Method and system for data analysis and synthesis
AssigneeThe University of Sydney
InventorsArman Melkumyan, Fabio Tozeto Ramos
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Abstract
A system (100) for analysing and synthesising a plurality of sources of sample data (310, 320) by automated learning and regression. The system includes data storage (110) with a stored multi-task covariance function, and an evaluation processor (102) in communication with the data storage (110). The evaluation processor (102) performs regression using the stored sample data and multi-task covariance function and synthesises prediction data for use in graphical display or digital control.
Claims31
A system for analyzing and synthesizing data from a plurality of sources of sample data by Gaussian process learning and regression, the system comprising:
- data storage with a stored multi-task covariance function and associated hyperparameters, and
- an evaluation processor in communication with the data storage that:
- performs Gaussian process regression using the stored sample data and multi-task covariance function with the hyperparameters and
- synthesizes prediction data for use in graphical display or digital control,
- wherein the multi-task covariance function is a combination of a plurality of stationary covariance functions.
A method of computerized data analysis and synthesis for estimation of a desired first quantity comprising:
- measuring the first quantity and at least one other second quantity within a domain of interest to generate first and second sampled datasets,
- storing the sampled datasets,
- selecting first and second stationary covariance functions for application to the first and second datasets,
- determining a multi-task covariance function determined from the selected first and second covariance functions,
- training a multi-task Gaussian process by computing and storing optimized hyperparameter values associated with the multi-task covariance function using the stored first and second datasets, and
- performing Gaussian process regression using the selected multi-task covariance function, computed and stored hyperparameters and stored datasets to predict unknown values of the first quantity within the domain of interest.
A method for determining a Gaussian process for regression of a plurality of related tasks comprising:
- receiving a data set associated with each one of the plurality of related tasks;
- receiving one covariance function associated with each one of the related tasks;
- and
- using the data sets and covariance functions to determine a multi-task covariance function, for use with the multi-task Gaussian process.
A method for evaluating a task from a Gaussian process regression model, wherein the task is one of a plurality of dependent tasks, and the Gaussian process regression model includes a Gaussian process, the Gaussian process being associated with a covariance function, the covariance function being a multi-task covariance function.
A computer program comprising machine-readable program code for controlling the operation of a data processing apparatus on which the program code executes to perform a method for determining a Gaussian process for regression of a plurality of related tasks comprising:
- receiving a data set associated with each one of the plurality of related tasks;
- receiving one covariance function associated with each one of the related tasks;
- and
- using the data sets and covariance functions to determine a multi-task covariance function, for use with the multi-task Gaussian process.
A computer program product comprising machine-readable program code recorded on a machine-readable recording medium, for controlling the operation of a data processing apparatus on which the program code executes to perform a method for determining a Gaussian process for regression of a plurality of related tasks comprising:
- receiving a data set associated with each one of the plurality of related tasks;
- receiving one covariance function associated with each one of the related tasks;
- and
- using the data sets and covariance functions to determine a multi-task covariance function, for use with the multi-task Gaussian process.
A system for analyzing a plurality of data sets, each data set associated with a single-task covariance function, the system comprising:
- a multi-task Gaussian process training processor that analyzes the plurality of data sets simultaneously to determine a multi-task covariance function,
- wherein the multi-task covariance function is a combination of the single-task covariance functions.
A system for synthesizing a data set from a test input data set, wherein the data set comprises data from one of a plurality of data types, each data type being associated with a single-task covariance function, the system comprising:
- a multi-task Gaussian process associated with a multi-task covariance function, wherein the multi-task covariance function is a combination of the single-task covariance functions;
- and
- a Gaussian process evaluation processor that inputs the test input data set, and uses the multi-task Gaussian process to synthesize the data set.
A method for computer regression of a plurality of related tasks, the method comprising:
- receiving a data set associated with each one of the plurality of related modelling tasks;
- assigning a data set kernel for each of the data sets;
- simultaneously modelling the data sets using a kernel process in which the kernel is a convolution of the data set kernels.
A method for computer regression of a plurality of related tasks, the method comprising:
- receiving values for inputs X, targets y, covariance function K, noise level σn2, and test input X*, wherein X, y and X* are in the form of block vectors and K is in the form of a block matrix comprising covariance functions for each input X along its diagonal and cross-covariance functions formed by a convolution of covariance functions outside of its diagonal;
- applying the covariance function K to the inputs X, targets y, noise level σn2, and test input X*, in a predictive process and outputting a model of the inputs X.
A computer system or computer readable medium including instructions for a method comprising:
- receiving a data set associated with each one of a plurality of related modelling tasks;
- simultaneously modelling the data sets using a kernel process in which the kernel is a convolution of kernels assigned to each data set.
A computer system or computer readable medium including instructions for a method comprising:
- implementing regression of a plurality of related tasks, by:
- receiving values for inputs X, targets y, covariance function K, noise level σn2, and test input X*, wherein X, y and X* are in the form of block vectors and K is in the form of a block matrix comprising covariance functions for each input X along its diagonal and cross-covariance functions formed by a convolution of covariance functions outside of its diagonal;
- applying the covariance function K to the inputs X, targets y, covariance function K, noise level σn2, and test input X*, in a predictive process and outputting a model of the inputs X.
Dependencies are inferred from the claim text.