MullOverThing

Useful tips for everyday

# Is MCMC variational inference?

## Is MCMC variational inference?

Thus, variational inference is suited to large data sets and scenarios where we want to quickly explore many models; MCMC is suited to smaller data sets and scenarios where we happily pay a heavier computational cost for more precise samples.

### What are Bayesian neural network posteriors really like?

What Are Bayesian Neural Network Posteriors Really Like? The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. To in- vestigate foundational questions in Bayesian deep learning, we instead use full-batch Hamiltonian Monte Carlo (HMC) on modern architectures.

#### How does Bayesian neural network work?

A Bayesian neural network (BNN) refers to extending standard networks with posterior inference. Standard NN training via optimization is (from a probabilistic perspective) equivalent to maximum likelihood estimation (MLE) for the weights. Using MLE ignores any uncertainty that we may have in the proper weight values.

Where is variational inference used?

In modern machine learning, variational (Bayesian) inference, which we will refer to here as variational Bayes, is most often used to infer the conditional distribution over the latent variables given the observations (and parameters). This is also known as the posterior distribution over the latent variables.

How is ELBO calculated?

The ELBO is the negative KL diver- gence of Equation (12) plus log p(x), which is a constant with respect to q(z). Maximizing the ELBO is equivalent to minimizing the KL divergence. = [log p(x|z)] − KL (q(z)p(z)).

## Is variational inference faster than MCMC?

We find that variational inference is much faster than MCMC and nested sampling techniques for most of these problems while providing competitive results.

### Why is MCMC Bayesian?

MCMC can be used in Bayesian inference in order to generate, directly from the “not normalised part” of the posterior, samples to work with instead of dealing with intractable computations.

#### Are neural networks Bayesian?

Bayesian neural networks are stochastic neural networks with priors. with all other possible parametrizations discarded. The cost function is often defined as the log likelihood of the training set, sometimes with a regularization term to penalize parametrizations.

What is Bayesian deep learning?

A Bayesian Neural Network (BNN) is simply posterior inference applied to a neural network architecture. To be precise, a prior distribution is specified for each weight and bias. Because of their huge parameter space, however, inferring the posterior is even more difficult than usual.

Are Bayesian neural networks useful?

Bayesian neural nets are useful for solving problems in domains where data is scarce, as a way to prevent overfitting. Example applications are molecular biology and medical diagnosis (areas where data often come from costly and difficult experimental work).

## Is deep learning Bayesian?

Bayesian deep learning is a field at the intersection between deep learning and Bayesian probability theory. These deep architectures can model complex tasks by leveraging the hierarchical representation power of deep learning, while also being able to infer complex multi-modal posterior distributions.