Systems and method are disclosed for determining complex interactions among system inputs by using semi-Restricted Boltzmann Machines (RBMs) with factorized gated interactions of different orders to model complex interactions among system inputs; applying semi-RBMs to train a deep neural network with high-order within-layer interactions for learning a distance metric and a feature mapping; and tuning the deep neural network by minimizing margin violations between positive query document pairs and corresponding negative pairs.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for determining complex interactions among system inputs, comprising: using semi-Restricted Boltzmann Machines (RBMs) with factorized gated interactions of different orders to model complex interactions among system inputs, applying semi-RBMs to train a deep neural network with high-order within-layer interactions for learning a distance metric and a feature mapping; and tuning the deep neural network by minimizing margin violations between positive query document pairs and corresponding negative pairs. 2. The method of claim 1, comprising identifying complex nonlinear system input interactions for data denoising and data visualization. 3. The method of claim 1, wherein the semi-RBMs have gated interactions with a combination of orders ranging from 1 to m to approximate an arbitrary-order combinatorial input feature interactions in words and in Transcription Factors (TFs). 4. The method of claim 1, wherein hidden units of the semi-RBMs act as binary switches controlling interactions between input features. 5. The method of claim 1, comprising using factorization to reduce the number of parameters. The method of claim 1, comprising sampling from the semi-RBMs by using either fast deterministic damped mean-field updates or prolonged Gibbs sampling. 6. The method of claim 1, wherein parameters of semi-RBMs are learned using Contrastive Divergence. 7. The method of claim 1, wherein after a semi-RBM is learned, comprising treating inferred hidden activities of input data as new data to learn another semi-RBM and forming a deep belief net with gated high order interactions. 8. The method of claim 1, wherein with pairs of discrete representations of a query and a document, using semi-RBMs with gated arbitrary-order interactions to pre-train a deep neural network and generating a similarity score between a query and a document, in which a penultimate layer corresponds to a non-linear feature embedding of the original system input features. 9. The method of claim 8, further comprising using back-propagation to fine-tune parameters of the deep gated high-order neural network to make positive pairs of query, wherein document always have larger similarity scores than negative pairs based on margin maximization. 10. The method of claim 1, comprising modeling complex interactions between different words in documents and queries and predicting the bindings of TFs given some other TFs for understanding deep semantic information for information retrieval and TF binding redundancy and TF interactions for gene regulation. 11. The method of claim 1, comprising applying high-order semi-RBMs for modeling feature interactions including word interactions in documents or protein interactions in biology. 12. The method of claim 1, wherein the deep neural network has multiple layers. 13. The method of claim 1, comprising providing a given discretized query and document representation as input to a non-linear SSI system, and applying the semi-RBMs to pre-train the SSI system. 14. The method of claim 13, comprising fine-tuning the non-linear SSI system using back-propagation to minimize a margin-based rank loss. 15. The method of claim 13, wherein the discrete document representation includes a Bag of Word representation or a discretized term frequency—inverse document frequency(TF-IDF) representation. 16. The method of claim 1, comprising training by minimizing a margin ranking loss on a tuple (q, d+, d−): ∑ ( q , d + , d - )  max  ( 0 , 1 - f  ( q , d + ) + f  ( q , d - ) ) , where q is the query, d+ is a relevant document, and d− is an irrelevant document, f(·,·) is a similarity score.