Related papers: Learning Discriminative Stein Kernel for SPD Matri…

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…

Symmetric positive definite (SPD) matrices are useful for capturing second-order statistics of visual data. To compare two SPD matrices, several measures are available, such as the affine-invariant Riemannian metric, Jeffreys divergence,…

Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…

Stein variational gradient descent (SVGD) and its variants have shown promising successes in approximate inference for complex distributions. In practice, we notice that the kernel used in SVGD-based methods has a decisive effect on the…

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…

Kernelized Stein discrepancy (KSD), though being extensively used in goodness-of-fit tests and model learning, suffers from the curse-of-dimensionality. We address this issue by proposing the sliced Stein discrepancy and its scalable and…

Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

A central challenge in Bayesian inference is efficiently approximating posterior distributions. Stein Variational Gradient Descent (SVGD) is a popular variational inference method which transports a set of particles to approximate a target…

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…

Learning a kernel matrix from relative comparison human feedback is an important problem with applications in collaborative filtering, object retrieval, and search. For learning a kernel over a large number of objects, existing methods face…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis…

The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of…