Abstract: A treatment model that is a first neural network is trained to optimize a treatment loss function based on a treatment variable t using a plurality of observation vectors by regressing t on x(1),z. The trained treatment model is executed to compute an estimated treatment variable value {circumflex over (t)}i for each observation vector. An outcome model that is a second neural network is trained to optimize an outcome loss function by regressing y on x(2) and an estimated treatment variable t. The trained outcome model is executed to compute an estimated first unknown function value {circumflex over (?)}(xi(2)) and an estimated second unknown function value {circumflex over (?)}(xi(2)) for each observation vector. An influence function value is computed for a parameter of interest using {circumflex over (?)}(xi(2)) and {circumflex over (?)}(xi(2)). A value is computed for the predefined parameter of interest using the computed influence function value.

Abstract: Exemplary embodiments relate to the problem of determining measurements in a distributed computing environment in which observations relating to the measurements are distributed amongst two or more nodes. Each node, which stores a number of node-specific observations, makes available its observation count and a number of observation sketches. The observations are merged into an array, and the sketches from each node are combined into overall summary sketches representing a summary of the observations across all the nodes. The summary sketches may then be used to approximate the measurement. The described techniques allow for the computation of arbitrary measurements (i.e., measurements that are not predetermined and for whose calculation the environment is not preconfigured) in a grid computing environment with a technical advantage of having very few rounds of data communication (e.g., two or less) required between the nodes in the computing grid.

Abstract: Exemplary embodiments relate to the problem of determining measurements in a distributed computing environment in which observations relating to the measurements are distributed amongst two or more nodes. Each node, which stores a number of node-specific observations, makes available its observation count and a number of observation sketches. The observations are merged into an array, and the sketches from each node are combined into overall summary sketches representing a summary of the observations across all the nodes. The summary sketches may then be used to approximate the measurement. The described techniques allow for the computation of arbitrary measurements (i.e., measurements that are not predetermined and for whose calculation the environment is not preconfigured) in a grid computing environment with a technical advantage of having very few rounds of data communication (e.g., two or less) required between the nodes in the computing grid.

Abstract: A computing device determines upper and lower bounds of a largest singular value for an approximate decomposition of a dataset. An approximate decomposition is computed using either a principal components or a singular value decomposition algorithm. A lower bound of a largest singular value is computed for the computed approximate decomposition using a first linear approximation to a function of a singular value ratio. A first set of coefficients for a second linear approximation to an error function is computed for the function of the singular value ratio using the computed approximate decomposition. A second set of coefficients for a third linear approximation is computed using the computed first set of coefficients. An upper bound of the largest singular value is computed using the computed second set of coefficients. The upper bound and the lower bound are output to provide an estimate of a quality of the decomposition.