Related papers: Kernel-Gradient Drifting Models
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…
Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the…
We propose Drifting Field Policy (DFP), a non-ODE one-step generative policy built on the drifting model paradigm. We frame the policy update as a reverse-KL Wasserstein-2 gradient flow toward a soft target policy, so that each DFP update…
Artificial neural networks have revolutionized machine learning in recent years, but a complete theoretical framework for their learning process is still lacking. Substantial advances were achieved for wide networks, within two disparate…
In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on…
Permutation invariance is fundamental in molecular point-cloud generation, yet most diffusion models enforce it indirectly via permutation-equivariant networks on an ordered space. We propose to model diffusion directly on the quotient…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…
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.…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…
Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for…