Estimation of MMD (maximum mean discrepancy, a divergence measure on kernel-endowed domains) in the presence of outliers, using the median-of-means principle.
Adaptivity: features & kernel parameters are chosen to optimize power. The power of the tests matches quadratic-time tests. The returned features indicate why the two distributions differ.
Applications:
NLP (distinguishing articles from two categories),
computer vision (differentiating positive and negative emotions).
A gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure from the sample path, by fitting an exponential family model in a Reproducing Kernel Hilbert Space.
Applications:
sampling from the marginal posterior of hyper-parameters in Gaussian process classification,
A probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships; 'Bayesian LLE'.
Application: climate data analysis.
Kernel-EP (Kernel based just-in-time Expectation Propagation):
A fast, online algorithm for nonparametric learning of EP message updates.
Structured-sparse dictionary learning method which (i) is online, (ii) allows overlapping group structures with (iii) non-convex group-structure inducing regularization, and (iv) handles incomplete observations.