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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., Comment: Paper accepted at European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD) 2024

Accurate uncertainty quantification is necessary to enhance the reliability of deep learning models in real-world applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic predictions of deep learning models. Such PIs are useful or "high-quality" as long as they are sufficiently narrow and capture most of the probability density. In this paper, we present a method to learn prediction intervals for regression-based neural networks automatically in addition to the conventional target predictions. In particular, we train two companion neural networks: one that uses one output, the target estimate, and another that uses two outputs, the upper and lower bounds of the corresponding PI. Our main contribution is the design of a novel loss function for the PI-generation network that takes into account the output of the target-estimation network and has two optimization objectives: minimizing the mean prediction interval width and ensuring the PI integrity using constraints that maximize the prediction interval probability coverage implicitly. Furthermore, we introduce a self-adaptive coefficient that balances both objectives within the loss function, which alleviates the task of fine-tuning. Experiments using a synthetic dataset, eight benchmark datasets, and a real-world crop yield prediction dataset showed that our method was able to maintain a nominal probability coverage and produce significantly narrower PIs without detriment to its target estimation accuracy when compared to those PIs generated by three state-of-the-art neural-network-based methods. In other words, our method was shown to produce higher-quality PIs., Comment: Accepted at the IEEE Transactions on Neural Networks and Learning Systems

Protein content in wheat plays a significant role when determining the price of wheat production. The Grain mixing problem aims to find the optimal bin pair combination with an appropriate mixing ratio to load each truck that will yield a maximum profit when sold to a set of local grain elevators. In this paper, we presented two complexity proofs for the grain mixing problem and showed that finding the optimal solutions for the grain mixing problem remains hard. These proofs follow a reduction from the $3$-dimensional matching ($3$-DM) problem and a more restricted version of the $3$-DM known as planar $3$-DM problem respectively. The complexity proofs do suggest that the exact algorithm to find the optimal solution for the grain mixing problem may be infeasible.

Crop yield prediction is one of the tasks of Precision Agriculture that can be automated based on multi-source periodic observations of the fields. We tackle the yield prediction problem using a Convolutional Neural Network (CNN) trained on data that combines radar satellite imagery and on-ground information. We present a CNN architecture called Hyper3DNetReg that takes in a multi-channel input image and outputs a two-dimensional raster, where each pixel represents the predicted yield value of the corresponding input pixel. We utilize radar data acquired from the Sentinel-1 satellites, while the on-ground data correspond to a set of six raster features: nitrogen rate applied, precipitation, slope, elevation, topographic position index (TPI), and aspect. 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 experiments over four fields of winter wheat and show that our proposed methodology yields better results than five compared methods, including multiple linear regression, an ensemble of feedforward networks using AdaBoost, a stacked autoencoder, and two other CNN architectures., Comment: Accepted to appear in the SPIE Future Sensing Technologies 2021