An analytic comparison of regularization methods for Gaussian Processes

Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of experiments and global optimization. Nearly all of the applications of GPs require the inversion of a covariance matrix that, in practice, is often ill-conditioned. Regularization methodologies are then employed with consequences on the GPs that need to be better understood.The two principal methods to deal with ill-conditioned covariance matrices are i) pseudoinverse and ii) adding a positive constant to the diagonal (the so-called nugget regularization).The first part of this paper provides an algebraic comparison of PI and nugget regularizations. Redundant points, responsible for covariance matrix singularity, are defined. It is proven that pseudoinverse regularization, contrarily to nugget regularization, averages the output values and makes the variance zero at redundant points. However, pseudoinverse and nugget regularizations become equivalent as the nugget value vanishes. A measure for data-model discrepancy is proposed which serves for choosing a regularization technique.In the second part of the paper, a distribution-wise GP is introduced that interpolates Gaussian distributions instead of data points. Distribution-wise GP can be seen as an improved regularization method for GPs

Decoupled UMDO formulation for interdisciplinary coupling satisfaction under uncertainty

International audienceAt early design phases, taking into account uncertainty for the optimization of a multidisciplinary system is essential to establish the optimal system characteristics and performances. Uncertainty Multidisciplinary Design Optimization (UMDO) formulations have to eciently organize the dierent disciplinary analyses, the uncertainty propagation, the optimization, but also the handling of interdisciplinary couplings under uncertainty. A decoupled UMDO formulation (Individual Discipline Feasible - Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the instantiations of the uncertain variables is presented in this paper. Ensuring coupling satisfaction in instantiations is essential to ensure the equivalence between the coupled and decoupled UMDO problem formulations. The proposed approach relies on the iterative construction of surrogate models based on Polynomial Chaos Expansion in order to represent at the convergence of the optimization problem, the coupling functional relations as a coupled approach under uncertainty does. The performances of the proposed formulation is assessed on an analytic test case and on the design of a new Vega launch vehicle upper stage

An Experimental Investigation into the Evaluation of Explainability Methods for Computer Vision

EXplainable Artificial Intelligence (XAI) aims to help users to grasp the reasoning behind the predictions of an Artificial Intelligence (AI) system. Many XAI approaches have emerged in recent years. Consequently, the subfield related to the evaluation of XAI methods has gained considerable attention, with the aim of determining which methods provide the best explanation using various approaches and criteria. However, the literature lacks a comparison of the evaluation metrics themselves that could be used to evaluate XAI methods. This work aims to partially fill this gap by comparing 14 different metrics when applied to nine state-of-the-art XAI methods and three dummy methods (e.g., random saliency maps) used as references. Experimental results on image data show which of these metrics produce highly correlated results, indicating potential redundancy. We also demonstrate the significant impact of varying the baseline hyperparameter on the evaluation metric values. Finally, we use dummy methods to assess the reliability of metrics in terms of ranking, pointing out their limitations.EXplainable Artificial Intelligence (XAI) aims to help users to grasp the reasoning behind the predictions of an Artificial Intelligence (AI) system. Many XAI approaches have emerged in recent years. Consequently, the subfield related to the evaluation of XAI methods has gained considerable attention, with the aim of determining which methods provide the best explanation using various approaches and criteria. However, the literature lacks a comparison of the evaluation metrics themselves that could be used to evaluate XAI methods. This work aims to partially fill this gap by comparing 14 different metrics when applied to nine state-of-the-art XAI methods and three dummy methods (e.g., random saliency maps) used as references. Experimental results on image data show which of these metrics produce highly correlated results, indicating potential redundancy. We also demonstrate the significant impact of varying the baseline hyperparameter on the evaluation metric values. Finally, we use dummy methods to assess the reliability of metrics in terms of ranking, pointing out their limitations

