Sas Institute Inc.

Ming-Chun Chang

David Bruce Elsheimer

Xilong Chen

Gunce Eryuruk Walton

Sylvie Tchumtchoua Kabisa

Wanxi Gu

Dillon Frame

Chuan Xu

Douglas Allan Cairns

Michael James Leonard

Jan Chvosta

Youngjin Park

Yang Zhao

Rajesh S Selukar

Michael Thomas Lamm

A system and method include generating a topological order of a DAG by creating residual series vectors, calculating normality statistic and MSE values for the residual series vectors, comparing the normality statistic values with a critical value, for each normality statistic value that is less than or equal to the critical value, adding a variable index to a temporary order list and the MSE value to an MSE list, counting a number of elements in the temporary order list, if the number of elements in the temporary order list is zero, updating an order list based on the normality statistic values or if the number of elements in the temporary order list is not zero, updating the order list based on at least one of the temporary order list or the MSE list, and outputting the order list as the topological order of the DAG.

Topological order determination in causal graphs

A point estimate value for an individual is computed using a Bayesian neural network model (BNN) by training a first BNN model that computes a weight mean value, a weight standard deviation value, a bias mean value, and a bias standard deviation value for each neuron of a plurality of neurons using observations. A plurality of BNN models is instantiated using the first BNN model. Instantiating each BNN model of the plurality of BNN models includes computing, for each neuron, a weight value using the weight mean value, the weight standard deviation value, and a weight random draw and a bias value using the bias mean value, the bias standard deviation value, and a bias random draw. Each instantiated BNN model is executed with the observations to compute a statistical parameter value for each observation vector of the observations. The point estimate value is computed from the statistical parameter value.

Bayesian neural network point estimator

A treatment model trained to compute an estimated treatment variable value for each observation vector of a plurality of observation vectors is executed. Each observation vector includes covariate variable values, a treatment variable value, and an outcome variable value. An outcome model trained to compute an estimated outcome value for each observation vector using the treatment variable value for each observation vector is executed. A standard error value associated with the outcome model is computed using a first variance value computed using the treatment variable value of the plurality of observation vectors, using a second variance value computed using the treatment variable value and the estimated treatment variable value of the plurality of observation vectors, and using a third variance value computed using the estimated outcome value of the plurality of observation vectors. The standard error value is output.

Standard error for deep learning model outcome estimator

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,z. The trained treatment model is executed to compute an estimated treatment variable value {circumflex over (t)}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 xand an estimated treatment variable t. The trained outcome model is executed to compute an estimated first unknown function value {circumflex over (&#x3b1;)}(x) and an estimated second unknown function value {circumflex over (&#x3b2;)}(x) for each observation vector. An influence function value is computed for a parameter of interest using {circumflex over (&#x3b1;)}(x) and {circumflex over (&#x3b2;)}(x). A value is computed for the predefined parameter of interest using the computed influence function value.

Causal inference and policy optimization system based on deep learning models

Computer-implemented systems and methods for providing a forecast using time series data that is indicative of a data generation activity occurring over a period of time. Candidate models and candidate input variables are received. For each candidate model, transfer functions are determined for the candidate input variables in order to relate a variable to be forecasted to the time series data. For each candidate model there is a selection of which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions. A model is selected from the candidate models to forecast the time series data using the selected input variables of the selected model.

Computer-implemented systems and methods for processing time series data

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Cary, NC, United States of America

Ming-Chun Chang