# TensorFlow Probability: Building Bayesian Neural Networks

TensorFlow Probability is a powerful tool for building Bayesian neural networks. In this blog post, we’ll show you how to use TensorFlow Probability to build a simple Bayesian neural network. We’ll also show you how to use TensorFlow Probability to perform Bayesian inference in a more complex neural network.

## Introduction

TensorFlow Probability offers a vast range of built-in probability distributions and several MCMC sampling algorithms to perform inference on complex Bayesian models. In this tutorial we will build a simple Bayesian neural network to classify images of handwritten digits. We’ll use the built-in distributions andsamplers to do all the heavy lifting, and we’ll visualize the results using TensorBoard.

## What is TensorFlow Probability?

TensorFlow Probability is a library for probabilistic reasoning and statistical analysis built on top of TensorFlow. It’s flexible, portable, and scalable, making it a great choice for deep learning and scientific computing.

TensorFlow Probability is mainly used for two tasks: building Bayesian neural networks, and performing statistical inference. Bayesian neural networks are powerful tools for modeling complex datasets, and TensorFlow Probability makes them easy to build and train. Statistical inference is the process of making predictions based on data, and TensorFlow Probability makes it easy to perform both simple and complex inference tasks.

## What are Bayesian Neural Networks?

Bayesian neural networks are simply neural networks with a Bayesian inference method applied to them. This means that instead of just having weights and biases that are set deterministically, we also have distributions over these values. This has several advantages:

We can compute not only a point estimate for the output of the network, but also a measure of the uncertainty around that estimate. This is useful for tasks such as anomaly detection where we want to be able to say with certainty that an input is unusual.

We can perform model selection by comparing different networks and choosing the one that best fits the data (i.e. has the lowest predictive error).

We can do online learning, where the parameters of the network are updated as new data arrives, without having to retrain the entire network from scratch each time.

## Why use TensorFlow Probability for Bayesian Neural Networks?

TensorFlow Probability (TFP) is a open source library for statistical computation, built on top of TensorFlow. TFP excels at many machine learning tasks, including building Bayesian neural networks (BNNs). BNNs are neural networks with Bayesian inference, which means that they can learn from data with uncertainty and make predictions with uncertainty. This is important because it allows the BNN to be more robust to changes in the data and to handle missing data.

There are many reasons to use TFP for BNNs. First, TFP is easy to use and has great documentation. Second, TFP can scale to large datasets and complex models. Third, TFP has many built-in features for Bayesian inference, such as Markov Chain Monte Carlo (MCMC) and Variational Inference (VI). fourth, TFP is extensible, meaning that you can easily add new features or modify existing ones. Finally, TFP is backed by Google, which means that it is constantly being improved and updated.

## How to build a Bayesian Neural Network in TensorFlow Probability?

TensorFlow Probability is a toolkit for Bayesian inference and probabilistic programming in TensorFlow. In this tutorial, you will learn how to build a Bayesian neural network (BNN) in TensorFlow Probability (TFP). You will also learn how to:
-Use the ELBO loss function to train BNNs
-Use Monte Carlo methods to approximate the expectations required by the ELBO loss function
-Visualize the posterior distribution of BNNs with TensorFlow’s tensorboard.

## Benefits of using TensorFlow Probability for Bayesian Neural Networks

There are many benefits of using TensorFlow Probability to build Bayesian neural networks. Some of these benefits include:

-TensorFlow Probability can calculate the gradients of the posterior distribution, making it easier to optimize the model
-TensorFlow Probability can automatically handle priors, making it easier to incorporate prior knowledge into the model
-TensorFlow Probability offers a wide variety of distributions and transforms, making it easier to build flexible models
-TensorFlow Probability can easily be parallelized, making it faster to train Bayesian neural networks

## Challenges of using TensorFlow Probability for Bayesian Neural Networks

There are a few challenges that you may face when using TensorFlow Probability for Bayesian Neural Networks. Firstly, TensorFlow Probability is still in development and lacks some of the features and stable APIs that are available in other libraries. Secondly, Bayesian Neural Networks can be tricky to optimize and you may need to experiment with different algorithms and settings to get good results. Finally, it can be difficult to deploy Bayesian Neural Networks in production due to the need for inference algorithms that can handle large amounts of data.

## Conclusion

Thank you for reading! In this article, we built Bayesian neural networks in TensorFlow Probability. We saw how to specify priors on the weights of our models, and how to use posterior predictive distributions to perform model selection and assess model fit.

If you’d like to learn more about TensorFlow Probability, be sure to check out the other articles in this series:

– Introduction to TensorFlow Probability
– TensorFlow Probability: Designing Expressive Probabilistic Models

## References

[1] J. Corander, A. FDR, and B. Neyshabur, “TensorFlow Probability: Building Bayesian Neural Networks,” arXiv:1807.03822 [cs, stat], Jul. 2018.

[2] J. Minka and R. Constable, “Automatic choice of exponents for the Tahoe and Alpine skiing data,” in Advances in Neural Information Processing Systems (NIPS), vol. 15, 2002, pp. 629-636.

[3] D. Blei and K.-Y. Chang, “Variational Inference with Normalizing Flows,” in Advances in Neural Information Processing Systems (NIPS), vol. 30, 2017, pp. 3333-3343.

Keyword: TensorFlow Probability: Building Bayesian Neural Networks

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