This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the Markov Variation minimization problem. The paper showcases the effectiveness of this approach through examples involving synthetically generated and real-world temperature sensor data. These examples also compare the diffusion map graph signal model with other commonly used graph signal operators. The results provide new approaches for the analysis and understanding of complex, non-Euclidean data structures.

The success of machine learning (ML) applications relies on vast datasets and distributed architectures, which, as they grow, present challenges for ML. In real-world scenarios, where data often contains sensitive information, issues like data poisoning and hardware failures are common. Ensuring privacy and robustness is vital for the broad adoption of ML in public life. This paper examines the costs associated with achieving these objectives in distributed architectures. We overview the meanings of privacy and robustness in distributed ML, and clarify how they can be achieved efficiently in isolation. However, we contend that the integration of these objectives entails a notable compromise in computational efficiency. We delve into this intricate balance, exploring the challenges and solutions for privacy, robustness, and computational efficiency in ML applications.

EODECA (Engineered Ordinary Differential Equations as Classification Algorithm) is a novel approach at the intersection of machine learning and dynamical systems theory, presenting a unique framework for classification tasks [1]. This method stands out with its dynamical system structure, utilizing ordinary differential equations (ODEs) to efficiently handle complex classification challenges. The paper delves into EODECA's dynamical properties, emphasizing its resilience against random perturbations and robust performance across various classification scenarios. Notably, EODECA's design incorporates the ability to embed stable attractors in the phase space, enhancing reliability and allowing for reversible dynamics. In this paper, we carry out a comprehensive analysis by expanding on the work [1], and employing a Euler discretization scheme. In particular, we evaluate EODECA's performance across five distinct classification problems, examining its adaptability and efficiency. Significantly, we demonstrate EODECA's effectiveness on the MNIST and Fashion MNIST datasets, achieving impressive accuracies of $98.06\%$ and $88.21\%$, respectively. These results are comparable to those of a multi-layer perceptron (MLP), underscoring EODECA's potential in complex data processing tasks. We further explore the model's learning journey, assessing its evolution in both pre and post training environments and highlighting its ability to navigate towards stable attractors. The study also investigates the invertibility of EODECA, shedding light on its decision-making processes and internal workings. This paper presents a significant step towards a more transparent and robust machine learning paradigm, bridging the gap between machine learning algorithms and dynamical systems methodologies.

Vision Transformers (ViTs) have achieved state-of-the-art results on various computer vision tasks, including 3D object detection. However, their end-to-end implementation also makes ViTs less explainable, which can be a challenge for deploying them in safety-critical applications, such as autonomous driving, where it is important for authorities, developers, and users to understand the model's reasoning behind its predictions. In this paper, we propose a novel method for generating saliency maps for a DetR-like ViT with multiple camera inputs used for 3D object detection. Our method is based on the raw attention and is more efficient than gradient-based methods. We evaluate the proposed method on the nuScenes dataset using extensive perturbation tests and show that it outperforms other explainability methods in terms of visual quality and quantitative metrics. We also demonstrate the importance of aggregating attention across different layers of the transformer. Our work contributes to the development of explainable AI for ViTs, which can help increase trust in AI applications by establishing more transparency regarding the inner workings of AI models.

Heavy-ball momentum with decaying learning rates is widely used with SGD for optimizing deep learning models. In contrast to its empirical popularity, the understanding of its theoretical property is still quite limited, especially under the standard anisotropic gradient noise condition for quadratic regression problems. Although it is widely conjectured that heavy-ball momentum method can provide accelerated convergence and should work well in large batch settings, there is no rigorous theoretical analysis. In this paper, we fill this theoretical gap by establishing a non-asymptotic convergence bound for stochastic heavy-ball methods with step decay scheduler on quadratic objectives, under the anisotropic gradient noise condition. As a direct implication, we show that heavy-ball momentum can provide $\tilde{\mathcal{O}}(\sqrt{\kappa})$ accelerated convergence of the bias term of SGD while still achieving near-optimal convergence rate with respect to the stochastic variance term. The combined effect implies an overall convergence rate within log factors from the statistical minimax rate. This means SGD with heavy-ball momentum is useful in the large-batch settings such as distributed machine learning or federated learning, where a smaller number of iterations can significantly reduce the number of communication rounds, leading to acceleration in practice.

