Related papers: Learning Random Kernel Approximations for Object R…
In this paper, we propose a fast surrogate leverage weighted sampling strategy to generate refined random Fourier features for kernel approximation. Compared to the current state-of-the-art method that uses the leverage weighted scheme…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
The transcriptomics of cancer tumors are characterized with tens of thousands of gene expression features. Patient prognosis or tumor stage can be assessed by machine learning techniques like supervised classification tasks given a gene…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Few-shot learning deals with the fundamental and challenging problem of learning from a few annotated samples, while being able to generalize well on new tasks. The crux of few-shot learning is to extract prior knowledge from related tasks…
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
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…
Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We…
In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions…
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations…
This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…
Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…
The method of random Fourier features (RFF), proposed in a seminal paper by Rahimi and Recht (NIPS'07), is a powerful technique to find approximate low-dimensional representations of points in (high-dimensional) kernel space, for…
The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective…
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…