Related papers: Learning from the Kernel and the Range Space

Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…

We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…

Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…

Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…

Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…

A key property of neural networks (both biological and artificial) is how they learn to represent and manipulate input information in order to solve a task. Different types of representations may be suited to different types of tasks,…

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…