Currently there are several theories for how neural activity may represent probability distributions.

In practice, however, recursive updating often leads to poor trade-off solutions across tasks because approximate inference is necessary for most models of interest.

It is often convenient to model high-dimensional datasets as probability distributions.

We will often use variational optimization. When the variational family is not made explicit it means that the optimization is over all functions with the correct domain and codomain, e.g.

The prior and likelihood are both modelling choices. A.1 Likelihoods for BNNs The likelihood is purely a function of the model prediction Φ As exact posterior inference via (11) is intractable, we instead rely on approximate inference algorithms, which can be broadly grouped into two classes based on their method of approximation. A concrete label can be obtained by choosing the class with highest output value. The Gaussian variational family is a common choice. Estimators for the integral in (15) are necessary.

Work done while at Harvard University.

Undirected graphical models are compact representations of joint probability distributions over random variables. To solve inference tasks of interest, graphical models of arbitrary topology can be trained using empirical risk minimization.

We demonstrate that BootDQNprior+'s lagged target parameters, which are essential to its performance, arise from applying approximate inference to the BBO posterior.