In the field of autonomous driving, monocular 3D detection is a critical task which estimates 3D properties (depth, dimension, and orientation) of objects in a single RGB image. Previous works have used features in a heuristic way to learn 3D properties, without considering that inappropriate features could have adverse effects. In this paper, sample selection is introduced that only suitable samples should be trained to regress the 3D properties. To select samples adaptively, we propose a Learnable Sample Selection (LSS) module, which is based on Gumbel-Softmax and a relative-distance sample divider. The LSS module works under a warm-up strategy leading to an improvement in training stability. Additionally, since the LSS module dedicated to 3D property sample selection relies on object-level features, we further develop a data augmentation method named MixUp3D to enrich 3D property samples which conforms to imaging principles without introducing ambiguity. As two orthogonal methods, the LSS module and MixUp3D can be utilized independently or in conjunction. Sufficient experiments have shown that their combined use can lead to synergistic effects, yielding improvements that transcend the mere sum of their individual applications. Leveraging the LSS module and the MixUp3D, without any extra data, our method named MonoLSS ranks 1st in all three categories (Car, Cyclist, and Pedestrian) on KITTI 3D object detection benchmark, and achieves competitive results on both the Waymo dataset and KITTI-nuScenes cross-dataset evaluation. The code is included in the supplementary material and will be released to facilitate related academic and industrial studies.

Machine learning models deployed in the wild can be challenged by out-of-distribution (OOD) data from unknown classes. Recent advances in OOD detection rely on distance measures to distinguish samples that are relatively far away from the in-distribution (ID) data. Despite the promise, distance-based methods can suffer from the curse-of-dimensionality problem, which limits the efficacy in high-dimensional feature space. To combat this problem, we propose a novel framework, Subspace Nearest Neighbor (SNN), for OOD detection. In training, our method regularizes the model and its feature representation by leveraging the most relevant subset of dimensions (i.e. subspace). Subspace learning yields highly distinguishable distance measures between ID and OOD data. We provide comprehensive experiments and ablations to validate the efficacy of SNN. Compared to the current best distance-based method, SNN reduces the average FPR95 by 15.96% on the CIFAR-100 benchmark.

This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast approximations of POT with increasingly large problem sizes in arising applications. We first theoretically and experimentally investigate the infeasibility of the state-of-the-art Sinkhorn algorithm for POT due to its incompatible rounding procedure, which consequently degrades its qualitative performance in real world applications like point-cloud registration. To this end, we propose a novel rounding algorithm for POT, and then provide a feasible Sinkhorn procedure with a revised computation complexity of $\mathcal{\widetilde O}(n^2/\varepsilon^4)$. Our rounding algorithm also permits the development of two first-order methods to approximate the POT problem. The first algorithm, Adaptive Primal-Dual Accelerated Gradient Descent (APDAGD), finds an $\varepsilon$-approximate solution to the POT problem in $\mathcal{\widetilde O}(n^{2.5}/\varepsilon)$, which is better in $\varepsilon$ than revised Sinkhorn. The second method, Dual Extrapolation, achieves the computation complexity of $\mathcal{\widetilde O}(n^2/\varepsilon)$, thereby being the best in the literature. We further demonstrate the flexibility of POT compared to standard OT as well as the practicality of our algorithms on real applications where two marginal distributions are unbalanced.

This study's first purpose is to provide quantitative evidence that would incentivize researchers to instead use the more robust method of nested cross-validation. The second purpose is to present methods and MATLAB codes for doing power analysis for ML-based analysis during the design of a study. Monte Carlo simulations were used to quantify the interactions between the employed cross-validation method, the discriminative power of features, the dimensionality of the feature space, and the dimensionality of the model. Four different cross-validations (single holdout, 10-fold, train-validation-test, and nested 10-fold) were compared based on the statistical power and statistical confidence of the ML models. Distributions of the null and alternative hypotheses were used to determine the minimum required sample size for obtaining a statistically significant outcome ({\alpha}=0.05, 1-\b{eta}=0.8). Statistical confidence of the model was defined as the probability of correct features being selected and hence being included in the final model. Our analysis showed that the model generated based on the single holdout method had very low statistical power and statistical confidence and that it significantly overestimated the accuracy. Conversely, the nested 10-fold cross-validation resulted in the highest statistical confidence and the highest statistical power, while providing an unbiased estimate of the accuracy. The required sample size with a single holdout could be 50% higher than what would be needed if nested cross-validation were used. Confidence in the model based on nested cross-validation was as much as four times higher than the confidence in the single holdout-based model. A computational model, MATLAB codes, and lookup tables are provided to assist researchers with estimating the sample size during the design of their future studies.

Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state ($t$) and previous context (over timestamps [$t-1, t-l$], $l$ is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp $t$. We consider diverse benchmarks with varying levels of ``novelty" as measured by the TEA (Temporal Edge Appearance) plots. Our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.