Related papers: Reinforcement Learning via Gaussian Processes with…
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…
Deep reinforcement learning (DRL) has empowered a variety of artificial intelligence fields, including pattern recognition, robotics, recommendation-systems, and gaming. Similarly, graph neural networks (GNN) have also demonstrated their…
The wide adoption of Convolutional Neural Networks (CNNs) in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in…
The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation…
Deep kernel learning (DKL) and related techniques aim to combine the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. One crucial aspect of these models is an expectation that, because…
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…
A recent line of works studied wide deep neural networks (DNNs) by approximating them as Gaussian Processes (GPs). A DNN trained with gradient flow was shown to map to a GP governed by the Neural Tangent Kernel (NTK), whereas earlier works…
Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over…
Neural bandits have been shown to provide an efficient solution to practical sequential decision tasks that have nonlinear reward functions. The main contributor to that success is approximate Bayesian inference, which enables neural…
Despite the effectiveness of multitask deep neural network (MTDNN), there is a limited theoretical understanding on how the information is shared across different tasks in MTDNN. In this work, we establish a formal connection between MTDNN…
A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive…
Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition…
Reinforcement learning systems require good representations to work well. For decades practical success in reinforcement learning was limited to small domains. Deep reinforcement learning systems, on the other hand, are scalable, not…
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success in adopting a deep network for feature extraction followed by a GP…
Kernel ridge regression (KRR) and Gaussian processes (GPs) are fundamental tools in statistics and machine learning, with recent applications to highly over-parameterized deep neural networks. The ability of these tools to learn a target…
Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…
Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data…
A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a…