arXiv research

Improved kernel quadrature with convex weights using subsampling.

We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to rela…

Kernel balancing weights are generalized as KRRR, providing better confidence intervals for treatment effects.

Toeplitz operators linked to submultiplicative filtrations and weighted Bergman kernels.

Develops method to construct Lie algebra weight system kernel using Vogel algebra.

The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.

The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse performance than using a single kernel. There are two possible reasons for the fail…

The paper studies invariant weighted Bergman metrics on domains.

New graph kernel for weighted directed networks using functor homology.

The study examines Fisher information matrices and neural tangent kernels for simple ReLU networks with random weights.

An interesting approach to analyzing neural networks that has received renewed attention is to examine the equivalent kernel of the neural network. This is based on the fact that a fully connected feedforward network with one hidden layer, a certain weight distribution, an activation function, and an infinite number of…

The paper develops heat kernel comparison theorems and applies them to spectral geometry.

Kernel Quantization improves CNN compression without sacrificing performance.

A new kernel measures brain network similarities, improving disease classification.

Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features wit…

Multiple kernel learning (MKL), structured sparsity, and multi-task learning have recently received considerable attention. In this paper, we show how different MKL algorithms can be understood as applications of either regularization on the kernel weights or block-norm-based regularization, which is more common in str…

Improved kernel ridge regression for large datasets using weighted random binning.

Generalizes neural tangent kernel analysis for two-layer networks with noise and regularization.

Fundamental weight systems identified as quantum states.

A novel Bayesian computation method using importance weighting improves numerical stability and performance.

The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.

Network quantization is one of the most hardware friendly techniques to enable the deployment of convolutional neural networks (CNNs) on low-power mobile devices. Recent network quantization techniques quantize each weight kernel in a convolutional layer independently for higher inference accuracy, since the weight ker…

New summary measures reveal geometric structure in weighted measures on manifolds.

Propose an XMSE-aware mixed estimator for EB that interpolates between ML and EB shrinkage.

We empirically investigate the best trade-off between sparse and uniformly-weighted multiple kernel learning (MKL) using the elastic-net regularization on real and simulated datasets. We find that the best trade-off parameter depends not only on the sparsity of the true kernel-weight spectrum but also on the linear dep…

Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed on the selected kernel. This note contributes to the study of universal, characte…

Positive weights improve kernel quadrature's accuracy.

In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels us…

Unified framework evaluates different nearest neighbor classification methods.

New method for causal inference with complex treatment compositions.

A new kernel improves tensor classification accuracy and reduces computation time.

The paper proposes a novel MKL approach for OCC using $\ell_p$-norm constraints.

Paper proposes a robust LPR method using similarity kernels.

Functional input neural networks approximate continuous functions on weighted spaces.

New random feature maps for Laplacian and related kernels.

In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the companion paper to prove an orbifold version of Donaldson Theorem.

Tree data are ubiquitous because they model a large variety of situations, e.g., the architecture of plants, the secondary structure of RNA, or the hierarchy of XML files. Nevertheless, the analysis of these non-Euclidean data is difficult per se. In this paper, we focus on the subtree kernel that is a convolution kern…

In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we defin…

This paper presents a novel multitask multiple kernel learning framework that efficiently learns the kernel weights leveraging the relationship across multiple tasks. The idea is to automatically infer this task relationship in the \textit{RKHS} space corresponding to the given base kernels. The problem is formulated a…

Multi-kernel learning has been well explored in the recent past and has exhibited promising outcomes for multi-class classification and regression tasks. In this paper, we present a multiple kernel learning approach for the One-class Classification (OCC) task and employ it for anomaly detection. Recently, the basic mul…

Optimizes kernel density ratios for better predictions and information measures.

Bayesian deep neural networks converge to processes with α-stable marginals under infinite variance weights.

A new weighted FDA method improves face recognition accuracy.

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

New scalable method balances hospital profit status and heart attack outcomes.

Paper converts deep networks to flat, equivalent kernel machines.