Related papers: Generalising maximum mean discrepancy: kernelised …
We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to construct determinantal point processes on…
Multiple kernel learning (MKL) algorithms combine different base kernels to obtain a more efficient representation in the feature space. Focusing on discriminative tasks, MKL has been used successfully for feature selection and finding the…
A machine learning model is calibrated if its predicted probability for an outcome matches the observed frequency for that outcome conditional on the model prediction. This property has become increasingly important as the impact of machine…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
Circumcenters play an important role in the design and analysis of accelerating various iterative methods in optimization. In this work, we propose Bregman (pseudo-)circumcenters associated with finite sets. We show the existence and give…
We present a generic dynamic programming method to compute the optimal clustering of $n$ scalar elements into $k$ pairwise disjoint intervals. This case includes 1D Euclidean $k$-means, $k$-medoids, $k$-medians, $k$-centers, etc. We extend…
We study certain weighted area integral means of analytic functions in the unit disc. We relate the growth of these means to the property of being mean H\"older continuous with respect to the Bergman space norm. In contrast with earlier…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…
Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special…
Commonly used $f$-divergences of measures, e.g., the Kullback-Leibler divergence, are subject to limitations regarding the support of the involved measures. A remedy is regularizing the $f$-divergence by a squared maximum mean discrepancy…
Recent works have characterized the function-space inductive bias of infinite-width bounded-norm single-hidden-layer neural networks as a kind of bounded-variation-type space. This novel neural network Banach space encompasses many…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks correspond to function spaces that are Hilbert spaces, these…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…