Xerox Corporation

Shengbo Guo

Guillaume M Bouchard

Onno R Zoeter

Christopher R Dance

Jean-Marc Andreoli

Cedric Archambeau

Mihajlo Grbovic

Dawei Yin

A system and method for generating an occupancy model are disclosed. The model is learned using occupancy data for zones, each zone including cells, which are occupied or not at a given time, each with a sensor, which may be reporting or not. The data provides an observed occupancy corresponding to a number of cells in the respective zone which have reporting sensors, and the number of those sensors which are reporting that the respective cell is occupied. The occupancy model is based on a demand model and a sensor noise model which accounts for behavior of the non-reporting sensors. The noise model assumes that the probability of a sensor being in the reporting state is dependent on whether the respective cell is occupied or not. The model can fit the occupancy data better than one which assumes that non-reporting cells are occupied with the same frequency as reporting ones.

System and method for generating an occupancy model

A method operates on observed relationship data between pairs of entities of a set of entities including entities of at least two (and optionally at least three) different entity types. An observed collective symmetric matrix is constructed in which element (n,m)=element (m,n) stores the observed relationship between entities indexed n and m when the observed relationship data includes this observed relationship. A prediction collective symmetric matrix is optimized in order to minimize a loss function comparing the observed collective symmetric matrix and the prediction collective symmetric matrix. A relationship between two entities of the set of entities is predicted using the optimized prediction collective symmetric matrix. Entities of the same entity type may be indexed using a contiguous set of indices such that the entity type maps to a contiguous set of rows and corresponding contiguous set of columns in the observed collective symmetric matrix.

Convex collective matrix factorization

Multi-task regression or classification includes optimizing parameters of a Bayesian model representing relationships between D features and P tasks, where D&#x2267;1 and P&#x2267;1, respective to training data comprising sets of values for the D features annotated with values for the P tasks. The Bayesian model includes a matrix-variate prior having features and tasks dimensions of dimensionality D and P respectively. The matrix-variate prior is partitioned into a plurality of blocks, and the optimizing of parameters of the Bayesian model includes inferring prior distributions for the blocks of the matrix-variate prior that induce sparseness of the plurality of blocks. Values of the P tasks are predicted for a set of input values for the D features using the optimized Bayesian model. The optimizing also includes decomposing the matrix-variate prior into a product of matrices including a matrix of reduced rank in the tasks dimension that encodes correlations between tasks.

Multi-task learning using bayesian model with enforced sparsity and leveraging of task correlations

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Saint Martin d'Heres, France

Shengbo Guo