Related papers: Random Fourier Signature Features
Kernel mean embedding is a useful tool to represent and compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and…
To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the…
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…
Recently, there has been an increased interest in the development of kernel methods for learning with sequential data. The signature kernel is a learning tool with potential to handle irregularly sampled, multivariate time series. In…
Kernel methods are powerful tools in statistical learning, but their cubic complexity in the sample size n limits their use on large-scale datasets. In this work, we introduce a scalable framework for kernel regression with O(n log n)…
We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly parameterized CDEs act as continuous-time reservoirs, mapping…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size,…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…
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…
In recent years, kernel methods are widespread in tasks of similarity measuring. Specifically, graph kernels are widely used in fields of bioinformatics, chemistry and financial data analysis. However, existing methods, especially entropy…
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to…