Each computer of a peer-to-peer (P2P) network performs an iterative computer-based modeling task defined by a set of training data including at least some training data that are not accessible to the other computers of the P2P network, and by a set of parameters including a shared parameter. The modeling task optimizes an objective function comparing a model parameterized by the set of parameters with the training data. Each iteration includes: performing an iterative gradient step update of parameter values stored at the computer based on the objective function; receiving parameter values of the shared parameter from other computers of the P2P network; adjusting the parameter value of the shared parameter stored at the computer by averaging the received parameter values; and sending the parameter value of the shared parameter stored at the computer to other computers of the P2P network.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A non-transitory storage medium storing instructions executable by a local computer to perform iterative computer-based modeling in conjunction with an electronic communication system configured to send parameter values of shared parameters from the local computer to remote computer-based modeling systems and to receive at the local computer parameter values of the shared parameters from remote computer-based modeling systems, the iterative computer-based modeling including the operations of: performing a gradient step to update parameter values of a set of parameters including at least parameter values of the shared parameters stored at the local computer, the iterative gradient step updates operating to optimize an objective function that is functionally dependent upon the set of parameters wherein the objective function quantitatively compares a model with a set of training data including at least some training data accessible by the local computer that are not accessible by the remote computer-based modeling systems; adjusting the parameter values of the shared parameters stored at the local computer by averaging parameter values of the shared parameters received at the local computer from remote computer-based modeling systems via the electronic communication system; and sending the parameter values of the shared parameters stored at the local computer from the local computer to remote computer-based modeling systems via the electronic communication system. 2. The non-transitory storage medium of claim 1 wherein each iteration of the iterative modeling process includes performing an iterative gradient step update, adjusting the parameter values, and sending the parameter values. 3. The non-transitory storage medium of claim 2 wherein in each iteration of the iterative modeling process the sending is performed after the adjusting and comprises sending the adjusted parameter values. 4. The non-transitory storage medium of claim 2 wherein the adjusting comprises adjusting the parameter value of each shared parameter by averaging the parameter values of the shared parameter received at the local computer according to: θui←auiiθui+Σ{θuij∈qui}auijθuij where θu denotes the shared parameter, θui is the parameter value for the shared parameter that is output by the iterative update, θuij ∈ qui is the set of parameter values for the shared parameter received at the local computer from remote computer-based modeling systems via the electronic communication system, auii is a weight assigned to the parameter value of the shared parameter stored at the local computer, and auij is a weight assigned to the parameter value of the shared parameter received at the local computer from the jth remote computer-based modeling system via the electronic communication system. 5. The non-transitory storage medium of claim 4 wherein Σ(auii+Σ{θuij∈qui}auij)=1 and the weights auii and auij have non-negative values. 6. The non-transitory storage medium of claim 4 wherein the iterative gradient step update comprises updating each shared parameter θu according to θui←auiiθui−γui∇θufi(θi) where fi(θi) denotes the objective function that is functionally dependent upon the set of parameters denoted θi, ∇θu denotes a gradient operator with respect to the shared parameter θu, and γui denotes a step size for the iterative gradient step update. 7. The non-transitory storage medium of claim 4 wherein the iterative gradient step update comprises a matrix factorization update factorizing a matrix Yi representing the set of training data into factor matrices Ui and Vi defined by the set of parameters θi to optimize an objective function fi(θi) quantifying a difference |UiVi−Yi|. 8. The non-transitory storage medium of claim 7 wherein the training data comprises text-based documents, the matrix Yi represents the text-based documents as a document-word matrix, the factor matrix Ui comprises parameters of the set of parameters representing document embeddings which are not shared parameters, and the factor matrix Vi comprises parameters of the set of parameters representing word embeddings which are the shared parameters of the set of parameters. 9. A computer-based modeling system comprising: a plurality of computers interconnected as a peer-to-peer (P2P) network by an electronic communication system configured to send parameter values of shared parameters between sender and recipient computers of the P2P network, wherein each computer of the P2P network is programmed to perform an iterative computer-based modeling task defined by a set of training data including at least some training data that are not accessible to the other computers of the P2P network and by a set of parameters including one or more shared parameters, the iterative computer-based modeling task optimizing an objective function that quantitatively compares a model parameterized by the set of parameters with the set of training data, wherein each iteration of the iterative computer-based modeling task includes: performing an iterative gradient step update of parameter values of the set of parameters stored at the computer based on the objective function; receiving parameter values of the one or more shared parameters of the set of parameters from other computers of the P2P network via the electronic communication system; adjusting the parameter values of the one or more shared parameters stored at the computer by averaging the received parameter values of the one or more shared parameters; and sending the parameter values of the one or more shared parameters stored at the computer to other computers of the P2P network via the electronic communication system. 