Primer on Bayesian Deep Learning

Author:Murphy | View: 21134 | Time: 2025-03-23 19:59:04

Introduction

This article belongs to the series "Probabilistic Deep Learning". This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e., know what they do not know.

Bayesian Deep Learning is an emerging field that combines the expressiveness and representational power of deep learning with the uncertainty modeling capabilities of Bayesian methods. The integration of these two paradigms offers a principled framework for addressing various challenges in deep learning, such as overfitting, weight uncertainty, and model comparison.

In this article, we provide a comprehensive introduction to Bayesian Deep Learning, covering its foundations, methodology, and recent advances. Our aim is to present the fundamental concepts and ideas in a clear and accessible manner, making it an ideal resource for researchers and practitioners who are new to the field.

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Figure 1: Motto for today: it is layers all the way down (source)

Deterministic, Probabilistic and Bayesian Deep Learning

Deep learning has achieved remarkable success in a wide range of applications, including computer vision, natural language processing, and game playing. Despite its successes, traditional deep learning models are inherently deterministic and provide limited ability to quantify uncertainty in their predictions. To address this issue, Bayesian deep learning and probabilistic deep learning have emerged as important paradigms that allow for incorporating uncertainty into deep learning models.

Bayesian deep learning and probabilistic deep learning represent important paradigms for incorporating uncertainty into deep learning models. These approaches offer several advantages over traditional deterministic deep learning, including the ability to provide uncertainty estimates and the ability to perform robust inference in the presence of out-of-distribution data.

In Bayesian deep learning, the model parameters are treated as random variables and a prior distribution is placed over them. This prior represents prior knowledge about the model parameters, such as their expected values or their distributional shape. The posterior distribution over the parameters is then updated through Bayesian inference, using the data to form a posterior that represents our updated beliefs about the parameters given the data. This results in a distribution over the model parameters and a measure of uncertainty in the model predictions.

Probabilistic deep learning, on the other hand, models the data-generating process as a probabilistic function. Given an input, the model predicts a distribution over outputs, allowing for the quantification of uncertainty in predictions. This approach is particularly useful for problems where the output space is complex, such as image generation or speech synthesis. In these cases, modeling the data-generating process as a probabilistic function allows for the capture of complex patterns in the data and the generation of high-quality outputs.

Both Bayesian deep learning and probabilistic deep learning are important and active areas of research, with recent advances in techniques such as Bayesian neural networks, variational inference, and deep generative models. Despite their potential benefits, these approaches remain challenging due to the computational and statistical difficulties posed by high-dimensional models and the large amounts of data typically used in deep learning. Nevertheless, significant progress has been made in this field in recent years, and there is much excitement and potential for future research in Bayesian deep learning and probabilistic deep learning.