Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian Process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other nonparametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and nu-SVR.

We present a new, massively parallel architecture for accelerating machine learning algorithms, based on arrays of variable-resolution arithmetic vector processing elements (VPE). Groups of VPEs operate in SIMD (single instruction multiple data) mode, and each group is connected to an independent memory bank. In this way memory bandwidth scales with the number of VPE, and the main data flows are local, keeping power dissipation low. With 256 VPEs, implemented on two FPGA (field programmable gate array) chips, we obtain a sustained speed of 19 GMACS (billion multiply-accumulate per sec.) for SVM training, and 86 GMACS for SVM classification. This performance is more than an order of magnitude higher than that of any FPGA implementation reported so far. The speed on one FPGA is similar to the fastest speeds published on a Graphics Processor for the MNIST problem, despite a clock rate of the FPGA that is six times lower. High performance at low clock rates makes this massively parallel architecture particularly attractive for embedded applications, where low power dissipation is critical. Tests with Convolutional Neural Networks and other learning algorithms are under way now.

Modern machine learning-based approaches to computer vision require very large databases of labeled images. Some contemporary vision systems already require on the order of millions of images for training (e.g., Omron face detector). While the collection of these large databases is becoming a bottleneck, new Internet-based services that allow labelers from around the world to be easily hired and managed provide a promising solution. However, using these services to label large databases brings with it new theoretical and practical challenges: (1) The labelers may have wide ranging levels of expertise which are unknown a priori, and in some cases may be adversarial; (2) images may vary in their level of difficulty; and (3) multiple labels for the same image must be combined to provide an estimate of the actual label of the image. Probabilistic approaches provide a principled way to approach these problems. In this paper we present a probabilistic model and use it to simultaneously infer the label of each image, the expertise of each labeler, and the difficulty of each image. On both simulated and real data, we demonstrate that the model outperforms the commonly used ``Majority Vote heuristic for inferring image labels, and is robust to both adversarial and noisy labelers.

We study the problem of decision-theoretic online learning (DTOL). Motivated by practical applications, we focus on DTOL when the number of actions is very large. Previous algorithms for learning in this framework have a tunable learning rate parameter, and a major barrier to using online-learning in practical applications is that it is not understood how to set this parameter optimally, particularly when the number of actions is large. In this paper, we offer a clean solution by proposing a novel and completely parameter-free algorithm for DTOL. In addition, we introduce a new notion of regret, which is more natural for applications with a large number of actions. We show that our algorithm achieves good performance with respect to this new notion of regret; in addition, it also achieves performance close to that of the best bounds achieved by previous algorithms with optimally-tuned parameters, according to previous notions of regret.

This paper introduces a new method for semi-supervised learning on high dimensional nonlinear manifolds, which includes a phase of unsupervised basis learning and a phase of supervised function learning. The learned bases provide a set of anchor points to form a local coordinate system, such that each data point x on the manifold can be locally approximated by a linear combination of its nearby anchor points, and the linear weights become its local coordinate coding. We show that a high dimensional nonlinear function can be approximated by a global linear function with respect to this coding scheme, and the approximation quality is ensured by the locality of such coding. The method turns a difficult nonlinear learning problem into a simple global linear learning problem, which overcomes some drawbacks of traditional local learning methods.

We propose a general method called truncated gradient to induce sparsity in the weights of online-learning algorithms with convex loss. This method has several essential properties. First, the degree of sparsity is continuous---a parameter controls the rate of sparsification from no sparsification to total sparsification. Second, the approach is theoretically motivated, and an instance of it can be regarded as an online counterpart of the popular $L_1$-regularization method in the batch setting. We prove that small rates of sparsification result in only small additional regret with respect to typical online-learning guarantees. Finally, the approach works well empirically. We apply it to several datasets and find that for datasets with large numbers of features, substantial sparsity is discoverable.

Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al., 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al., 2008) in constrained clustering. Although in theory SDPs can be efficiently solved, the high computational complexity incurred in numerically processing the huge linear matrix inequality constraints has rendered the SDP approach unscalable. In this paper, we show that a large class of kernel learning problems can be reformulated as semidefinite-quadratic-linear programs (SQLPs), which only contain a simple positive semidefinite constraint, a second-order cone constraint and a number of linear constraints. These constraints are much easier to process numerically, and the gain in speedup over previous approaches is at least of the order $m^{2.5}$, where m is the matrix dimension. Experimental results are also presented to show the superb computational efficiency of our approach.

The purpose of the paper is to explore the connection between multivariate homogeneity testsand AUC optimization. The latter problem has recently received much attention in the statistical learning literature. From the elementary observation that,in the two-sample problem setup, the null assumption corresponds to the situation where the area under the optimal ROC curve is equal to 1/2, we propose atwo-stage testing method based on data splitting. A nearly optimal scoring function in the AUC sense is first learnt from one of the two half-samples. Data from the remaining half-sample are then projected onto the real line and eventually rankedaccording to the scoring function computed at the first stage. The last step amounts to performing a standard Mann-Whitney Wilcoxon test in the onedimensional framework.We show that the learning step of the procedure does not affect the consistency of the test as well as its properties in terms of power, provided the ranking produced is accurate enough in the AUC sense. The results of a numerical experiment are eventually displayed in order to show the efficiency of the method.

This learning problem arises frequently in many application areas ranging from signal processing, computer vision, over robotics to computer graphics. We present a new algorithmic scheme for the solution of this general learning problem based on regularized empirical risk minimization. The regularization functional takes into account the geometry of input and output manifold, and we show that it implements a prior which is particularly natural. Moreover, we demonstrate that our algorithm performs well in a difficult surface registration problem.

We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.