So I'm going to reply to my own question in case it helps anyone else out. 
Had another look at the paper there, I had forgotten about the contrastive 
wake-sleep algorithm. That's what's used to train the algorithm completely 
unsupervised. 

On Tuesday, 12 July 2016 15:40:48 UTC+1, Jim O' Donoghue wrote:
>
> Hi There,
>
> Just wondering how you would fine-tune a DBN for a completely unsupervised 
> task i.e. practical implementation of "Fine-tune all the parameters of this 
> deep architecture with respect to a proxy for the DBN log- likelihood". 
>
> Would this be something like, for example, a negative log likelihood 
> between the original input and the reconstruction of the data when 
> propogated entirely up and down the network? What makes the final layer an 
> rbm and the rest just normally directed. Or would the only way you can do 
> this be to completely un-roll the network and fine-tune like a deep 
> autoencoder (as in reducing the dimensionality of data with neural 
> networks)? 
>
> Many thanks,
> Jim
>
>
>
>

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