Related papers: Manifold Random Features

Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional…

Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to \mathbb{R}^k$, that we interpret as random variables with…

Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance operators. We consider centered GRFs given as variational…

Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…

Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and…

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging the insight from (Ba et al.,…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…

The regularized random forest (RRF) was recently proposed for feature selection by building only one ensemble. In RRF the features are evaluated on a part of the training data at each tree node. We derive an upper bound for the number of…

We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…

Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race,…

Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are induced kernels. While…

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…

Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…

We present a simple yet powerful neural network that implicitly represents and renders 3D objects and scenes only from 2D observations. The network models 3D geometries as a general radiance field, which takes a set of 2D images with camera…

Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution for machine learning applications. This famous technique, known as Random Fourier…

Random feature (RF) method is a powerful kernel approximation technique, but is typically equipped with fixed activation functions, limiting its adaptability across diverse tasks. To overcome this limitation, we introduce the Random Feature…

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on…