  Recently, partial Bayesian neural networks (pBNNs), which only consider a
subset of the parameters to be stochastic, were shown to perform competitively
with full Bayesian neural networks. However, pBNNs are often multi-modal in the
latent variable space and thus challenging to approximate with parametric
models. To address this problem, we propose an efficient sampling-based
training strategy, wherein the training of a pBNN is formulated as simulating a
Feynman--Kac model. We then describe variations of sequential Monte Carlo
samplers that allow us to simultaneously estimate the parameters and the latent
posterior distribution of this model at a tractable computational cost. Using
various synthetic and real-world datasets we show that our proposed training
scheme outperforms the state of the art in terms of predictive performance.
