Abstract: A distributed computing device stores user preference data representing preferences of a user with respect to a portion of a set of items. The distributed computing device randomly samples the user preference data to calculate sampled user preference data. The distributed computing device iteratively executes, in conjunction with additional distributed computing devices connected by a network, a process to determine a consensus result for the sampled user preference data. The consensus result is based on the sampled user preference data and additional sampled user preference data calculated by the additional distributed computing devices and based on preferences of additional users. The distributed computing device determines a recommendation model based on the consensus result, the recommendation model reflecting preferences of the user and additional users.

Abstract: A distributed computing device generates a gradient descent matrix based on data received by the distributed computing device and a model stored on the distributed computing device. The distributed computing device calculates a sampled gradient descent matrix based on the gradient descent matrix and a random matrix. The distributed computing device iteratively executes a process to determine a consensus gradient descent matrix in conjunction with a plurality of additional distributed computing devices connected by a network to the distributed computing device. The consensus gradient descent matrix is based on the sampled gradient descent matrix and a plurality of additional sampled gradient decent matrices calculated by the plurality of additional distributed computing devices. The distributed computing device updates the model stored on the distributed computing device based on the consensus gradient descent matrix.

Abstract: A distributed computing device calculates word counts for each of a set of documents. The word counts are represented as values, each representing a number of times a corresponding word appears in one of the set of documents. The distributed computing device randomly samples the word counts to calculate sampled word counts. The distributed computing device and additional distributed computing devices iteratively execute a process to determine a consensus result for the sampled word counts based on the sampled word counts and additional sampled word counts calculated by the additional distributed computing devices. The distributed computing device determines a latent semantic index (LSI) subspace based on the consensus result for the sampled word count and reflecting contents of the set and additional sets of documents. The distributed computing device projects a document into the LSI subspace to determine the latent semantic content of the document.

Abstract: A distributed computing device stores user preference data representing preferences of a user with respect to a portion of a set of items. The distributed computing device randomly samples the user preference data to calculate sampled user preference data. The distributed computing device iteratively executes, in conjunction with additional distributed computing devices connected by a network, a process to determine a consensus result for the sampled user preference data. The consensus result is based on the sampled user preference data and additional sampled user preference data calculated by the additional distributed computing devices and based on preferences of additional users. The distributed computing device determines a recommendation model based on the consensus result, the recommendation model reflecting preferences of the user and additional users.

Abstract: A distributed computing device calculates word counts for each of a set of documents. The word counts are represented as values, each representing a number of times a corresponding word appears in one of the set of documents. The distributed computing device randomly samples the word counts to calculate sampled word counts. The distributed computing device and additional distributed computing devices iteratively execute a process to determine a consensus result for the sampled word counts based on the sampled word counts and additional sampled word counts calculated by the additional distributed computing devices. The distributed computing device determines a latent semantic index (LSI) subspace based on the consensus result for the sampled word count and reflecting contents of the set and additional sets of documents. The distributed computing device projects a document into the LSI subspace to determine the latent semantic content of the document.

Abstract: A distributed computing device stores user preference data representing preferences of a user with respect to a portion of a set of items. The distributed computing device randomly samples the user preference data to calculate sampled user preference data. The distributed computing device iteratively executes, in conjunction with additional distributed computing devices connected by a network, a process to determine a consensus result for the sampled user preference data. The consensus result is based on the sampled user preference data and additional sampled user preference data calculated by the additional distributed computing devices and based on preferences of additional users. The distributed computing device determines a recommendation model based on the consensus result, the recommendation model reflecting preferences of the user and additional users.

Abstract: A distributed computing device calculates word counts for each of a set of documents. The word counts are represented as values, each representing a number of times a corresponding word appears in one of the set of documents. The distributed computing device randomly samples the word counts to calculate sampled word counts. The distributed computing device and additional distributed computing devices iteratively execute a process to determine a consensus result for the sampled word counts based on the sampled word counts and additional sampled word counts calculated by the additional distributed computing devices. The distributed computing device determines a latent semantic index (LSI) subspace based on the consensus result for the sampled word count and reflecting contents of the set and additional sets of documents. The distributed computing device projects a document into the LSI subspace to determine the latent semantic content of the document.

Abstract: A distributed computing device stores user preference data representing preferences of a user with respect to a portion of a set of items. The distributed computing device randomly samples the user preference data to calculate sampled user preference data. The distributed computing device iteratively executes, in conjunction with additional distributed computing devices connected by a network, a process to determine a consensus result for the sampled user preference data. The consensus result is based on the sampled user preference data and additional sampled user preference data calculated by the additional distributed computing devices and based on preferences of additional users. The distributed computing device determines a recommendation model based on the consensus result, the recommendation model reflecting preferences of the user and additional users.

Abstract: A distributed computing device generates a gradient descent matrix based on data received by the distributed computing device and a model stored on the distributed computing device. The distributed computing device calculates a sampled gradient descent matrix based on the gradient descent matrix and a random matrix. The distributed computing device iteratively executes a process to determine a consensus gradient descent matrix in conjunction with a plurality of additional distributed computing devices connected by a network to the distributed computing device. The consensus gradient descent matrix is based on the sampled gradient descent matrix and a plurality of additional sampled gradient decent matrices calculated by the plurality of additional distributed computing devices. The distributed computing device updates the model stored on the distributed computing device based on the consensus gradient descent matrix.