Related papers: Learning the Kernel for Classification and Regress…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…
Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification,…
In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such…
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…
We introduce property-independent kernels for machine learning modeling of arbitrarily many molecular properties. The kernels encode molecular structures for training sets of varying size, as well as similarity measures sufficiently diffuse…
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…
Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…
Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
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…
Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the…
The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…
The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses…
Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…
In this article, we show that solving the system of linear equations by manipulating the kernel and the range space is equivalent to solving the problem of least squares error approximation. This establishes the ground for a gradient-free…
Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
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…