Training a Deep Belief Network (DBN) involves sequentially training Restricted Boltzmann Machines (RBMs). First, an RBM is trained to maximize $\mathbb{E}_{v\sim p_{data}}\mathbf{log}p(v)$ using contrastive divergence or stochastic maximum likelihood. Second, another RBM is trained to approximately maximize $\mathbb{E}_{v\sim p_{data}}\mathbb{E}_{h^{(1)}\sim p^{(1)}(h^{(1)}|v)}\mathbf{log}p^{(2)}(h^{(1)})$, where $p^{(1)}$ is the probability distribution represented by the first RBM and $p^{(2)}$ is the probability distribution represented by the second RBM.