相关论文: The Mondrian Kernel

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…

Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not…

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…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

Modeling multiple sampling densities within a hierarchical framework enables borrowing of information across samples. These density random effects can act as kernels in latent variable models to represent exchangeable subgroups or clusters.…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…

Random forests are a popular class of algorithms used for regression and classification. The algorithm introduced by Breiman in 2001 and many of its variants are ensembles of randomized decision trees built from axis-aligned partitions of…

Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successful general-purpose machine learning algorithms of modern times. In this…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…

Dot product kernels, such as polynomial and exponential (softmax) kernels, are among the most widely used kernels in machine learning, as they enable modeling the interactions between input features, which is crucial in applications like…

The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive…

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we…

To present Mercer large-scale kernel machines from a ridge function perspective, we recall the results by Lin and Pinkus from {\it Fundamentality of ridge functions}. We consider the main result of the recent paper by Rachimi and Recht,…

Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…