Related papers: Gradient-based kernel dimension reduction for supe…

By leveraging the kernel trick in the output space, kernel-induced losses provide a principled way to define structured output prediction tasks for a wide variety of output modalities. In particular, they have been successfully used in the…

We propose an efficient distributed online learning protocol for low-latency real-time services. It extends a previously presented protocol to kernelized online learners that represent their models by a support vector expansion. While such…

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…

We in this paper consider Fr\'echet sufficient dimension reduction with responses being complex random objects in a metric space and high dimension Euclidean predictors. We propose a novel approach called weighted inverse regression…

Feature ranking and selection is a widely used approach in various applications of supervised dimensionality reduction in discriminative machine learning. Nevertheless there exists significant evidence on feature ranking and selection…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…

We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the…

This paper addresses the challenge of dimension reduction (DR) in Bayesian inference of high-resolution two-or three-dimensional fields, where a priori parametrizations require a large number of terms. The underlying idea is common to…

Representation learning is an important step in the machine learning pipeline. Given the current biological sequencing data volume, learning an explicit representation is prohibitive due to the dimensionality of the resulting feature…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…

We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error…

Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…

Deep neural networks have recently achieved state of the art performance thanks to new training algorithms for rapid parameter estimation and new regularization methods to reduce overfitting. However, in practice the network architecture…

In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to…

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…