Computer Science
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The Computer Science Department at Montana State University supports the Mission of the College of Engineering and the University through its teaching, research, and service activities. The Department educates undergraduate and graduate students in the principles and practices of computer science, preparing them for computing careers and for a lifetime of learning.
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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 Counterfactual Explanations of Neural Network-Generated Response Curves(IEEE, 2023-06) Morales, Giorgio; Sheppard, JohnResponse curves exhibit the magnitude of the response of a sensitive system to a varying stimulus. However, response of such systems may be sensitive to multiple stimuli (i.e., input features) that are not necessarily independent. As a consequence, the shape of response curves generated for a selected input feature (referred to as “active feature”) might depend on the values of the other input features (referred to as “passive features”). In this work we consider the case of systems whose response is approximated using regression neural networks. We propose to use counterfactual explanations (CFEs) for the identification of the features with the highest relevance on the shape of response curves generated by neural network black boxes. CFEs are generated by a genetic algorithm-based approach that solves a multi-objective optimization problem. In particular, given a response curve generated for an active feature, a CFE finds the minimum combination of passive features that need to be modified to alter the shape of the response curve. We tested our method on a synthetic dataset with 1-D inputs and two crop yield prediction datasets with 2-D inputs. The relevance ranking of features and feature combinations obtained on the synthetic dataset coincided with the analysis of the equation that was used to generate the problem. Results obtained on the yield prediction datasets revealed that the impact on fertilizer responsivity of passive features depends on the terrain characteristics of each field.Item Improved Yield Prediction of Winter Wheat Using a Novel Two-Dimensional Deep Regression Neural Network Trained via Remote Sensing(MDPI AG, 2023-01) Morales, Giorgio; Sheppard, John W.; Hedgedus, Paul B.; Maxwell, Bruce D.In recent years, the use of remotely sensed and on-ground observations of crop fields, in conjunction with machine learning techniques, has led to highly accurate crop yield estimations. In this work, we propose to further improve the yield prediction task by using Convolutional Neural Networks (CNNs) given their unique ability to exploit the spatial information of small regions of the field. We present a novel CNN architecture called Hyper3DNetReg that takes in a multi-channel input raster and, unlike previous approaches, outputs a two-dimensional raster, where each output pixel represents the predicted yield value of the corresponding input pixel. Our proposed method then generates a yield prediction map by aggregating the overlapping yield prediction patches obtained throughout the field. Our data consist of a set of eight rasterized remotely-sensed features: nitrogen rate applied, precipitation, slope, elevation, topographic position index (TPI), aspect, and two radar backscatter coefficients acquired from the Sentinel-1 satellites. We use data collected during the early stage of the winter wheat growing season (March) to predict yield values during the harvest season (August). We present leave-one-out cross-validation experiments for rain-fed winter wheat over four fields and show that our proposed methodology produces better predictions than five compared methods, including Bayesian multiple linear regression, standard multiple linear regression, random forest, an ensemble of feedforward networks using AdaBoost, a stacked autoencoder, and two other CNN architectures.