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1. A Causal Lens for Peeking into Black Box Predictive Models: Predictive Model Interpretation via Causal Attribution

   Khademi, Aria ; Honavar, Vasant ( January 2020 , ArXivorg)

   null (Ed.)

   With the increasing adoption of predictive models trained using machine learning across a wide range of high-stakes applications, e.g., health care, security, criminal justice, finance, and education, there is a growing need for effective techniques for explaining such models and their predictions. We aim to address this problem in settings where the predictive model is a black box; That is, we can only observe the response of the model to various inputs, but have no knowledge about the internal structure of the predictive model, its parameters, the objective function, and the algorithm used to optimize the model. We reduce the problem of interpreting a black box predictive model to that of estimating the causal effects of each of the model inputs on the model output, from observations of the model inputs and the corresponding outputs. We estimate the causal effects of model inputs on model output using variants of the Rubin Neyman potential outcomes framework for estimating causal effects from observational data. We show how the resulting causal attribution of responsibility for model output to the different model inputs can be used to interpret the predictive model and to explain its predictions. We present results of experiments that demonstrate the effectiveness of our approach to the interpretation of black box predictive models via causal attribution in the case of deep neural network models trained on one synthetic data set (where the input variables that impact the output variable are known by design) and two real-world data sets: Handwritten digit classification, and Parkinson's disease severity prediction. Because our approach does not require knowledge about the predictive model algorithm and is free of assumptions regarding the black box predictive model except that its input-output responses be observable, it can be applied, in principle, to any black box predictive model. 

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2. Cost-Effectiveness and Value-of-Information Analysis Using Machine Learning–Based Metamodeling: A Case of Hepatitis C Treatment

   https://doi.org/10.1177/0272989X221125418  

   McCandlish, John Austin ; Ayer, Turgay ; Chhatwal, Jagpreet ( September 2022 , Medical Decision Making)

   Metamodels can address some of the limitations of complex simulation models by formulating a mathematical relationship between input parameters and simulation model outcomes. Our objective was to develop and compare the performance of a machine learning (ML)–based metamodel against a conventional metamodeling approach in replicating the findings of a complex simulation model.

   We constructed 3 ML-based metamodels using random forest, support vector regression, and artificial neural networks and a linear regression-based metamodel from a previously validated microsimulation model of the natural history hepatitis C virus (HCV) consisting of 40 input parameters. Outcomes of interest included societal costs and quality-adjusted life-years (QALYs), the incremental cost-effectiveness (ICER) of HCV treatment versus no treatment, cost-effectiveness analysis curve (CEAC), and expected value of perfect information (EVPI). We evaluated metamodel performance using root mean squared error (RMSE) and Pearson’s R²on the normalized data.

   The R²values for the linear regression metamodel for QALYs without treatment, QALYs with treatment, societal cost without treatment, societal cost with treatment, and ICER were 0.92, 0.98, 0.85, 0.92, and 0.60, respectively. The corresponding R²values for our ML-based metamodels were 0.96, 0.97, 0.90, 0.95, and 0.49 for support vector regression; 0.99, 0.83, 0.99, 0.99, and 0.82 for artificial neural network; and 0.99, 0.99, 0.99, 0.99, and 0.98 for random forest. Similar trends were observed for RMSE. The CEAC and EVPI curves produced by the random forest metamodel matched the results of the simulation output more closely than the linear regression metamodel.

   ML-based metamodels generally outperformed traditional linear regression metamodels at replicating results from complex simulation models, with random forest metamodels performing best.

   Decision-analytic models are frequently used by policy makers and other stakeholders to assess the impact of new medical technologies and interventions. However, complex models can impose limitations on conducting probabilistic sensitivity analysis and value-of-information analysis, and may not be suitable for developing online decision-support tools. Metamodels, which accurately formulate a mathematical relationship between input parameters and model outcomes, can replicate complex simulation models and address the above limitation. The machine learning–based random forest model can outperform linear regression in replicating the findings of a complex simulation model. Such a metamodel can be used for conducting cost-effectiveness and value-of-information analyses or developing online decision support tools.

