# Neural Autoregressive Density Estimation
Inspired by [[Boltzmann Machines#Restricted Boltzmann Machines]] but with tractable density estimation Each conditional modelled with sigmoidal neural net like in RBMs.
Parameter matrix $W$ maps past inputs $v_{<i}$ to hidden feature $\boldsymbol{h}_{i}$
Parameter matrix $V$ generates pixel $v_{i}$ given the hidden feature $\boldsymbol{h}_{i}$
Map past input to a hidden state, only take into account past inputs
$
\boldsymbol{h}_{i}=\sigma\left(\boldsymbol{c}+W_{:<i} \boldsymbol{v}_{<i}\right)
$
Sample future ouput given a hidden state
$
p\left(v_{i} \mid v_{<i}\right)=\sigma\left(b_{i}+\left(V^{T}\right)_{i,} \boldsymbol{h}_{i}\right)
$
Uses teacher forcing for training
- During training use ground truth past inputs $v_{<i}$
- During testing use predicted past inputs $\hat{v}_{<i}$
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## References