Abstract: A tensor decomposition method, system, and computer program product include compressing multi-dimensional data by truncated tensor-tensor decompositions.

Abstract: Methods and systems for model discovery include forming a mathematical program based on a set of observational data to generate an objective function and one or more constraints. The mathematical program represents a model space as an expression tree comprising operators and operands. The mathematical program is solved by optimizing the objective function subject to the one or more constraints to determine a model in the model space that best fits the set of observational data.

Abstract: Techniques for generating and managing, including simulating and training, deep tensor neural networks are presented. A deep tensor neural network comprises a graph of nodes connected via weighted edges. A network management component (NMC) extracts features from tensor-formatted input data based on tensor-formatted parameters. NMC evolves tensor-formatted input data based on a defined tensor-tensor layer evolution rule, the network generating output data based on evolution of the tensor-formatted input data. The network is activated by non-linear activation functions, wherein the weighted edges and non-linear activation functions operate, based on tensor-tensor functions, to evolve tensor-formatted input data. NMC trains the network based on tensor-formatted training data, comparing output training data output from the network to simulated output data, based on a defined loss function, to determine an update.

Abstract: A computer-implemented method is presented for optimal experimental design to correct a misspecified model approximating a behavior of a dynamic system. The method includes formulating an experiment, determining experimental settings for configuring controllable experimental parameters based on mutual information and submodularity, measuring informative values associated with each choice of experimental design, as prescribed by the controllable experimental parameters, and learning a correction function based on the measured informative values. The computer-implemented method further includes determining an experimental design setup for gaining information content, and combining the experimental design setup with the experimental settings to construct a corrected model of the dynamic system.

Abstract: A system, method and computer program product for quickly and approximately solving structured regression problems. In one aspect, the system, method and computer program product are applied to problems that arise naturally in various statistical modeling settings—when the design matrix is a Vandermonde matrix or a sequence of such matrices. Using the Vandermonde matrix structure further accelerates the solution of the regression problem, achieving running times that are faster than “input sparsity”. The modeling framework speedup benefits of randomized regression for solving structured regression problems.

Abstract: A method includes computing a diffusion vector starting with a seed, querying nodes for connections, reweighting diffusion vector based on the degrees, sorting nodes based upon magnitude in the reweighted diffusion vector which is obtained through wave relaxation solution of a time-dependent initial value problem, detecting a community through a sweep over the nodes according to their rank, and selecting a prefix that minimizes or maximizes an objective function.

Abstract: Embodiments of the invention relate to sketching for M-estimators for performing regression. One embodiment includes providing one or more sets of input data. A matrix A and a vector b are generated using the input data. A processor device is used for processing the matrix A and the vector b based on a randomized sketching matrix S. A vector x that minimizes a normalized measure function is determined based on the matrix A and the vector b. A relationship between the input data is determined based on the vector x.

Abstract: Methods and systems for model discovery include forming a mathematical program based on a set of observational data to generate an objective function and one or more constraints. The mathematical program represents a model space as an expression tree comprising operators and operands. The mathematical program is solved by optimizing the objective function subject to the one or more constraints to determine a model in the model space that best fits the set of observational data.

Abstract: Embodiments of the invention relate to sketching for M-estimators for performing regression. One embodiment includes providing one or more sets of input data. A matrix A and a vector b are generated using the input data. A processor device is used for processing the matrix A and the vector b based on a randomized sketching matrix S. A vector x that minimizes a normalized measure function is determined based on the matrix A and the vector b. A relationship between the input data is determined based on the vector x.

Abstract: A system, method and computer program product for quickly and approximately solving structured regression problems. In one aspect, the system, method and computer program product are applied to problems that arise naturally in various statistical modeling settings—when the design matrix is a Vandermonde matrix or a sequence of such matrices. Using the Vandermonde matrix structure further accelerates the solution of the regression problem, achieving running times that are faster than “input sparsity”. The modeling framework speedup benefits of randomized regression for solving structured regression problems.

Abstract: Systems and methods to reduce I/O (input/output) with regard to out-of-core liner solvers and/or to speed up out-of-core linear solvers.

Abstract: Systems and methods to reduce I/O (input/output) with regard to out-of-core liner solvers and/or to speed up out-of-core linear solvers.