Related papers: Quadrature-based features for kernel approximation
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
There is currently a huge effort to understand the potential and limitations of variational quantum machine learning (QML) based on the optimization of parameterized quantum circuits. Recent proposals toward dequantizing variational QML…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way…
Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…
An infinitely wide model is a weighted integration $\int \varphi(x,v) d \mu(v)$ of feature maps. This model excels at handling an infinite number of features, and thus it has been adopted to the theoretical study of deep learning. Kernel…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…
Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…
Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
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…
The proliferation of high-dimensional data from sources such as social media, sensor networks, and online platforms has created new challenges for clustering algorithms. Multi-view clustering, which integrates complementary information from…
Positive-definite kernel functions are fundamental elements of kernel methods and Gaussian processes. A well-known construction of such functions comes from Bochner's characterization, which connects a positive-definite function with a…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
The Neural Tangent Kernel (NTK) has discovered connections between deep neural networks and kernel methods with insights of optimization and generalization. Motivated by this, recent works report that NTK can achieve better performances…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
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…