Systems and methods are disclosed for operating a Restricted Boltzmann Machine (RBM) by determining a corrected energy function of high-order semi-RBMs (hs-RBMs) without self-interaction; performing distributed pre-training of the hs-RBM; adjusting weights of the hs-RBM using contrastive divergence; generating predictions by Gibbs Sampling or by determining conditional probabilities with hidden units integrated out; and generating predictions.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for operating a Restricted Boltzmann Machine (RBM), comprising: determining a corrected energy function of high-order semi-RBMs (hs-RBMs) without self-interaction; performing distributed pre-training of the hs-RBM; adjusting weights of the hs-RBM using contrastive divergence; generating predictions by Gibbs Sampling or by determining conditional probabilities with hidden units integrated out; generating predictions. 2. The method of claim 1, wherein the distributed pre-training comprises maximizing pseudo-log-likelihood using alternating direction method of multipliers (ADMM). 3. The method of claim 1, comprising deploying mcRBM and high-order semi-RBMs on discrete data for large-scale matrix completion and collaborative filtering. 4. The method of claim 1, comprising performing distributed optimization for training RBM and high-order semi-RBM. 5. The method of claim 1, comprising training the hs-RBM in a probabilistic discriminative way by integrating out hidden units. 6. The method of claim 1, comprising training a mean-covariance RBM (mcRBM). 7. The method of claim 6, wherein the mcRBM is an undirected graphical model that defines a joint distribution over the configurations of visible units v and hidden units h by an energy function in which there is no connection between hidden units. 8. The method of claim 7, comprising determining the energy function as: E  ( υ , h g , h m ) = 1 2  ∑ f   ( ∑ i   υ i  C if ) 2  ( ∑ k   h k  w kf ) - ∑ i   α i  υ i - ∑ k   b k  h k g - ∑ ij   υ i  h j m  w ij - ∑ k   c k  h k m where Hm and hg, respectively, denotes mean hidden units and covariance hidden units. 9. The method of claim 7, comprising modifying the energy function of the mcRBM for modeling binary data as: E  ( υ , h g , h m ) = - 1 2  ∑ f   ( ( ∑ i   υ i  C if ) 2 - ∑ i   υ i 2  Cif 2 )  ( ∑ k   h k  w kf ) - ∑ ij   υ i  h j m  w ij + bias_terms 10. The method of claim 1, comprising using the hs-RBM for modeling continuous data. 11. The method of claim 1, comprising using an absolute value of the energy terms to ensure a final energy function is bounded below for hs-RBMs with an odd number of feature interactions. 12. The method of claim 11, comprising modeling mean and third-order interactions between continuous feature values using an energy function without correction E  ( υ , h g   3 , h m ) = 1 3  ∑ f   ( abs ( ∑ i   υ i  C if ) ) 3  ( ∑ k   h k g   3  w kf ) - ∑ i   α i  υ i - ∑ k   b k  h k g   3 - ∑ ij   υ i  h j m  wij - ∑ k   c k  h k m . 13. The method of claim 1, comprising performing Distributed Learning of hs-RBM using alternating direction method of multipliers (ADMM). 14. The method of claim 13, comprising maximizing pseudo-log-likelihood of training data and using ADMM to split computations across different visible units to learn parameters as a warm start, and using contrastive divergence to fine-tune the parameters to approximately maximize the log-likelihood of the training data. 15. The method of claim 1, comprising performing discriminative training of hs-RBM by integrating out hidden units. 16. The method of claim 15, comprising making predictions using hs-RBM with a visible unit to denote a class label y. 17. The method of claim 16, comprising determining a conditional probability of p(y|x) by integrating out all hidden units. 18. The method of claim 16, comprising applying a stochastic gradient descent to optimize parameters by maximizing the sum of the log-conditional probabilities over training data.