Related papers: Gaussian RBF Centered Kernel Alignment (CKA) in th…

In this paper, we study error bounds for {\em Bayesian quadrature} (BQ), with an emphasis on noisy settings, randomized algorithms, and average-case performance measures. We seek to approximate the integral of functions in a {\em…

Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. One popular approach is to formulate it as an optimization problem using the generalized median. Previous methods like…

Neural responses encode information that is useful for a variety of downstream tasks. A common approach to understand these systems is to build regression models or ``decoders'' that reconstruct features of the stimulus from neural…

A key property of neural networks driving their success is their ability to learn features from data. Understanding feature learning from a theoretical viewpoint is an emerging field with many open questions. In this work we capture…

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…

We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random…

Analyzing the similarity of internal representations has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such…

Molecules are commonly represented as SMILES strings, which can be readily converted to fixed-size molecular fingerprints. These fingerprints serve as feature vectors to train ML/DL models for molecular property prediction tasks in the…

Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two…

Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS)…

Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being…

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

The goal of this work is to shed light on the remarkable phenomenon of transition to linearity of certain neural networks as their width approaches infinity. We show that the transition to linearity of the model and, equivalently, constancy…

The rate of convergence of weighted kernel herding (WKH) and sequential Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating integrals with respect to some target probability measure, is investigated. Under…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Despite the recent deep learning (DL) revolution, kernel machines still remain powerful methods for action recognition. DL has brought the use of large datasets and this is typically a problem for kernel approaches, which are not scaling up…

With the inspiration of vision transformers, the concept of depth-wise convolution revisits to provide a large Effective Receptive Field (ERF) using Large Kernel (LK) sizes for medical image segmentation. However, the segmentation…

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…

Modern deep networks are heavily overparameterized yet often generalize well, suggesting a form of low intrinsic complexity not reflected by parameter counts. We study this complexity at initialization through the effective rank of the…