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Subsampled natural gradient descent (SNG) has been used to enable high-precision scientific machine learning, but standard analyses based on stochastic preconditioning fail to provide insight into realistic small-sample settings. We…

We present UncertaintyRAG, a novel approach for long-context Retrieval-Augmented Generation (RAG) that utilizes Signal-to-Noise Ratio (SNR)-based span uncertainty to estimate similarity between text chunks. This span uncertainty enhances…

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Backpropagation underpins modern deep learning, yet its reliance on global gradient synchronization limits scalability and incurs high memory costs. In contrast, fully local learning rules are more efficient but often struggle to maintain…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Localizing more sources than sensors with a sparse linear array (SLA) has long relied on minimizing a distance between two covariance matrices and recent algorithms often utilize semidefinite programming (SDP). Although deep neural network…

Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…

Stochastic variational inference is an established way to carry out approximate Bayesian inference for deep models. While there have been effective proposals for good initializations for loss minimization in deep learning, far less…

Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…

Fine-tuned Large Language Models (LLMs) often suffer from overconfidence and poor calibration, particularly when fine-tuned on small datasets. To address these challenges, we propose a simple combination of Low-Rank Adaptation (LoRA) with…

Standard deep learning relies on Backpropagation (BP), which is constrained by biologically implausible weight symmetry and suffers from significant gradient interference within dense representations. To mitigate these bottlenecks, we…

The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…

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…

We consider the use of deep learning for covariance estimation. We propose to globally learn a neural network that will then be applied locally at inference time. Leveraging recent advancements in self-supervised foundational models, we…

Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of…