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Empirically-determined scaling laws have been broadly successful in predicting the evolution of large machine learning models with training data and number of parameters. As a consequence, they have been useful for optimizing the allocation…

We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates…

Anomaly detection based on one-class classification algorithms is broadly used in many applied domains like image processing (e.g. detection of whether a patient is "cancerous" or "healthy" from mammography image), network intrusion…

Neural scaling laws provide a predictable recipe for AI advancement: reducing numerical precision should linearly improve computational efficiency and energy profile ($E \propto \mathrm{bits}$). In this paper, we demonstrate that this…

Designing categorical kernels is a major challenge for Gaussian process regression with continuous and categorical inputs. Despite previous studies, it is difficult to identify a preferred method, either because the evaluation metrics, the…

Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by…

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training…

The increased computerization in recent years has resulted in the production of a variety of different software, however measures need to be taken to ensure that the produced software isn't defective. Many researchers have worked in this…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite…

For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions:…

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…

This work concerns a comparison of SVM kernel methods in text categorization tasks. In particular I define a kernel function that estimates the similarity between two objects computing by their compressed lengths. In fact, compression…

Semi-supervised learning plays an important role in large-scale machine learning. Properly using additional unlabeled data (largely available nowadays) often can improve the machine learning accuracy. However, if the machine learning model…

Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and…

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning…

Accurate estimation of dataset complexity is crucial for evaluating and comparing link prediction models for knowledge graphs (KGs). The Cumulative Spectral Gradient (CSG) metric derived from probabilistic divergence between classes within…

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…

Low precision training and inference affect both the quality and cost of language models, but current scaling laws do not account for this. In this work, we devise "precision-aware" scaling laws for both training and inference. We propose…