*13 March 2017*

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

- understanding: 7/10
- code: github.com/clinicalml/structuredinference

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

- form of
- the reformulation of the ELBO

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 posteriorâ€¦

other forms of such as

- ,
- ,
- ,
- ,

but performs best.

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

experiments on

- 2d linear gaussian state space model:
- is in
- is in
- is 25
- (number of data sets) is 5000

- polyphonic music
- is in ??
- is in
- is ??
- is ??

- ehr patient data
- is in
- is in
- is 18
- is 15000

- Krishnan, R. G., Shalit, U., & Sontag, D. (2017). Structured Inference Networks for Nonlinear State Space Models. In
*AAAI*.@inproceedings{krishnan2016structured, title = {Structured Inference Networks for Nonlinear State Space Models}, author = {Krishnan, Rahul G and Shalit, Uri and Sontag, David}, booktitle = {AAAI}, year = {2017} }

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