High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of important or anomalous information from these large datastreams. While recent advances in online learning have led to novel and rapidly converging algorithms, these methods are unable to adapt to nonstationary environments arising in real-world problems. This paper describes a dynamic mirror descent framework which addresses this challenge, yielding low theoretical regret bounds and accurate, adaptive, and computationally efficient algorithms which are applicable to broad classes of problems. The methods are capable of learning and adapting to an underlying and possibly time-varying dynamical model. Empirical results in the context of dynamic texture analysis, solar flare detection, sequential compressed sensing of a dynamic scene, traffic surveillance,tracking self-exciting point processes and network behavior in the Enron email corpus support the core theoretical findings.

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.

Abstract-- This paper presents a novel approach for incremental semiparametric inverse dynamics learning. In particular, we consider the mixture of two approaches: Parametric modeling based on rigid body dynamics equations and nonparametric modeling based on incremental kernel methods, with no prior information on the mechanical properties of the system. We validate the proposed technique learning the dynamics of one arm of the iCub humanoid robot. I. INTRODUCTION In order to control a robot a model describing the relation between the actuator inputs, the interactions with the world and bodies accelerations is required. This model is called the dynamics model of the robot.

The majority of traditional classification ru les minimizing the expected probability of error (0-1 loss) are inappropriate if the class probability distributions are ill-defined or impossible to estimate. We argue that in such cases class domains should be used instead of class distributions or densities to construct a reliable decision function. Proposals are presented for some evaluation criteria and classifier learning schemes, illustrated by an example.

We consider general non-Euclidean distance measures between real world objects that need to be classified. It is assumed that objects are represented by distances to other objects only. Conditions for zero-error dissimilarity based classifiers are derived. Additional conditions are given under which the zero-error decision boundary is a continues function of the distances to a finite set of training samples. These conditions affect the objects as well as the distance measure used. It is argued that they can be met in practice.

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent.

Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are not self-intersected, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of convergence guarantee and adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a new regularized principal graph learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected $\ell_1$ graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.

Machine learning algorithms are increasingly influencing our decisions and interacting with us in all parts of our daily lives. Therefore, just like for power plants, highways, and myriad other engineered sociotechnical systems, we must consider the safety of systems involving machine learning. In this paper, we first discuss the definition of safety in terms of risk, epistemic uncertainty, and the harm incurred by unwanted outcomes. Then we examine dimensions, such as the choice of cost function and the appropriateness of minimizing the empirical average training cost, along which certain real-world applications may not be completely amenable to the foundational principle of modern statistical machine learning: empirical risk minimization. In particular, we note an emerging dichotomy of applications: ones in which safety is important and risk minimization is not the complete story (we name these Type A applications), and ones in which safety is not so critical and risk minimization is sufficient (we name these Type B applications). Finally, we discuss how four different strategies for achieving safety in engineering (inherently safe design, safety reserves, safe fail, and procedural safeguards) can be mapped to the machine learning context through interpretability and causality of predictive models, objectives beyond expected prediction accuracy, human involvement for labeling difficult or rare examples, and user experience design of software.

Asynchronous distributed stochastic gradient descent methods have trouble converging because of stale gradients. A gradient update sent to a parameter server by a client is stale if the parameters used to calculate that gradient have since been updated on the server. Approaches have been proposed to circumvent this problem that quantify staleness in terms of the number of elapsed updates. In this work, we propose a novel method that quantifies staleness in terms of moving averages of gradient statistics. We show that this method outperforms previous methods with respect to convergence speed and scalability to many clients. We also discuss how an extension to this method can be used to dramatically reduce bandwidth costs in a distributed training context. In particular, our method allows reduction of total bandwidth usage by a factor of 5 with little impact on cost convergence. We also describe (and link to) a software library that we have used to simulate these algorithms deterministically on a single machine.

Slow feature analysis (SFA) is an unsupervised-learning algorithm that extracts slowly varying features from a multi-dimensional time series. A supervised extension to SFA for classification and regression is graph-based SFA (GSFA). GSFA is based on the preservation of similarities, which are specified by a graph structure derived from the labels. It has been shown that hierarchical GSFA (HGSFA) allows learning from images and other high-dimensional data. The feature space spanned by HGSFA is complex due to the composition of the nonlinearities of the nodes in the network. However, we show that the network discards useful information prematurely before it reaches higher nodes, resulting in suboptimal global slowness and an under-exploited feature space. To counteract these problems, we propose an extension called hierarchical information-preserving GSFA (HiGSFA), where information preservation complements the slowness-maximization goal. We build a 10-layer HiGSFA network to estimate human age from facial photographs of the MORPH-II database, achieving a mean absolute error of 3.50 years, improving the state-of-the-art performance. HiGSFA and HGSFA support multiple-labels and offer a rich feature space, feed-forward training, and linear complexity in the number of samples and dimensions. Furthermore, HiGSFA outperforms HGSFA in terms of feature slowness, estimation accuracy and input reconstruction, giving rise to a promising hierarchical supervised-learning approach.