10. The computer-based modeling system of claim 9 wherein in each iteration of the computer-based modeling the adjusting is performed after the iterative gradient step update and the sending is performed after the adjusting. 11. The computer-based modeling system of claim 9 wherein the adjusting comprises adjusting the parameter value of each shared parameter by averaging the parameter values of the shared parameter received at the local computer according to: θui←auiiθui+Σ{θuij∈qui}auijθuij where θu denotes the shared parameter, θui is the parameter value for the shared parameter stored at the computer before the updating, θuij ∈ qui is the set of parameter values for the shared parameter received during the receiving operation, auii is a weight assigned to the parameter value of the shared parameter stored at the computer, and auij is a weight assigned to the parameter value of the shared parameter received during the receiving operation from a jth other computer of the P2P network. 12. The computer-based modeling system of claim 11 wherein Σ(auii+Σ{θuij∈qui}auij)=1 and the weights auii and auij have non-negative values. 13. The computer-based modeling system of claim 11 wherein the iterative gradient step update comprises a matrix factorization update factorizing a matrix Yi representing the set of training data into factor matrices Ui and Vi defined by the set of parameters θi to optimize an objective function fi(θi) quantifying a difference |UiVi−Yi|. 14. The computer-based modeling system of claim 13 wherein the training data comprises text-based documents, the matrix Yi represents the text-based documents as a document-word matrix, the factor matrix Ui comprises parameters of the set of parameters representing document embeddings which are not shared parameters, and the factor matrix Vi comprises parameters of the set of parameters representing word embeddings which are the shared parameters of the set of parameters. 15. The computer-based modeling system of claim 9 wherein two computers of the P2P network are programmed to perform iterative computer-based modeling tasks with different models parameterized by different sets of parameters having at least one shared parameter in common. 16. The computer-based modeling system of claim 9 wherein the electronic communication system defines a Uniform Resource Identifier (URI) representing each shared parameter, and the receiving and sending operations each comprise accessing the one or more URIs representing the one or more shared parameters. 17. A method performed in conjunction with a plurality of computers interconnected as a peer-to-peer (P2P) network, the method comprising: at each computer of the P2P network, performing an iterative computer-based modeling task using the computer to optimize an objective function that quantitatively measures the fit of a model parameterized by a set of parameters including one or more shared parameters to a set of training data including at least some training data not accessible by the other computers of the P2P network, wherein each iteration of the iterative computer-based modeling task includes: performing an iterative gradient step update of parameter values of the set of parameters stored at the computer to improve the fit of the model to the set of training data as measured by the objective function; receiving parameter values of the one or more shared parameters from other computers of the P2P network; after performing the iterative gradient step update, adjusting the parameter values of the one or more shared parameters stored at the computer by averaging the received parameter values of the one or more shared parameters; and after performing the adjusting, sending the parameter values of the one or more shared parameters stored at the computer to other computers of the P2P network. 18. The method of claim 17 wherein the adjusting comprises adjusting the parameter value of each shared parameter by averaging the received parameter values of the shared parameter according to: θui←auiiθui+Σ{θuij∈qui}auijθuij where θu denotes the shared parameter, θui is the parameter value for the shared parameter stored at the computer before the updating, θuij ∈ qui is the set of parameter values for the shared parameter received during the receiving operation, auii is a weight assigned to the parameter value of the shared parameter stored at the computer, and auij is a weight assigned to the parameter value of the shared parameter received during the receiving operation from a jth other computer of the P2P network. 19. The method of claim 17 wherein the iterative computer-based modeling task comprises matrix factorization of a matrix Yi representing the set of training data into factor matrices Ui and Vi defined by the set of parameters, and the objective function measures the fit of the product UiVi to the matrix Yi. 20. The method of claim 19 wherein the training data comprises text-based documents and the matrix Yi represents the text-based documents as a document-word matrix. 21. The method of claim 17 wherein different computers of the P2P network perform generally different iterative computer-based modeling tasks with generally different models parameterized by generally different sets of parameters but having some shared parameters in common.