highlighting both theoretical and practical applications. In the context of $\ell_2$ boosting, we start with a weak linear learner defined by a kernel $K$. We show that boosting with this learner is equivalent to estimation with a special {\it boosting kernel} that depends on $K$, as well as on the regression matrix, noise variance, and hyperparameters. The number of boosting iterations is modeled as a continuous hyperparameter, and fit along with other parameters using standard techniques. We then generalize the boosting kernel to a broad new class of boosting approaches for more general weak learners, including those based on the $\ell_1$, hinge and Vapnik losses. The approach allows fast hyperparameter tuning for this general class, and has a wide range of applications, including robust regression and classification. We illustrate some of these applications with numerical examples on synthetic and real data.

We consider the best-arm identification problem in multi-armed bandits, which focuses purely on exploration. A player is given a fixed budget to explore a finite set of arms, and the rewards of each arm are drawn independently from a fixed, unknown distribution. The player aims to identify the arm with the largest expected reward. We propose a general framework to unify sequential elimination algorithms, where the arms are dismissed iteratively until a unique arm is left. Our analysis reveals a novel performance measure expressed in terms of the sampling mechanism and number of eliminated arms at each round. Based on this result, we develop an algorithm that divides the budget according to a nonlinear function of remaining arms at each round. We provide theoretical guarantees for the algorithm, characterizing the suitable nonlinearity for different problem environments described by the number of competitive arms. Matching the theoretical results, our experiments show that the nonlinear algorithm outperforms the state-of-the-art. We finally study the side-observation model, where pulling an arm reveals the rewards of its related arms, and we establish improved theoretical guarantees in the pure-exploration setting.

Domain adaptation is transfer learning which aims to generalize a learning model across training and testing data with different distributions. Most previous research tackle this problem in seeking a shared feature representation between source and target domains while reducing the mismatch of their data distributions. In this paper, we propose a close yet discriminative domain adaptation method, namely CDDA, which generates a latent feature representation with two interesting properties. First, the discrepancy between the source and target domain, measured in terms of both marginal and conditional probability distribution via Maximum Mean Discrepancy is minimized so as to attract two domains close to each other. More importantly, we also design a repulsive force term, which maximizes the distances between each label dependent sub-domain to all others so as to drag different class dependent sub-domains far away from each other and thereby increase the discriminative power of the adapted domain. Moreover, given the fact that the underlying data manifold could have complex geometric structure, we further propose the constraints of label smoothness and geometric structure consistency for label propagation. Extensive experiments are conducted on 36 cross-domain image classification tasks over four public datasets. The comprehensive results show that the proposed method consistently outperforms the state-of-the-art methods with significant margins.

Matrix factorisation methods decompose multivariate observations as linear combinations of latent feature vectors. The Indian Buffet Process (IBP) provides a way to model the number of latent features required for a good approximation in terms of regularised reconstruction error. Previous work has focussed on latent feature vectors with independent entries. We extend the model to include nondiagonal latent covariance structures representing characteristics such as smoothness. This is done by . Using simulations we demonstrate that under appropriate conditions a smoothness prior helps to recover the true latent features, while denoising more accurately. We demonstrate our method on a real neuroimaging dataset, where computational tractability is a sufficient challenge that the efficient strategy presented here is essential.

As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important to boost the cross-media retrieval. Motivated by the strong ability of deep neural network in feature representation and comparison functions learning, we propose the Unified Network for Cross-media Similarity Metric (UNCSM) to associate cross-media shared representation learning with distance metric in a unified framework. First, we design a two-pathway deep network pretrained with contrastive loss, and employ double triplet similarity loss for fine-tuning to learn the shared representation for each media type by modeling the relative semantic similarity. Second, the metric network is designed for effectively calculating the cross-media similarity of the shared representation, by modeling the pairwise similar and dissimilar constraints. Compared to the existing methods which mostly ignore the dissimilar constraints and only use sample distance metric as Euclidean distance separately, our UNCSM approach unifies the representation learning and distance metric to preserve the relative similarity as well as embrace more complex similarity functions for further improving the cross-media retrieval accuracy. The experimental results show that our UNCSM approach outperforms 8 state-of-the-art methods on 4 widely-used cross-media datasets.

We describe a method for learning word embeddings with data-dependent dimensionality. Our Stochastic Dimensionality Skip-Gram (SD-SG) and Stochastic Dimensionality Continuous Bag-of-Words (SD-CBOW) are nonparametric analogs of Mikolov et al.'s (2013) well-known 'word2vec' models. Vector dimensionality is made dynamic by employing techniques used by Cote & Larochelle (2016) to define an RBM with an infinite number of hidden units. We show qualitatively and quantitatively that SD-SG and SD-CBOW are competitive with their fixed-dimension counterparts while providing a distribution over embedding dimensionalities, which offers a window into how semantics distribute across dimensions.

Rick and Morty fans, you've got a week to get VR-ready for the series' debut in the virtual realm. Adult Swim and Owlchemy Labs, creator of Job Simulator, announced today that the long-awaited VR title, Rick and Morty: Virtual Rick-ality, will land on April 20th (4/20, of course). The Oculus Rift and HTC Vive game puts you in the shoes of a Morty clone -- which means you should be prepared to be in constant danger. You'll be able to explore Rick's lab, the family home and, naturally, alternate worlds. And yes, it looks like there's lots of Job Simulator DNA in there.