This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of Approximate Inertial Manifolds (AIMs); the particular motivation is the so-called post-processing Galerkin method of Garcia-Archilla, Novo and Titi. Its applicability can be extended: the need for accurate truncated Galerkin projections and for deriving closed-formed corrections can be circumvented using machine learning tools. When the right latent variables are not a priori known, we illustrate how autoencoders as well as Diffusion Maps (a manifold learning scheme) can be used to discover good sets of latent variables and test their explainability. The proposed methodology can express the ROMs in terms of (a) theoretical (Fourier coefficients), (b) linear data-driven (POD modes) and/or (c) nonlinear data-driven (Diffusion Maps) coordinates. Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing. We use the Chafee-Infante reaction-diffusion and the Kuramoto-Sivashinsky dissipative partial differential equations to illustrate and successfully test the overall framework.

Hate speech on social media threatens the mental and physical well-being of individuals and is further responsible for real-world violence. An important driver behind the spread of hate speech and thus why hateful posts can go viral are reshares, yet little is known about why users reshare hate speech. In this paper, we present a comprehensive, causal analysis of the user attributes that make users reshare hate speech. However, causal inference from observational social media data is challenging, because such data likely suffer from selection bias, and there is further confounding due to differences in the vulnerability of users to hate speech. We develop a novel, three-step causal framework: (1) We debias the observational social media data by applying inverse propensity scoring. (2) We use the debiased propensity scores to model the latent vulnerability of users to hate speech as a latent embedding. (3) We model the causal effects of user attributes on users' probability of sharing hate speech, while controlling for the latent vulnerability of users to hate speech. Compared to existing baselines, a particular strength of our framework is that it models causal effects that are non-linear, yet still explainable. We find that users with fewer followers, fewer friends, and fewer posts share more hate speech. Younger accounts, in return, share less hate speech. Overall, understanding the factors that drive users to share hate speech is crucial for detecting individuals at risk of engaging in harmful behavior and for designing effective mitigation strategies.

Electric load forecasting is an indispensable component of electric power system planning and management. Inaccurate load forecasting may lead to the threat of outages or a waste of energy. Accurate electric load forecasting is challenging when there is limited data or even no data, such as load forecasting in holiday, or under extreme weather conditions. As high-stakes decision-making usually follows after load forecasting, model interpretability is crucial for the adoption of forecasting models. In this paper, we propose an interactive GAM which is not only interpretable but also can incorporate specific domain knowledge in electric power industry for improved performance. This boosting-based GAM leverages piecewise linear functions and can be learned through our efficient algorithm. In both public benchmark and electricity datasets, our interactive GAM outperforms current state-of-the-art methods and demonstrates good generalization ability in the cases of extreme weather events. We launched a user-friendly web-based tool based on interactive GAM and already incorporated it into our eForecaster product, a unified AI platform for electricity forecasting.

Malware authors have seen obfuscation as the mean to bypass malware detectors based on static analysis features. For Android, several studies have confirmed that many anti-malware products are easily evaded with simple program transformations. As opposed to these works, ML detection proposals for Android leveraging static analysis features have also been proposed as obfuscation-resilient. Therefore, it needs to be determined to what extent the use of a specific obfuscation strategy or tool poses a risk for the validity of ML malware detectors for Android based on static analysis features. To shed some light in this regard, in this article we assess the impact of specific obfuscation techniques on common features extracted using static analysis and determine whether the changes are significant enough to undermine the effectiveness of ML malware detectors that rely on these features. The experimental results suggest that obfuscation techniques affect all static analysis features to varying degrees across different tools. However, certain features retain their validity for ML malware detection even in the presence of obfuscation. Based on these findings, we propose a ML malware detector for Android that is robust against obfuscation and outperforms current state-of-the-art detectors.

Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that the model is well-specified, an assumption that is violated in most practical applications, since the required knowledge is rarely available. As a result, the produced uncertainty estimates can become very misleading; for example the prediction intervals (PIs) produced for the 95\% confidence level may cover much less than 95\% of the true labels. To address this issue, this paper introduces an extension of GPR based on a Machine Learning framework called, Conformal Prediction (CP). This extension guarantees the production of PIs with the required coverage even when the model is completely misspecified. The proposed approach combines the advantages of GPR with the valid coverage guarantee of CP, while the performed experimental results demonstrate its superiority over existing methods.

