Abstract
Artificial neural networks (ANNs) are powerful empirical approaches used to model databases with a high degree of accuracy. Despite their recognition as universal approximators, many practitioners are skeptical about adopting their routine usage due to lack of model transparency. To improve the clarity of model prediction and correct the apparent lack of comprehension, researchers have utilized a variety of methodologies to extract the underlying variable relationships within ANNs, such as sensitivity analysis (SA). The theoretical basis of local SA (that predictors are independent and inputs other than variable of interest remain “fixed” at predefined values) is challenged in global SA, where, in addition to altering the attribute of interest, the remaining predictors are varied concurrently across their respective ranges. Here, a regression-based global methodology, state-based sensitivity analysis (SBSA), is proposed for measuring the importance of predictor variables upon a modeled response within ANNs. SBSA was applied to network models of a synthetic database having a defined structure and exhibiting multicollinearity. SBSA achieved the most accurate portrayal of predictor-response relationships (compared to local SA and Connected Weights Analysis), closely approximating the actual variability of the modeled system. From this, it is anticipated that skepticisms concerning the delineation of predictor influences and their uncertainty domains upon a modeled output within ANNs will be curtailed.
Highlights
Variable nonlinearity, correlation, and noise are characteristic, yet inseparable components of real-world databases
To illustrate the functionality of this approach, consider a feed-forward backpropagation Multilayer feed-forward perceptrons (MLPs) comprised of inputs (xi,...,I), multiple processing elements (PEj,...,J) in one hidden layer (HL), and one output (y)
Seni = y∑wxi,PEj PEwPEj,PEo, where PE and yj are the derivative values of the HL and output activation function and wxiPEj and wPEj,PEo are the weights between the input-hidden and hidden-output layers, respectively
Summary
Correlation, and noise are characteristic, yet inseparable components of real-world databases. Predictor-response associations are encoded incomprehensibly as weight and bias values within a multilayered topology, providing little (or no) apparent realization to users regarding network functionality of and/or knowledge extraction for the modeled process (Figure 1) This “black-box” trait remains the main constraint. Because ambient and water temperatures typically would be highly correlated (yet not perfectly related due to distinct physical properties of water and air), analyzing the network’s predictive uncertainty in regard to ambient temperature alone, while keeping the value of water temperature static, is neither appropriate nor logical In this simplistic example, the assumption of independence and nonassociation between these two inputs imposes an unrealistic portrayal of model capability/uncertainty, a situation that becomes more perplexing when, in addition to correlative processes, database input/output relationships are nonlinear. The values of remaining predictors were allowed to vary concurrently across respective data ranges and in correspondence to those of the predictor of interest
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
