The convergence rates of PGA are also provided.

Principal geodesic analysis (PGA) is a generalization of principal component analysis (PCA) for dimensionality reduction of data on a Riemannian manifold. Currently PGA is defined as a geometric fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present a latent variable model for PGA that provides a probabilistic framework for factor analysis on manifolds. To compute maximum likelihood estimates of the parameters in our model, we develop a Monte Carlo Expectation Maximization algorithm, where the expectation is approximated by Hamiltonian Monte Carlo sampling of the latent variables. We demonstrate the ability of our method to recover the ground truth parameters in simulated sphere data, as well as its effectiveness in analyzing shape variability of a corpus callosum data set from human brain images.

Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones, and solved with computationally efficient optimization approaches based on first-order information, such as the gradient descent method. However, for unconstrained problems, balancing the minimization of the objective function with the reduction of constraint violations is challenging. We consider the class of time-dependent minimization problems with increasing (possibly) nonlinear and non-convex objective function and non-decreasing (possibly) nonlinear and non-convex inequality constraints. To efficiently solve them, we propose a penalty-based guardrail algorithm (PGA). This algorithm adapts a standard penalty-based method by dynamically updating the right-hand side of the constraints with a guardrail variable which adds a margin to prevent violations. We evaluate PGA on two novel application domains: a simplified model of a district heating system and an optimization model derived from learned deep neural networks. Our method significantly outperforms mathematical programming solvers and the standard penalty-based method, and achieves better performance and faster convergence than a state-of-the-art algorithm (IPDD) within a specified time limit.

Earthquake-induced liquefaction can cause substantial lateral spreading, posing threats to infrastructure. Machine learning (ML) can improve lateral spreading prediction models by capturing complex soil characteristics and site conditions. However, the "black box" nature of ML models can hinder their adoption in critical decision-making. This study addresses this limitation by using SHapley Additive exPlanations (SHAP) to interpret an eXtreme Gradient Boosting (XGB) model for lateral spreading prediction, trained on data from the 2011 Christchurch Earthquake. SHAP analysis reveals the factors driving the model's predictions, enhancing transparency and allowing for comparison with established engineering knowledge. The results demonstrate that the XGB model successfully identifies the importance of soil characteristics derived from Cone Penetration Test (CPT) data in predicting lateral spreading, validating its alignment with domain understanding. This work highlights the value of explainable machine learning for reliable and informed decision-making in geotechnical engineering and hazard assessment.

Principal geodesic analysis (PGA) is a generalization of principal component analysis (PCA) for dimensionality reduction of data on a Riemannian manifold. Currently PGA is defined as a geometric fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present a latent variable model for PGA that provides a probabilistic framework for factor analysis on manifolds. To compute maximum likelihood estimates of the parameters in our model, we develop a Monte Carlo Expectation Maximization algorithm, where the expectation is approximated by Hamiltonian Monte Carlo sampling of the latent variables. We demonstrate the ability of our method to recover the ground truth parameters in simulated sphere data, as well as its effectiveness in analyzing shape variability of a corpus callosum data set from human brain images.

Language-Conditioned Robotic Grasping (LCRG) aims to develop robots that ground and grasp objects based on natural language instructions. While robots capable of recognizing personal objects like "my wallet" can interact more naturally with non-expert users, current LCRG systems primarily limit robots to understanding only generic expressions. To this end, we introduce a task scenario GraspMine with a novel dataset that aims to locate and grasp personal objects given personal indicators via learning from a single human-robot interaction. To address GraspMine, we propose Personalized Grasping Agent (PGA), that learns personal objects by propagating user-given information through a Reminiscence-a collection of raw images from the user's environment. Specifically, PGA acquires personal object information by a user presenting a personal object with its associated indicator, followed by PGA inspecting the object by rotating it. Based on the acquired information, PGA pseudo-labels objects in the Reminiscence by our proposed label propagation algorithm. Harnessing the information acquired from the interactions and the pseudo-labeled objects in the Reminiscence, PGA adapts the object grounding model to grasp personal objects. Experiments on GraspMine show that PGA significantly outperforms baseline methods both in offline and online settings, signifying its effectiveness and personalization applicability on real-world scenarios. Finally, qualitative analysis shows the effectiveness of PGA through a detailed investigation of results in each phase.

