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Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded…
Particle image velocimetry (PIV) is an effective tool in experimental fluid mechanics to extract flow fields from images. Recently, convolutional neural networks (CNNs) have been used to perform PIV analysis with accuracy on par with…
The willingness to trust predictions formulated by automatic algorithms is key in a vast number of domains. However, a vast number of deep architectures are only able to formulate predictions without an associated uncertainty. In this…
Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome…
Batch Normalization (BN) has proven to be an effective algorithm for deep neural network training by normalizing the input to each neuron and reducing the internal covariate shift. The space of weight vectors in the BN layer can be…
The standard approaches to neural network implementation yield powerful function approximation capabilities but are limited in their abilities to learn meta representations and reason probabilistic uncertainties in their predictions.…
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…
Classical parameter-space Bayesian inference for Bayesian neural networks (BNNs) suffers from several unresolved prior issues, such as knowledge encoding intractability and pathological behaviours in deep networks, which can lead to…
Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap,…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…
Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network from finite samples of input-output pairs is often referred to…
Mathematical solvers use parametrized Optimization Problems (OPs) as inputs to yield optimal decisions. In many real-world settings, some of these parameters are unknown or uncertain. Recent research focuses on predicting the value of these…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et…
To reduce training costs, several Deep neural networks (DNNs) that can learn from a small set of HF data and a sufficient number of low-fidelity (LF) data have been proposed. In these established neural networks, a parallel structure is…
Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from…
Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability…
Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…