Analytic system based on multiple task learning with incomplete data

A computing device comprising:

• a processor;
• and
• a non-transitory computer-readable medium operably coupled to the processor, the computer-readable medium having computer-readable instructions stored thereon that, when executed by the processor, cause the computing device to
• for each of a plurality of related tasks,
• compute an augmented observation matrix using an observation matrix and a predefined probability value that a value is missing in the observation matrix, wherein the observation matrix includes a plurality of observation vectors, wherein each observation vector includes a plurality of values, wherein each value of the plurality of values is associated with a variable to define a plurality of variables;
• compute a plug-in autocovariance matrix using the computed augmented observation matrix and a noise value;
• and
• compute a plug-in covariance vector using a target vector, the computed augmented observation matrix, and the noise value, wherein the target vector includes a target value associated with each of the plurality of observation vectors, the target value is an indicator of a characteristic of the associated observation vector;
• compute a weight matrix used to predict the target value for each of the plurality of variables and each of the plurality of related tasks;
• (a) compute a gradient descent matrix using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, wherein the gradient descent matrix is computed using {tilde over (W)}=Ŵt-1−η({tilde over (∇)}+λŴt-1RRT), where Ŵt-1 is the computed weight matrix, where η is a predefined step size, λ is a predefined sparsity penalization weight value, R is the predefined relationship matrix, and {tilde over (∇)}=ΓiŴit-1−γi for i=1, . . . , K, where K is a number of the of the plurality of related tasks, Γi is the plug-in autocovariance matrix, and γi is the plug-in covariance vector;
• (b) compute an updated weight matrix using the computed gradient descent matrix;
• repeat (a) and (b) with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied;
• and
• when the convergence criterion is satisfied,
• read a new observation vector from a scoring dataset;
• compute a predicted target value for each task of the plurality of related tasks using the computed updated weight matrix and the read new observation vector;
• and
• output the computed predicted target value for each task.

A method of computing an updated weight matrix used to compute a predicted value, the method comprising:

• for each of a plurality of related tasks,
• compute, by a computing device, an augmented observation matrix using an observation matrix and a predefined probability value that a value is missing in the observation matrix, wherein the observation matrix includes a plurality of observation vectors, wherein each observation vector includes a plurality of values, wherein each value of the plurality of values is associated with a variable to define a plurality of variables;
• compute, by the computing device, a plug-in autocovariance matrix using the computed augmented observation matrix and a noise value;
• and
• compute, by the computing device, a plug-in covariance vector using a target vector, the computed augmented observation matrix, and the noise value, wherein the target vector includes a target value associated with each of the plurality of observation vectors, the target value is an indicator of a characteristic of the associated observation vector;
• compute, by the computing device, a weight matrix used to predict the target value for each of the plurality of variables and each of the plurality of related tasks;
• (a) compute, by the computing device, a gradient descent matrix using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, wherein the gradient descent matrix is computed using {tilde over (W)}=Ŵt-1−η({tilde over (∇)}+λŴt-1RRT), where Ŵt-1 is the computed weight matrix, where η is a predefined step size, λ is a predefined sparsity penalization weight value, R is the predefined relationship matrix, and ΓiŴit-1−γi for i=1, . . . , K, where K is a number of the of the plurality of related tasks, Γi is the plug-in autocovariance matrix, and γi is the plug-in covariance vector;
• (b) compute, by the computing device, an updated weight matrix using the computed gradient descent matrix;
• repeat, by the computing device, (a) and (b) with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied;
• and
• when the convergence criterion is satisfied,
• read, by the computing device, a new observation vector from a scoring dataset;
• compute, by the computing device, a predicted target value for each task of the plurality of related tasks using the computed updated weight matrix and the read new observation vector;
• and
• output, by the computing device, the computed predicted target value for each task.