Publications by Colleges and Departments (MSU - Bozeman)
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Item Univariate Skeleton Prediction in Multivariate Systems Using Transformers(Springer Nature, 2024-08) Morales, Giorgio; Sheppard, John W.Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains the relationship between each variable and the system’s response. To begin to address this, we propose an explainable neural SR method that generates univariate symbolic skeletons that aim to explain how each variable influences the system’s response. By analyzing multiple sets of data generated artificially, where one input variable varies while others are fixed, relationships are modeled separately for each input variable. The response of such artificial data sets is estimated using a regression neural network (NN). Finally, the multiple sets of input–response pairs are processed by a pre-trained Multi-Set Transformer that solves a problem we termed Multi-Set Skeleton Prediction and outputs a univariate symbolic skeleton. Thus, such skeletons represent explanations of the function approximated by the regression NN. Experimental results demonstrate that this method learns skeleton expressions matching the underlying functions and outperforms two GP-based and two neural SR methods.Item Toward polarization-enhanced water quality remote sensing measurements from UAVs(SPIE, 2024-05) Morgan, P. Flint; Weller, Wyatt W.; Maxwell, Dylan J.; Hamp, Shannon M.; Venkatesulu, Erica; Shaw, Joseph A.; Whitaker, Bradley M.; Roddewig, Michael R.Montana and similar regions contain numerous rivers and lakes that are too small to be spatially resolved by satellites that provide water quality estimates. Unoccupied Aerial Vehicles (UAVs) can be used to obtain such data with much higher spatial and temporal resolution. Water properties are traditionally retrieved from passively measured spectral radiance, but polarization has been shown to improve retrievals of the attenuation-to-absorption ratio to enable calculation of the scattering coefficient for in-water particulate matter. This feeds into improved retrievals of other parameters such as the bulk refractive index and particle size distribution. This presentation will describe experiments conducted to develop a data set for water remote sensing using combined UAV-based hyperspectral and polarization cameras supplemented with in-situ sampling at Flathead Lake in northwestern Montana and the results of preliminary data analysis. A symbolic regression model was used to derive two equations: one relating DoLP, AoP, and the linear Stokes parameters at wavelengths of 440 nm, 550 nm and 660 nm, to chlorophyll-a content, and one relating the same data to the attenuation-to-absorption ratio for 440 nm, 550 nm and 660 nm. Symbolic regression is a machine learning algorithm where the inputs are vectors and the output is an analytic expression, typically chosen by a genetic algorithm. An advantage of this approach is that the explainability of a simple equation can be combined with the accuracy of less explainable models, such as the genetic algorithm.