16,880 research outputs found
Online Learning of Noisy Data with Kernels
We study online learning when individual instances are corrupted by
adversarially chosen random noise. We assume the noise distribution is unknown,
and may change over time with no restriction other than having zero mean and
bounded variance. Our technique relies on a family of unbiased estimators for
non-linear functions, which may be of independent interest. We show that a
variant of online gradient descent can learn functions in any dot-product
(e.g., polynomial) or Gaussian kernel space with any analytic convex loss
function. Our variant uses randomized estimates that need to query a random
number of noisy copies of each instance, where with high probability this
number is upper bounded by a constant. Allowing such multiple queries cannot be
avoided: Indeed, we show that online learning is in general impossible when
only one noisy copy of each instance can be accessed.Comment: This is a full version of the paper appearing in the 23rd
International Conference on Learning Theory (COLT 2010
Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes
Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair
Matrix completion and extrapolation via kernel regression
Matrix completion and extrapolation (MCEX) are dealt with here over
reproducing kernel Hilbert spaces (RKHSs) in order to account for prior
information present in the available data. Aiming at a faster and
low-complexity solver, the task is formulated as a kernel ridge regression. The
resultant MCEX algorithm can also afford online implementation, while the class
of kernel functions also encompasses several existing approaches to MC with
prior information. Numerical tests on synthetic and real datasets show that the
novel approach performs faster than widespread methods such as alternating
least squares (ALS) or stochastic gradient descent (SGD), and that the recovery
error is reduced, especially when dealing with noisy data
Identification of functionally related enzymes by learning-to-rank methods
Enzyme sequences and structures are routinely used in the biological sciences
as queries to search for functionally related enzymes in online databases. To
this end, one usually departs from some notion of similarity, comparing two
enzymes by looking for correspondences in their sequences, structures or
surfaces. For a given query, the search operation results in a ranking of the
enzymes in the database, from very similar to dissimilar enzymes, while
information about the biological function of annotated database enzymes is
ignored.
In this work we show that rankings of that kind can be substantially improved
by applying kernel-based learning algorithms. This approach enables the
detection of statistical dependencies between similarities of the active cleft
and the biological function of annotated enzymes. This is in contrast to
search-based approaches, which do not take annotated training data into
account. Similarity measures based on the active cleft are known to outperform
sequence-based or structure-based measures under certain conditions. We
consider the Enzyme Commission (EC) classification hierarchy for obtaining
annotated enzymes during the training phase. The results of a set of sizeable
experiments indicate a consistent and significant improvement for a set of
similarity measures that exploit information about small cavities in the
surface of enzymes
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