Successful material selection is critical in designing and manufacturing products for design automation. Designers leverage their knowledge and experience to create high-quality designs by selecting the most appropriate materials through performance, manufacturability, and sustainability evaluation. Intelligent tools can help designers with varying expertise by providing recommendations learned from prior designs. To enable this, we introduce a graph representation learning framework that supports the material prediction of bodies in assemblies. We formulate the material selection task as a node-level prediction task over the assembly graph representation of CAD models and tackle it using Graph Neural Networks (GNNs). Evaluations over three experimental protocols performed on the Fusion 360 Gallery dataset indicate the feasibility of our approach, achieving a 0.75 top-3 micro-f1 score. The proposed framework can scale to large datasets and incorporate designers' knowledge into the learning process. These capabilities allow the framework to serve as a recommendation system for design automation and a baseline for future work, narrowing the gap between human designers and intelligent design agents.

Graph clustering is the process of grouping vertices into densely connected sets called clusters. We tailor two mathematical programming formulations from the literature, to this problem. In doing so, we obtain a heuristic approximation to the intra-cluster density maximization problem. We use two variations of a Boltzmann machine heuristic to obtain numerical solutions. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations. They also establish the superiority of the Boltzmann machine over the traditional exact solver. In the case of smaller less complex graphs, Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi fails to return meaningful results within a reasonable time frame. Finally, we also note that both our clustering formulations, the distance minimization and $K$-medoids, yield clusters of superior quality to those obtained with the Louvain algorithm.

Causal and attribution studies are essential for earth scientific discoveries and critical for informing climate, ecology, and water policies. However, the current generation of methods needs to keep pace with the complexity of scientific and stakeholder challenges and data availability combined with the adequacy of data-driven methods. Unless carefully informed by physics, they run the risk of conflating correlation with causation or getting overwhelmed by estimation inaccuracies. Given that natural experiments, controlled trials, interventions, and counterfactual examinations are often impractical, information-theoretic methods have been developed and are being continually refined in the earth sciences. Here we show that transfer entropy-based causal graphs, which have recently become popular in the earth sciences with high-profile discoveries, can be spurious even when augmented with statistical significance. We develop a subsample-based ensemble approach for robust causality analysis. Simulated data, and observations in climate and ecohydrology, suggest the robustness and consistency of this approach.

Unexplainable black-box models create scenarios where anomalies cause deleterious responses, thus creating unacceptable risks. These risks have motivated the field of eXplainable Artificial Intelligence (XAI) to improve trust by evaluating local interpretability in black-box neural networks. Unfortunately, the ground truth is unavailable for the model's decision, so evaluation is limited to qualitative assessment. Further, interpretability may lead to inaccurate conclusions about the model or a false sense of trust. We propose to improve XAI from the vantage point of the user's trust by exploring a black-box model's latent feature space. We present an approach, ProtoShotXAI, that uses a Prototypical few-shot network to explore the contrastive manifold between nonlinear features of different classes. A user explores the manifold by perturbing the input features of a query sample and recording the response for a subset of exemplars from any class. Our approach is the first locally interpretable XAI model that can be extended to, and demonstrated on, few-shot networks. We compare ProtoShotXAI to the state-of-the-art XAI approaches on MNIST, Omniglot, and ImageNet to demonstrate, both quantitatively and qualitatively, that ProtoShotXAI provides more flexibility for model exploration. Finally, ProtoShotXAI also demonstrates novel explainabilty and detectabilty on adversarial samples.

Image clustering is a very useful technique that is widely applied to various areas, including remote sensing. Recently, visual representations by self-supervised learning have greatly improved the performance of image clustering. To further improve the well-trained clustering models, this paper proposes a novel method by first ranking samples within each cluster based on the confidence in their belonging to the current cluster and then using the ranking to formulate a weighted cross-entropy loss to train the model. For ranking the samples, we developed a method for computing the likelihood of samples belonging to the current clusters based on whether they are situated in densely populated neighborhoods, while for training the model, we give a strategy for weighting the ranked samples. We present extensive experimental results that demonstrate that the new technique can be used to improve the State-of-the-Art image clustering models, achieving accuracy performance gains ranging from $2.1\%$ to $15.9\%$. Performing our method on a variety of datasets from remote sensing, we show that our method can be effectively applied to remote--sensing images.

Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in NMF can be constrained to be samples of nonnegative rational functions, which allow fairly general models; this is referred to as NMF using rational functions (R-NMF). We first show that, under mild assumptions, R-NMF has an essentially unique factorization unlike NMF, which is crucial in applications where ground-truth factors need to be recovered such as blind source separation problems. Then we present different approaches to solve R-NMF: the R-HANLS, R-ANLS and R-NLS methods. From our tests, no method significantly outperforms the others, and a trade-off should be done between time and accuracy. Indeed, R-HANLS is fast and accurate for large problems, while R-ANLS is more accurate, but also more resources demanding, both in time and memory. R-NLS is very accurate but only for small problems. Moreover, we show that R-NMF outperforms NMF in various tasks including the recovery of semi-synthetic continuous signals, and a classification problem of real hyperspectral signals.

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function, and then use this quantity to estimate the linear functional. We prove non-asymptotic upper bounds on the mean-squared error of such procedures: these bounds reveal that in order to obtain non-asymptotically optimal procedures, the error in estimating the treatment effect should be minimized in a certain weighted $L^2$-norm. We analyze a two-stage procedure based on constrained regression in this weighted norm, and establish its instance-dependent optimality in finite samples via matching non-asymptotic local minimax lower bounds. These results show that the optimal non-asymptotic risk, in addition to depending on the asymptotically efficient variance, depends on the weighted norm distance between the true outcome function and its approximation by the richest function class supported by the sample size.

Consequently, many point cloud feature detection methods have been proposed in the literature to automate some workflows, such as their classification or semantic segmentation. Nevertheless, the performance of point cloud automated systems significantly lags behind their image counterparts. While part of this failure stems from the irregularity, unstructuredness, and disorder of point clouds, which makes the task of point cloud feature detection significantly more challenging than the image one, we argue that a lack of inspiration from the image domain might be the primary cause of such a gap. Indeed, given the overwhelming success of Convolutional Neural Networks (CNNs) in image feature detection, it seems reasonable to design their point cloud counterparts, but none of the proposed approaches closely resembles them. Specifically, even though many approaches generalise the convolution operation in point clouds, they fail to emulate the CNNs multiple-feature detection and pooling operations. For this reason, we propose a graph convolution-based unit, dubbed Shrinking unit, that can be stacked vertically and horizontally for the design of CNN-like 3D point cloud feature extractors. Given that self, local and global correlations between points in a point cloud convey crucial spatial geometric information, we also leverage them during the feature extraction process. We evaluate our proposal by designing a feature extractor model for the ModelNet-10 benchmark dataset and achieve 90.64% classification accuracy, demonstrating that our innovative idea is effective.

The ever-increasing quantity of multivariate process data is driving a need for skilled engineers to analyze, interpret, and build models from such data. Multivariate data analytics relies heavily on linear algebra, optimization, and statistics and can be challenging for students to understand given that most curricula do not have strong coverage in the latter three topics. This article describes interactive software - the Latent Variable Demonstrator (LAVADE) - for teaching, learning, and understanding latent variable methods. In this software, users can interactively compare latent variable methods such as Partial Least Squares (PLS), and Principal Component Regression (PCR) with other regression methods such as Least Absolute Shrinkage and Selection Operator (lasso), Ridge Regression (RR), and Elastic Net (EN). LAVADE helps to build intuition on choosing appropriate methods, hyperparameter tuning, and model coefficient interpretation, fostering a conceptual understanding of the algorithms' differences. The software contains a data generation method and three chemical process datasets, allowing for comparing results of datasets with different levels of complexity. LAVADE is released as open-source software so that others can apply and advance the tool for use in teaching or research.

The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched and the effect of random linear projections on measures such as intrinsic dimensionality still is an ongoing effort. In this paper, we investigate the less explored depths of linear projections onto explicit subspaces of varying dimensionality and the expectations of variance that ensue. The result is a new family of bounds for Euclidean distances and inner products. We showcase the quality of these bounds as well as investigate the intimate relation to intrinsic dimensionality estimation.