We consider the problem of recovering a low-rank tensor from its noisy observation.

We then take a discriminative approach, training linear and simple non-linear classifiers to identify learning rules from features based on these observables.

Consequently, the iteration of SGD, unlike GD, is not deterministic even when it is started at a fixed initial condition.

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate covariance function parameter posteriors. This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in support of the function but otherwise free-form. The result is a Hybrid Monte-Carlo sampling scheme which allows for a non-Gaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducing-point sparse GPs. Code to replicate each experiment in this paper is available at github.com/sparseMCMC .

Neural Information Processing Systems http://nips.cc/

We have made the source code available.

Modern prediction problems arising in multilabel learning and learning to rank pose unique challenges to the classical theory of supervised learning. These problems have large prediction and label spaces of a combinatorial nature and involve sophisticated loss functions. We offer a general framework to derive mistake driven online algorithms and associated loss bounds. The key ingredients in our framework are a general loss function, a general vector space representation of predictions, and a notion of margin with respect to a general norm. Our general algorithm, Predtron, yields the perceptron algorithm and its variants when instan-tiated on classic problems such as binary classification, multiclass classification, ordinal regression, and multilabel classification. For multilabel ranking and subset ranking, we derive novel algorithms, notions of margins, and loss bounds. A simulation study confirms the behavior predicted by our bounds and demonstrates the flexibility of the design choices in our framework.