Symmetries in a dynamical system provide an opportunity to dramatically improve the performance of data-driven models. For fluid flows, such models are needed for tasks related to design, understanding, prediction, and control. In this work we exploit the symmetries of the Navier-Stokes equations (NSE) and use simulation data to find the manifold where the long-time dynamics live, which has many fewer degrees of freedom than the full state representation, and the evolution equation for the dynamics on that manifold. We call this method ''symmetry charting''. The first step is to map to a ''fundamental chart'', which is a region in the state space of the flow to which all other regions can be mapped by a symmetry operation. To map to the fundamental chart we identify a set of indicators from the Fourier transform that uniquely identify the symmetries of the system. We then find a low-dimensional coordinate representation of the data in the fundamental chart with the use of an autoencoder. We use a variation called an implicit rank minimizing autoencoder with weight decay, which in addition to compressing the dimension of the data, also gives estimates of how many dimensions are needed to represent the data: i.e. the dimension of the invariant manifold of the long-time dynamics. Finally, we learn dynamics on this manifold with the use of neural ordinary differential equations. We apply symmetry charting to two-dimensional Kolmogorov flow in a chaotic bursting regime. This system has a continuous translation symmetry, and discrete rotation and shift-reflect symmetries. With this framework we observe that less data is needed to learn accurate data-driven models, more robust estimates of the manifold dimension are obtained, equivariance of the NSE is satisfied, better short-time tracking with respect to the true data is observed, and long-time statistics are correctly captured.

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to manually label these instances. Semi-supervised support vector machines (S3VMs) extend the well-known SVM classifiers to the semi-supervised approach, aiming at maximizing the margin between samples in the presence of unlabeled data. By leveraging both labeled and unlabeled data, S3VMs attempt to achieve better accuracy and robustness compared to traditional SVMs. Unfortunately, the resulting optimization problem is non-convex and hence difficult to solve exactly. In this paper, we present a new branch-and-cut approach for S3VMs using semidefinite programming (SDP) relaxations. We apply optimality-based bound tightening to bound the feasible set. Box constraints allow us to include valid inequalities, strengthening the lower bound. The resulting SDP relaxation provides bounds significantly stronger than the ones available in the literature. For the upper bound, instead, we define a local search exploiting the solution of the SDP relaxation. Computational results highlight the efficiency of the algorithm, showing its capability to solve instances with a number of data points 10 times larger than the ones solved in the literature.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

Climate change mitigation in urban mobility requires policies reconfiguring urban form to increase accessibility and facilitate low-carbon modes of transport. However, current policy research has insufficiently assessed urban form effects on car travel at three levels: (1) Causality -- Can causality be established beyond theoretical and correlation-based analyses? (2) Generalizability -- Do relationships hold across different cities and world regions? (3) Context specificity -- How do relationships vary across neighborhoods of a city? Here, we address all three gaps via causal graph discovery and explainable machine learning to detect urban form effects on intra-city car travel, based on mobility data of six cities across three continents. We find significant causal effects of urban form on trip emissions and inter-feature effects, which had been neglected in previous work. Our results demonstrate that destination accessibility matters most overall, while low density and low connectivity also sharply increase CO$_2$ emissions. These general trends are similar across cities but we find idiosyncratic effects that can lead to substantially different recommendations. In more monocentric cities, we identify spatial corridors -- about 10--50 km from the city center -- where subcenter-oriented development is more relevant than increased access to the main center. Our work demonstrates a novel application of machine learning that enables new research addressing the needs of causality, generalizability, and contextual specificity for scaling evidence-based urban climate solutions.

In a constant evolving world, change detection is of prime importance to keep updated maps. To better sense areas with complex geometry (urban areas in particular), considering 3D data appears to be an interesting alternative to classical 2D images. In this context, 3D point clouds (PCs), whether obtained through LiDAR or photogrammetric techniques, provide valuable information. While recent studies showed the considerable benefit of using deep learning-based methods to detect and characterize changes into raw 3D PCs, these studies rely on large annotated training data to obtain accurate results. The collection of these annotations are tricky and time-consuming. The availability of unsupervised or weakly supervised approaches is then of prime interest. In this paper, we propose an unsupervised method, called DeepCluster 3D Change Detection (DC3DCD), to detect and categorize multiclass changes at point level. We classify our approach in the unsupervised family given the fact that we extract in a completely unsupervised way a number of clusters associated with potential changes. Let us precise that in the end of the process, the user has only to assign a label to each of these clusters to derive the final change map. Our method builds upon the DeepCluster approach, originally designed for image classification, to handle complex raw 3D PCs and perform change segmentation task. An assessment of the method on both simulated and real public dataset is provided. The proposed method allows to outperform fully-supervised traditional machine learning algorithm and to be competitive with fully-supervised deep learning networks applied on rasterization of 3D PCs with a mean of IoU over classes of change of 57.06\% and 66.69\% for the simulated and the real datasets, respectively.

