Related papers: Persistence kernels for classification: A comparat…
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…
This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems for persistence barcodes, generalized persistence,…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as…
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of…
Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular,…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
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…
Kernel continual learning by \citet{derakhshani2021kernel} has recently emerged as a strong continual learner due to its non-parametric ability to tackle task interference and catastrophic forgetting. Unfortunately its success comes at the…
Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…
Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…
Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to…