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Learning curves are a fundamental primitive in supervised learning, describing how an algorithm's performance improves with more data and providing a quantitative measure of its generalization ability. Formally, a learning curve plots the…
Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…
We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…
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…
$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…
Fine-grained visual classification (FGVC) aims to distinguish the sub-classes of the same category and its essential solution is to mine the subtle and discriminative regions. Convolution neural networks (CNNs), which employ the cross…
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel. We explore a numerical approximation approach to kernel…
Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…
Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels.…
This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…
Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are…
Deep Reinforcement Learning (RL) has demonstrated success in solving complex sequential decision-making problems by integrating neural networks with the RL framework. However, training deep RL models poses several challenges, such as the…
This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the role of key properties of the kernel, such as its spectral…
In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the…
Predicting student performance under varying data distributions is a challenging task. This study proposes a method to improve prediction accuracy by employing transfer learning techniques on the dataset with varying distributions. Using…
Transfer learning has become an essential technique to exploit information from the source domain to boost performance of the target task. Despite the prevalence in high-dimensional data, heterogeneity and heavy tails are insufficiently…
In the recent past, automatic selection or combination of kernels (or features) based on multiple kernel learning (MKL) approaches has been receiving significant attention from various research communities. Though MKL has been extensively…