相关论文: Approximate Gaussianity Beyond Initialisation in N…

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

There has been a recent surge of interest in modeling neural networks (NNs) as Gaussian processes. In the limit of a NN of infinite width the NN becomes equivalent to a Gaussian process. Here we demonstrate that for an ensemble of large,…

Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties…

Given a determinate (multivariate) probability measure $\mu$, we characterize Gaussian mixtures $\nu\_\phi$ which minimize the Wasserstein distance $W\_2(\mu,\nu\_\phi)$ to $\mu$ when the mixing probability measure $\phi$ on the parameters…

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…

We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…

A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned…

We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…

Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Neural Processes (NPs) are a class of models that learn a mapping from a context set of input-output pairs to a distribution over functions. They are traditionally trained using maximum likelihood with a KL divergence regularization term.…

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…

Lack of ground-truth MR images impedes the common supervised training of neural networks for image reconstruction. To cope with this challenge, this paper leverages unpaired adversarial training for reconstruction networks, where the inputs…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Standard formulations of GANs, where a continuous function deforms a connected latent space, have been shown to be misspecified when fitting different classes of images. In particular, the generator will necessarily sample some low-quality…

Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…

Learning generative models is challenging for a network edge node with limited data and computing power. Since tasks in similar environments share model similarity, it is plausible to leverage pre-trained generative models from the cloud or…

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

Learning probability distributions on the weights of neural networks (NNs) has recently proven beneficial in many applications. Bayesian methods, such as Stein variational gradient descent (SVGD), offer an elegant framework to reason about…