Deep Reinforcement Learning (RL) has emerged as a powerful paradigm for training neural policies to solve complex control tasks. However, these policies tend to be overfit to the exact specifications of the task and environment they were trained on, and thus do not perform well when conditions deviate slightly or when composed hierarchically to solve even more complex tasks. Recent work has shown that training a mixture of policies, as opposed to a single one, that are driven to explore different regions of the state-action space can address this shortcoming by generating a diverse set of behaviors, referred to as skills, that can be collectively used to great effect in adaptation tasks or for hierarchical planning. This is typically realized by including a diversity term - often derived from information theory - in the objective function optimized by RL. However these approaches often require careful hyperparameter tuning to be effective. In this work, we demonstrate that less widely-used neuroevolution methods, specifically Quality Diversity (QD), are a competitive alternative to information-theory-augmented RL for skill discovery. Through an extensive empirical evaluation comparing eight state-of-the-art algorithms (four flagship algorithms from each line of work) on the basis of (i) metrics directly evaluating the skills' diversity, (ii) the skills' performance on adaptation tasks, and (iii) the skills' performance when used as primitives for hierarchical planning; QD methods are found to provide equal, and sometimes improved, performance whilst being less sensitive to hyperparameters and more scalable. As no single method is found to provide near-optimal performance across all environments, there is a rich scope for further research which we support by proposing future directions and providing optimized open-source implementations.

As the study of graph neural networks becomes more intensive and comprehensive, their robustness and security have received great research interest. The existing global attack methods treat all nodes in the graph as their attack targets. Although existing methods have achieved excellent results, there is still considerable space for improvement. The key problem is that the current approaches rigidly follow the definition of global attacks. They ignore an important issue, i.e., different nodes have different robustness and are not equally resilient to attacks. From a global attacker's view, we should arrange the attack budget wisely, rather than wasting them on highly robust nodes. To this end, we propose a totally new method named partial graph attack (PGA), which selects the vulnerable nodes as attack targets. First, to select the vulnerable items, we propose a hierarchical target selection policy, which allows attackers to only focus on easy-to-attack nodes. Then, we propose a cost-effective anchor-picking policy to pick the most promising anchors for adding or removing edges, and a more aggressive iterative greedy-based attack method to perform more efficient attacks. Extensive experimental results demonstrate that PGA can achieve significant improvements in both attack effect and attack efficiency compared to other existing graph global attack methods.

The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new approach is proposed to train SVC and optimize the selection of Gaussian kernel parameters. We first formulate the training and parameter selection of SVC as a minimax optimization problem named as MaxMin-L2-SVC-NCH, in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal Gaussian kernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is not needed. We then propose a projected gradient algorithm (PGA) for training L2-SVC-NCH. The famous sequential minimal optimization (SMO) algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility than the SMO. Furthermore, the solution of the maximization problem is done by a gradient ascent algorithm with dynamic learning rate. The comparative experiments between MaxMin-L2-SVC-NCH and the previous best approaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained while maintaining competitive test accuracy. These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVC tasks.

Deep hashing has been extensively applied to massive image retrieval due to its efficiency and effectiveness. Recently, several adversarial attacks have been presented to reveal the vulnerability of deep hashing models against adversarial examples. However, existing attack methods suffer from degraded performance or inefficiency because they underutilize the semantic relations between original samples or spend a lot of time learning these relations with a deep neural network. In this paper, we propose a novel Pharos-guided Attack, dubbed PgA, to evaluate the adversarial robustness of deep hashing networks reliably and efficiently. Specifically, we design pharos code to represent the semantics of the benign image, which preserves the similarity to semantically relevant samples and dissimilarity to irrelevant ones. It is proven that we can quickly calculate the pharos code via a simple math formula. Accordingly, PgA can directly conduct a reliable and efficient attack on deep hashing-based retrieval by maximizing the similarity between the hash code of the adversarial example and the pharos code. Extensive experiments on the benchmark datasets verify that the proposed algorithm outperforms the prior state-of-the-arts in both attack strength and speed.