    

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3. A Hypergradient Approach to Robust Regression without Correspondence

   Xie, Yujia ; Mao, Yixiu ; Zuo, Simiao ; Xu, Hongteng ; Ye, Xiaojing ; Zhao, Tuo ; Zha, Hongyuan ( April 2021 , International Conference on Learning Representations)

   null (Ed.)

   We consider a regression problem, where the correspondence between the input and output data is not available. Such shuffled data are commonly observed in many real world problems. Take flow cytometry as an example: the measuring instruments are unable to preserve the correspondence between the samples and the measurements. Due to the combinatorial nature of the problem, most of the existing methods are only applicable when the sample size is small, and are limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework --- ROBOT --- for the shuffled regression problem, which is applicable to large data and complex models. Specifically, we propose to formulate regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we propose to develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression model, and therefore it allows us to find a better descent direction for the model parameters by differentiating through the data correspondence. ROBOT is quite general, and can be further extended to an inexact correspondence setting, where the input and output data are not necessarily exactly aligned. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking. 

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4. Reducing Simulation Input-Model Risk via Input Model Averaging

   https://doi.org/https://doi.org/10.1287/ijoc.2020.0994  

   Nelson, Barry L. ; Wan, A.T.K. ; Zou, G ; Xinyu Zhang, X ; Jiang, X ( October 2020 , INFORMS journal on computing)

   null (Ed.)

   Input uncertainty is an aspect of simulation model risk that arises when the driving input distributions are derived or “fit” to real-world, historical data. Although there has been significant progress on quantifying and hedging against input uncertainty, there has been no direct attempt to reduce it via better input modeling. The meaning of “better” depends on the context and the objective: Our context is when (a) there are one or more families of parametric distributions that are plausible choices; (b) the real-world historical data are not expected to perfectly conform to any of them; and (c) our primary goal is to obtain higher-fidelity simulation output rather than to discover the “true” distribution. In this paper, we show that frequentist model averaging can be an effective way to create input models that better represent the true, unknown input distribution, thereby reducing model risk. Input model averaging builds from standard input modeling practice, is not computationally burdensome, requires no change in how the simulation is executed nor any follow-up experiments, and is available on the Comprehensive R Archive Network (CRAN). We provide theoretical and empirical support for our approach. 

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5. Multiblock Parameter Calibration in Computer Models

   https://doi.org/10.1287/ijds.2023.0029  

   Jeong, Cheoljoon ; Xu, Ziang ; Berahas, Albert S. ; Byon, Eunshin ; Cetin, Kristen ( October 2023 , INFORMS Journal on Data Science)

   Parameter calibration aims to estimate unobservable parameters used in a computer model by using physical process responses and computer model outputs. In the literature, existing studies calibrate all parameters simultaneously using an entire data set. However, in certain applications, some parameters are associated with only a subset of data. For example, in the building energy simulation, cooling (heating) season parameters should be calibrated using data collected during the cooling (heating) season only. This study provides a new multiblock calibration approach that considers such heterogeneity. Unlike existing studies that build emulators for the computer model response, such as the widely used Bayesian calibration approach, we consider multiple loss functions to be minimized, each for a block of parameters that use the corresponding data set, and estimate the parameters using a nonlinear optimization technique. We present the convergence properties under certain conditions and quantify the parameter estimation uncertainties. The superiority of our approach is demonstrated through numerical studies and a real-world building energy simulation case study.

   History: Bianca Maria Colosimo served as the senior editor for this article.

   Funding: This work was partially supported by the National Science Foundation [Grants CMMI-1662553, CMMI-2226348, and CBET-1804321].

   Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://codeocean.com/capsule/8623151/tree/v1 and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0029 ).

    

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