Field phenotyping for African crops: overview and perspectives

Improvements in crop productivity are required to meet the dietary demands of the rapidly-increasing African population. The development of key staple crop cultivars that are high-yielding and resilient to biotic and abiotic stresses is essential. To contribute to this objective, high-throughput plant phenotyping approaches are important enablers for the African plant science community to measure complex quantitative phenotypes and to establish the genetic basis of agriculturally relevant traits. These advances will facilitate the screening of germplasm for optimum performance and adaptation to low-input agriculture and resource-constrained environments. Increasing the capacity to investigate plant function and structure through non-invasive technologies is an effective strategy to aid plant breeding and additionally may contribute to precision agriculture. However, despite the significant global advances in basic knowledge and sensor technology for plant phenotyping, Africa still lags behind in the development and implementation of these systems due to several practical, financial, geographical and political barriers. Currently, field phenotyping is mostly carried out by manual methods that are prone to error, costly, labor-intensive and may come with adverse economic implications. Therefore, improvements in advanced field phenotyping capabilities and appropriate implementation are key factors for success in modern breeding and agricultural monitoring. In this review, we provide an overview of the current state of field phenotyping and the challenges limiting its implementation in some African countries. We suggest that the lack of appropriate field phenotyping infrastructures is impeding the development of improved crop cultivars and will have a detrimental impact on the agricultural sector and on food security. We highlight the prospects for integrating emerging and advanced low-cost phenotyping technologies into breeding protocols and characterizing crop responses to environmental challenges in field experimentation. Finally, we explore strategies for overcoming the barriers and maximizing the full potential of emerging field phenotyping technologies in African agriculture. This review paper will open new windows and provide new perspectives for breeders and the entire plant science community in Africa.BBSRC: BB/P016855/

Modeling the spatial-spectral characteristics of plants for nutrient status identification using hyperspectral data and deep learning methods

Sustainable fertilizer management in precision agriculture is essential for both economic and environmental reasons. To effectively manage fertilizer input, various methods are employed to monitor and track plant nutrient status. One such method is hyperspectral imaging, which has been on the rise in recent times. It is a remote sensing tool used to monitor plant physiological changes in response to environmental conditions and nutrient availability. However, conventional hyperspectral processing mainly focuses on either the spectral or spatial information of plants. This study aims to develop a hybrid convolution neural network (CNN) capable of simultaneously extracting spatial and spectral information from quinoa and cowpea plants to identify their nutrient status at different growth stages. To achieve this, a nutrient experiment with four treatments (high and low levels of nitrogen and phosphorus) was conducted in a glasshouse. A hybrid CNN model comprising a 3D CNN (extracts joint spectral-spatial information) and a 2D CNN (for abstract spatial information extraction) was proposed. Three pre-processing techniques, including second-order derivative, standard normal variate, and linear discriminant analysis, were applied to selected regions of interest within the plant spectral hypercube. Together with the raw data, these datasets were used as inputs to train the proposed model. This was done to assess the impact of different pre-processing techniques on hyperspectral-based nutrient phenotyping. The performance of the proposed model was compared with a 3D CNN, a 2D CNN, and a Hybrid Spectral Network (HybridSN) model. Effective wavebands were selected from the best-performing dataset using a greedy stepwise-based correlation feature selection (CFS) technique. The selected wavebands were then used to retrain the models to identify the nutrient status at five selected plant growth stages. From the results, the proposed hybrid model achieved a classification accuracy of over 94% on the test dataset, demonstrating its potential for identifying nitrogen and phosphorus status in cowpea and quinoa at different growth stages

Machine learning methods for automatic segmentation of images of field-and glasshouse-based plants for high-throughput phenotyping

Image segmentation is a fundamental but critical step for achieving automated high- throughput phenotyping. While conventional segmentation methods perform well in homogenous environments, the performance decreases when used in more complex environments. This study aimed to develop a fast and robust neural-network-based segmentation tool to phenotype plants in both field and glasshouse environments in a high-throughput manner. Digital images of cowpea (from glasshouse) and wheat (from field) with different nutrient supplies across their full growth cycle were acquired. Image patches from 20 randomly selected images from the acquired dataset were transformed from their original RGB format to multiple color spaces. The pixels in the patches were annotated as foreground and background with a pixel having a feature vector of 24 color properties. A feature selection technique was applied to choose the sensitive features, which were used to train a multilayer perceptron network (MLP) and two other traditional machine learning models: support vector machines (SVMs) and random forest (RF). The performance of these models, together with two standard color-index segmentation techniques (excess green (ExG) and excess green–red (ExGR)), was compared. The proposed method outperformed the other methods in producing quality segmented images with over 98%-pixel classification accuracy. Regression models developed from the different segmentation methods to predict Soil Plant Analysis Development (SPAD) values of cowpea and wheat showed that images from the proposed MLP method produced models with high predictive power and accuracy comparably. This method will be an essential tool for the development of a data analysis pipeline for high-throughput plant phenotyping. The proposed technique is capable of learning from different environmental conditions, with a high level of robustness