Oja's algorithm is a well known online algorithm studied mainly in the context of stochastic principal component analysis. We make a simple observation, yet to the best of our knowledge a novel one, that when applied to a any (not necessarily stochastic) sequence of symmetric matrices which share common eigenvectors, the regret of Oja's algorithm could be directly bounded in terms of the regret of the well known multiplicative weights update method for the problem of prediction with expert advice. Several applications to optimization with quadratic forms over the unit sphere in $\reals^n$ are discussed.

Short-term load forecasting (STLF) is crucial for the daily operation of power grids. However, the non-linearity, non-stationarity, and randomness characterizing electricity demand time series renders STLF a challenging task. Various forecasting approaches have been proposed for improving STLF, including neural network (NN) models which are trained using data from multiple electricity demand series that may not necessary include the target series. In the present study, we investigate the performance of this special case of STLF, called transfer learning (TL), by considering a set of 27 time series that represent the national day-ahead electricity demand of indicative European countries. We employ a popular and easy-to-implement NN model and perform a clustering analysis to identify similar patterns among the series and assist TL. In this context, two different TL approaches, with and without the clustering step, are compiled and compared against each other as well as a typical NN training setup. Our results demonstrate that TL can outperform the conventional approach, especially when clustering techniques are considered.

Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine the role of GD in inducing implicit regularization for tensor optimization, particularly within the context of the lifted matrix sensing framework. This framework has been recently proposed to address the non-convex matrix sensing problem by transforming spurious solutions into strict saddles when optimizing over symmetric, rank-1 tensors. We show that, with sufficiently small initialization scale, GD applied to this lifted problem results in approximate rank-1 tensors and critical points with escape directions. Our findings underscore the significance of the tensor parametrization of matrix sensing, in combination with first-order methods, in achieving global optimality in such problems.

For graph self-supervised learning (GSSL), masked autoencoder (MAE) follows the generative paradigm and learns to reconstruct masked graph edges or node features. Contrastive Learning (CL) maximizes the similarity between augmented views of the same graph and is widely used for GSSL. However, MAE and CL are considered separately in existing works for GSSL. We observe that the MAE and CL paradigms are complementary and propose the graph contrastive masked autoencoder (GCMAE) framework to unify them. Specifically, by focusing on local edges or node features, MAE cannot capture global information of the graph and is sensitive to particular edges and features. On the contrary, CL excels in extracting global information because it considers the relation between graphs. As such, we equip GCMAE with an MAE branch and a CL branch, and the two branches share a common encoder, which allows the MAE branch to exploit the global information extracted by the CL branch. To force GCMAE to capture global graph structures, we train it to reconstruct the entire adjacency matrix instead of only the masked edges as in existing works. Moreover, a discrimination loss is proposed for feature reconstruction, which improves the disparity between node embeddings rather than reducing the reconstruction error to tackle the feature smoothing problem of MAE. We evaluate GCMAE on four popular graph tasks (i.e., node classification, node clustering, link prediction, and graph classification) and compare with 14 state-of-the-art baselines. The results show that GCMAE consistently provides good accuracy across these tasks, and the maximum accuracy improvement is up to 3.2% compared with the best-performing baseline.

We present an analysis tool based on joint matrix factorization for comparing latent representations of multilingual and monolingual models. An alternative to probing, this tool allows us to analyze multiple sets of representations in a joint manner. Using this tool, we study to what extent and how morphosyntactic features are reflected in the representations learned by multilingual pre-trained models. We conduct a large-scale empirical study of over 33 languages and 17 morphosyntactic categories. Our findings demonstrate variations in the encoding of morphosyntactic information across upper and lower layers, with category-specific differences influenced by language properties. Hierarchical clustering of the factorization outputs yields a tree structure that is related to phylogenetic trees manually crafted by linguists. Moreover, we find the factorization outputs exhibit strong associations with performance observed across different cross-lingual tasks. We release our code to facilitate future research.