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πVAE: a stochastic process prior for Bayesian deep learning with MCMC [article]

Swapnil Mishra, Seth Flaxman, Tresnia Berah, Harrison Zhu, Mikko Pakkanen, Samir Bhatt
2022 arXiv   pre-print
We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder (πVAE).  ...  The πVAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use πVAE to learn low dimensional embeddings of function classes.  ...  πVAE is a stochastic process Claim. πVAE is a stochastic process. Proof.  ... 
arXiv:2002.06873v5 fatcat:u7qfhxo6wjdqtnqyuwqf22wdce

ℱ-EBM: Energy Based Learning of Functional Data [article]

Jen Ning Lim, Sebastian Vollmer, Lorenz Wolf, Andrew Duncan
2022 arXiv   pre-print
The proposed infinite-dimensional EBM employs a latent Gaussian process, which is weighted spectrally by an energy function parameterised with a neural network.  ...  Recently, Mishra et al. [2020] proposed π-VAE, a method for encoding stochastic processes using variational autoencoders, as a means of developing an efficient prior for stochastic process models.  ...  The encoder and decoder was a 3-layer neural network with 512 hidden units with ReLU activations with the same skip connection. We trained the model up to 1000 epochs with early stopping. • π-VAE.  ... 
arXiv:2202.01929v1 fatcat:gb7my555nff27ixyzbmzwypgsm

A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges [article]

Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, Vladimir Makarenkov, Saeid Nahavandi
2021 arXiv   pre-print
Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes.  ...  (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring  ...  Since VAEs are not stochastic processes, they are limited to encode finite-dimensional priors. To alleviate this limitation, Mishra et al. [137] developed the prior encoding VAE, i.e., πVAE.  ... 
arXiv:2011.06225v4 fatcat:wwnl7duqwbcqbavat225jkns5u

A review of uncertainty quantification in deep learning: Techniques, applications and challenges

Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U. Rajendra Acharya, Vladimir Makarenkov, Saeid Nahavandi
2021 Information Fusion  
recent advances in UQ methods used in deep learning, investigates the application of these methods in reinforcement learning, and highlights fundamental research challenges and directions associated with  ...  Uncertainty quantification (UQ) methods play a pivotal role in reducing the impact of uncertainties during both optimization and decision making processes.  ...  Since VAEs are not stochastic processes, they are limited to encoding finite-dimensional priors. To address this limitation, Mishra et al. [137] developed the prior encoding VAE, i.e., 𝜋VAE.  ... 
doi:10.1016/j.inffus.2021.05.008 fatcat:yschhguyxbfntftj6jv4dgywxm