Incorporating invariances into a learning algorithm is a common problem in machine learning. We provide a convex formulation which can deal with arbitrary loss functions and arbitrary losses. In addition, it is a drop-in replacement for most optimization algorithms for kernels, including solvers of the SVMStruct family. The advantage of our setting is that it relies on column generation instead of modifying the underlying optimization problem directly.

Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing the variance of their embeddings while preserving the local distances of the original data. We show that MVU also optimizes a statistical dependence measure which aims to retain the identity of individual observations under the distancepreserving constraints. This general view allows us to design "colored" variants of MVU, which produce low-dimensional representations for a given task, e.g.

We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1/ɛ) steps to ɛ precision for general convex problems and in O(log(1/ɛ)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.

We derive an equation for temporal difference learning from statistical principles. Specifically, we start with the variational principle and then bootstrap to produce an updating rule for discounted state value estimates. The resulting equation is similar to the standard equation for temporal difference learning with eligibility traces, so called TD(λ), however it lacks the parameter α that specifies the learning rate. In the place of this free parameter there is now an equation for the learning rate that is specific to each state transition. We experimentally test this new learning rule against TD(λ) and find that it offers superior performance in various settings. Finally, we make some preliminary investigations into how to extend our new temporal difference algorithm to reinforcement learning. To do this we combine our update equation with both Watkins' Q(λ) and Sarsa(λ) and find that it again offers superior performance without a learning rate parameter.

Although kernel measures of independence have been widely applied in machine learning (notably in kernel ICA), there is as yet no method to determine whether they have detected statistically significant dependence. We provide a novel test of the independence hypothesis for one particular kernel independence measure, the Hilbert-Schmidt independence criterion (HSIC).

We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to max-product but unlike max-product it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable parameters such as step size or tree weights. We also describe a generalization of the method to cluster based potentials. The new method is tested on synthetic and real-world problems, and compares favorably with previous approaches.

Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing thevariance of their embeddings while preserving the local distances of the original data. We show that MVU also optimizes a statistical dependence measure which aims to retain the identity of individual observations under the distancepreserving constraints.This general view allows us to design "colored" variants of MVU, which produce low-dimensional representations for a given task, e.g.

Incorporating invariances into a learning algorithm is a common problem in machine learning.We provide a convex formulation which can deal with arbitrary loss functions and arbitrary losses. In addition, it is a drop-in replacement for most optimization algorithms for kernels, including solvers of the SVMStruct family. The advantage of our setting is that it relies on column generation instead of modifying theunderlying optimization problem directly.

Guided by the goal of obtaining an optimization algorithm that is both fast and yielding good generalization, we study the descent direction maximizing the decrease in generalization error or the probability of not increasing generalization error. The surprising result is that from both the Bayesian and frequentist perspectives this can yield the natural gradient direction. Although that direction can be very expensive to compute we develop an efficient, general, online approximation to the natural gradient descent which is suited to large scale problems. We report experimental results showing much faster convergence in computation time and in number of iterations with TONGA (Topmoumoute Online natural Gradient Algorithm) than with stochastic gradient descent, even on very large datasets.

Statistical tests of independence have been associated with a broad variety of dependence measures. Classical tests such as Spearman's,0 and Kendall's 7' are widely applied, however they are not