Related papers: Manifold Random Features
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations…
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…
Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still…
We propose a novel parameter estimation procedure that works efficiently for conditional random fields (CRF). This algorithm is an extension to the maximum likelihood estimation (MLE), using loss functions defined by Bregman divergences…
Conditional Random Field (CRF) and recurrent neural models have achieved success in structured prediction. More recently, there is a marriage of CRF and recurrent neural models, so that we can gain from both non-linear dense features and…
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…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
This paper proposes a novel graph-based regularized regression estimator - the hierarchical feature regression (HFR) -, which mobilizes insights from the domains of machine learning and graph theory to estimate robust parameters for a…
Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…
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…
In recent years, deep learning based methods have shown success in essential medical image analysis tasks such as segmentation. Post-processing and refining the results of segmentation is a common practice to decrease the misclassifications…
Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions…
It is not until recently that graph neural networks (GNNs) are adopted to perform graph representation learning, among which, those based on the aggregation of features within the neighborhood of a node achieved great success. However,…
The recent discovery of the equivalence between infinitely wide neural networks (NNs) in the lazy training regime and Neural Tangent Kernels (NTKs) (Jacot et al., 2018) has revived interest in kernel methods. However, conventional wisdom…
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on…
Due to the dynamic nature of financial markets, maintaining models that produce precise predictions over time is difficult. Often the goal isn't just point prediction but determining uncertainty. Quantifying uncertainty, especially the…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
In this technical report, we explore the behavior of Recursive Feature Machines (RFMs), a type of novel kernel machine that recursively learns features via the average gradient outer product, through a series of experiments on regression…
Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based…