Related papers: The Uniformly Rotated Mondrian Kernel
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
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…
This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the…
Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
The use of correntropy as a similarity measure has been increasing in different scenarios due to the well-known ability to extract high-order statistic information from data. Recently, a new similarity measure between complex random…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…
The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…