A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Boosting Nyström improves accuracy of matrix approximations.
Derives kernel PCA with Nyström method for scalability.
This paper proposes a new Nystrom-based clustering algorithm for large-scale data.
Clarifies connections between Nyström and SVGP methods for scalable GPs.
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality approximations, the number of landmark points is chosen to be greater than the target rank. Ho…
Nyström KPCA balances computational efficiency and statistical accuracy.
Paper uses Koopman operator and Nyström method for efficient nonlinear control.
The Nyström methods have been popular techniques for scalable kernel based learning. They approximate explicit, low-dimensional feature mappings for kernel functions from the pairwise comparisons with the training data. However, Nyström methods are generally applied without the supervision provided by the training labe…
Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.
This paper tackles scalability issues in kernel logistic regression for large datasets.
We develop an improved bound for the approximation error of the Nyström method under the assumption that there is a large eigengap in the spectrum of kernel matrix. This is based on the empirical observation that the eigengap has a significant impact on the approximation error of the Nyström method. Our approach is bas…
This paper improves spectral clustering for large datasets using the Nystrom method.
Method uses NMF for clustering with partial distance measurements.
The Nyström method improves learning efficiency for convex losses.
Kernel -means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear -means clustering algorithm. However, kernel -means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel …
Nyström approximation for scalable operator learning
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we present a novel algori…
Efficiently approximates kernel mean embeddings using Nyström method.
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this as…
We give the first algorithm for kernel Nyström approximation that runs in *linear time in the number of training points* and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of landmark points sampled by their *rid…
Nystrom approximation speeds up kernel model training.
Paper analyzes Nyström regularization for time series forecasting with sequential sub-sampling.
Improved Nyström approximation for kernel quadrature with theoretical guarantees.
New methods improve efficiency of sampling algorithms for complex systems.
Skyformer uses Gaussian kernel and Nyström method to speed up self-attention in transformers.
Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nyström method and preconditioning techniques. The Nyström approximation -- based on a subset of landmarks -- gives a low rank approximation of the kernel matrix, and is known to provide a form of impl…
Improved KSD test for faster GoF testing.
In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nyström subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are provided. Particularly, optimal learning rates are derived considerin…
We study Nyström type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that these approaches can achieve optimal learning bounds, provided the subsampling leve…
Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based on rank one updates to the eigendecomposition of the kernel matrix, which is mo…
Improved kernel Stein discrepancy for large-scale data.
Two algorithms estimate Wasserstein distance matrices from few entries for manifold learning.
This paper describes a new method for low rank kernel approximation called IKA. The main advantage of IKA is that it produces a function defined as a linear combination of arbitrarily chosen functions. In contrast the approximation produced by Nyström method is a linear combination of kernel evaluations. The pro…
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, making th…
Nyström subsampling with Tikhonov regularization for covariate shift adaptation under misspecified case
This paper studies a Nyström type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood, in spite of its practical importance. To model su…
We demonstrate that distributed block coordinate descent can quickly solve kernel regression and classification problems with millions of data points. Armed with this capability, we conduct a thorough comparison between the full kernel, the Nyström method, and random features on three large classification tasks from va…
Proposes a new method for optimizing large-scale models using Nyström approximation of the Hessian.
Paper proposes Nyström sketches for better adaptive compressive learning.
Efficiently approximates statistical leverage scores for faster KRR.
The abstract presents a new theorem using Ross-Witt Nyström correspondence and Berndtsson's theorem.
New asymmetric kernel methods improve feature learning.
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. T…
The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM ker…
Efficiently tests two distributions using Nyström approximation of MMD.
Recently, Nyström method has proved its prominence empirically and theoretically in speeding up the training of kernel machines while retaining satisfactory performances and accuracy. So far, there are several different approaches proposed to exploit Nyström method in scaling up kernel machines. However, there is no co…
We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nyström approach to kernel k-means. We analyze the statistical properties of the proposed method and show that it achieves the same accuracy of exact kernel k-means with only a fraction of co…
New method speeds up kernel-based machine learning for force field reconstruction.