Collaborative Filtering as AutoEncoding

After doing some reading it seems Collaborative Filtering, or the process of minimizing the distance $Y_{ij}-\mathbf{\Theta}_{jl}\mathbf{X}_{il}$ by alternately fitting for $\mathbf{\Theta}_{jl}$ and $\mathbf{X}_{il}$ is the same as sparse autoencoding, or using a restricted Boltzman machine. Will have more to say about this, in particular regarding Lasso -- L1 regularization -- regression and non-negative matrix factorization