Much research has been devoted to the problem of learning fair representations; however, they do not explicitly the relationship between latent representations. In many real-world applications, there may be causal relationships between latent representations. Furthermore, most fair representation learning methods focus on group-level fairness and are based on correlations, ignoring the causal relationships underlying the data. In this work, we theoretically demonstrate that using the structured representations enable downstream predictive models to achieve counterfactual fairness, and then we propose the Counterfactual Fairness Variational AutoEncoder (CF-VAE) to obtain structured representations with respect to domain knowledge. The experimental results show that the proposed method achieves better fairness and accuracy performance than the benchmark fairness methods.

Contrastive learning is an effective unsupervised method in graph representation learning. Recently, the data augmentation based contrastive learning method has been extended from images to graphs. However, most prior works are directly adapted from the models designed for images. Unlike the data augmentation on images, the data augmentation on graphs is far less intuitive and much harder to provide high-quality contrastive samples, which are the key to the performance of contrastive learning models. This leaves much space for improvement over the existing graph contrastive learning frameworks. In this work, by introducing an adversarial graph view and an information regularizer, we propose a simple but effective method, Adversarial Graph Contrastive Learning (ARIEL), to extract informative contrastive samples within a reasonable constraint. It consistently outperforms the current graph contrastive learning methods in the node classification task over various real-world datasets and further improves the robustness of graph contrastive learning. The code is at https://github.com/Shengyu-Feng/ARIEL.

We aim at capturing high-order statistics of feature vectors formed by a neural network, and propose end-to-end second- and higher-order pooling to form a tensor descriptor. Tensor descriptors require a robust similarity measure due to low numbers of aggregated vectors and the burstiness phenomenon, when a given feature appears more/less frequently than statistically expected. The Heat Diffusion Process (HDP) on a graph Laplacian is closely related to the Eigenvalue Power Normalization (EPN) of the covariance/autocorrelation matrix, whose inverse forms a loopy graph Laplacian. We show that the HDP and the EPN play the same role, i.e., to boost or dampen the magnitude of the eigenspectrum thus preventing the burstiness. We equip higher-order tensors with EPN which acts as a spectral detector of higher-order occurrences to prevent burstiness. We also prove that for a tensor of order r built from d dimensional feature descriptors, such a detector gives the likelihood if at least one higher-order occurrence is 'projected' into one of binom(d,r) subspaces represented by the tensor; thus forming a tensor power normalization metric endowed with binom(d,r) such 'detectors'. For experimental contributions, we apply several second- and higher-order pooling variants to action recognition, provide previously not presented comparisons of such pooling variants, and show state-of-the-art results on HMDB-51, YUP++ and MPII Cooking Activities.

The Adjusted Rand Index (ARI) is a widely used method for comparing hard clusterings, but requires a choice of random model that is often left implicit. Several recent works have extended the Rand Index to fuzzy clusterings, but the assumptions of the most common random model is difficult to justify in fuzzy settings. We propose a single framework for computing the ARI with three random models that are intuitive and explainable for both hard and fuzzy clusterings, along with the benefit of lower computational complexity. The theory and assumptions of the proposed models are contrasted with the existing permutation model. Computations on synthetic and benchmark data show that each model has distinct behaviour, meaning that accurate model selection is important for the reliability of results.

In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a given instance-label dataset is contaminated with class-conditional label noise, as opposed to uniform label noise. The existing theory builds on the asymptotic properties of the Maximum Likelihood Estimate for parametric logistic regression. However, the parametric assumptions on top of which these approaches are constructed are often too strong and unrealistic in practice. To alleviate this problem, in this paper we propose an alternative path by showing how similar procedures can be followed when the underlying model is a product of Local Maximum Likelihood Estimation that leads to more flexible nonparametric logistic regression models, which in turn are less susceptible to model misspecification. This different view allows for wider applicability of the tests by offering users access to a richer model class. Similarly to existing works, we assume we have access to anchor points which are provided by the users. We introduce the necessary ingredients for the adaptation of the hypothesis tests to the case of nonparametric logistic regression and empirically compare against the parametric approach presenting both synthetic and real-world case studies and discussing the advantages and limitations of the proposed approach.