arXiv research

Grassmannian packings improve CNN kernels' diversity and reduce sparsity.

2L-FUSE enhances feature sparsity through kernel learning.

Enhances KLR for indefinite kernels with $L_1$-norm regularization.

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…

Paper extends KPCA using dualization for faster, more robust algorithms.

The paper introduces a new method for feature selection without explicit sparsification.

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…

Exact Gaussian Processes for massive datasets using non-stationary sparsity-discovering kernels.

Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations between datasets. Despite their wide usage, they have one common limitation that…

The paper examines how kernel approximations affect Gaussian process regression in large data applications.

We present a data dependent generalization bound for a large class of regularized algorithms which implement structured sparsity constraints. The bound can be applied to standard squared-norm regularization, the Lasso, the group Lasso, some versions of the group Lasso with overlapping groups, multiple kernel learning a…

Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular network connections that not only demand extra representation efforts but also …

Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed under $\ell_1$ sparsity constrain (prior) in the input domain, recent studies hav…

This paper approximates scattered data using samplet coordinates with sparsity constraints.

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In …

New kernel enables exact GP analysis of massive datasets.

New GPU kernels boost deep learning speed and memory efficiency.

Study on signal detection in sparse additive models with nonasymptotic minimax rates.

Enhanced kernel ridgeless regression improves performance with LAB RBF kernels.

We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt sequentially. This is achieved by formulating the estimator as a probabilistic mode…

Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, severa…

Model compression techniques on Deep Neural Network (DNN) have been widely acknowledged as an effective way to achieve acceleration on a variety of platforms, and DNN weight pruning is a straightforward and effective method. There are currently two mainstreams of pruning methods representing two extremes of pruning reg…

Improved kernel herding algorithm for faster quadrature rule convergence.

We investigate the learning rate of multiple kernel learning (MKL) with $\ell_1$ and elastic-net regularizations. The elastic-net regularization is a composition of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total …

Deep neural networks define suitable reproducing kernel Banach spaces.

A new method discovers equations from data using Bayesian and kernel techniques.

Abstract perspective on quadratic programming for optimal portfolio allocation.

We consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernel…

A general framework of least squares support vector machine with low rank kernels, referred to as LR-LSSVM, is introduced in this paper. The special structure of low rank kernels with a controlled model size brings sparsity as well as computational efficiency to the proposed model. Meanwhile, a two-step optimization al…

In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised learning in a continuous-domain hybrid search space with gTV regu…

Paper converts deep networks to flat, equivalent kernel machines.

Study sparsity benefits in infinite feature contextual bandits.

Randomized feature models learn interaction kernels from agent paths.

Rocket algorithm classifies time-series data efficiently using random projections and natural sparsity.

A new method quickly identifies key variables and interactions.

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approa…

Wider neural networks perform better than deeper ones with the same number of parameters.

We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in the sparsity of the system and not in its size, and allows to provide error estim…

SpeqNets improve graph neural networks by scaling and adapting to graph sparsity.

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately, kernel means are faced with scalability issues. A single point evaluation of the …

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast…

Paper develops a new kernel expansion method using entropic optimal features for sparse and efficient kernel approximation.

TransBoost improves financial inclusion by evaluating individual financial risk.

TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.

Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing, promotes the nonparametric basi…

A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a certain class. In this paper, we forge a connection between random forests and ke…

Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.

New sparse GP model learns compositional kernels efficiently.