Tuan Anh Le

structured inference networks for nonlinear state space models (wip)

13 March 2017

notes on (Krishnan, Shalit, & Sontag, 2017).

basically vae on state space models (SSMs): learn model parameters of SSMs and at the same time learn an inference network. the SSM under consideration is the standard SSM. but the transition is a neural net. emission is also a neural net. everything is gaussian.

the novelty lies in

  1. form of
  2. the reformulation of the ELBO

form of

takes in the form \begin{align} q_{\phi}(x_{1:T} \given y_{1:T}) = q_{\phi}(x_1 \given x_1, \dotsc, x_T) \prod_{t = 2}^T q_{\phi}(x_t \given x_{t - 1}, y_t, \dotsc, y_T), \end{align} i.e. condition only on the last and the future s. this comes from considering the conditional independence structure of the posterior…

other forms of such as

but performs best.

reformulation of the ELBO

the elbo has some sort of weird form because everything is gaussian. reparametrization trick is thus not needed… check eq. 6.


experiments on


  1. Krishnan, R. G., Shalit, U., & Sontag, D. (2017). Structured Inference Networks for Nonlinear State Space Models. In AAAI.
      title = {Structured Inference Networks for Nonlinear State Space Models},
      author = {Krishnan, Rahul G and Shalit, Uri and Sontag, David},
      booktitle = {AAAI},
      year = {2017}