Related papers: Model selection of polynomial kernel regression

This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression under the framework of learning theory. The algorithm…

In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…

This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown…

In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the…

Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence…

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…

We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…

Regularization plays a vital role in the context of deep learning by preventing deep neural networks from the danger of overfitting. This paper proposes a novel deep learning regularization method named as DL-Reg, which carefully reduces…

Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…

Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly…

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on…

Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…

Regularization is a well recognized powerful strategy to improve the performance of a learning machine and $l^q$ regularization schemes with $0<q<\infty$ are central in use. It is known that different $q$ leads to different properties of…