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This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood Estimation (TMLE). Our method employs CNFs to refine TMLE, optimizing the Cram\'er-Rao bound and transitioning from a predefined distribution $p_0$ to a data-driven distribution $p_1$. We innovate further by embedding Wasserstein gradient flows within Fokker-Planck equations, thus imposing geometric structures that boost the robustness of CNFs, particularly in optimal transport theory. Our approach addresses the disparity between sample and population distributions, a critical factor in parameter estimation bias. We leverage optimal transport and Wasserstein gradient flows to develop causal inference methodologies with minimal variance in finite-sample settings, outperforming traditional methods like TMLE and AIPW. This novel framework, centered on Wasserstein gradient flows, minimizes variance in efficient influence functions under distribution $p_t$. Preliminary experiments showcase our method's superiority, yielding lower mean-squared errors compared to standard flows, thereby demonstrating the potential of geometry-aware normalizing Wasserstein flows in advancing statistical modeling and inference.

Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to $20\times \sim 5000\times$. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

Primal-dual methods have a natural application in Safe Reinforcement Learning (SRL), posed as a constrained policy optimization problem. In practice however, applying primal-dual methods to SRL is challenging, due to the inter-dependency of the learning rate (LR) and Lagrangian multipliers (dual variables) each time an embedded unconstrained RL problem is solved. In this paper, we propose, analyze and evaluate adaptive primal-dual (APD) methods for SRL, where two adaptive LRs are adjusted to the Lagrangian multipliers so as to optimize the policy in each iteration. We theoretically establish the convergence, optimality and feasibility of the APD algorithm. Finally, we conduct numerical evaluation of the practical APD algorithm with four well-known environments in Bullet-Safey-Gym employing two state-of-the-art SRL algorithms: PPO-Lagrangian and DDPG-Lagrangian. All experiments show that the practical APD algorithm outperforms (or achieves comparable performance) and attains more stable training than the constant LR cases. Additionally, we substantiate the robustness of selecting the two adaptive LRs by empirical evidence.

Interpretability and transparency are essential for incorporating causal effect models from observational data into policy decision-making. They can provide trust for the model in the absence of ground truth labels to evaluate the accuracy of such models. To date, attempts at transparent causal effect estimation consist of applying post hoc explanation methods to black-box models, which are not interpretable. Here, we present BICauseTree: an interpretable balancing method that identifies clusters where natural experiments occur locally. Our approach builds on decision trees with a customized objective function to improve balancing and reduce treatment allocation bias. Consequently, it can additionally detect subgroups presenting positivity violations, exclude them, and provide a covariate-based definition of the target population we can infer from and generalize to. We evaluate the method's performance using synthetic and realistic datasets, explore its bias-interpretability tradeoff, and show that it is comparable with existing approaches.

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged, providing guarantees even in high-dimensional settings where the number of variables surpasses the number of samples. However, these methods often fail to reliably control the FDR in the presence of highly dependent variable groups, a common characteristic in fields such as genomics and finance. To tackle this critical issue, we introduce a novel framework that accounts for general dependency structures. Our proposed dependency-aware T-Rex selector integrates hierarchical graphical models within the T-Rex framework to effectively harness the dependency structure among variables. Leveraging martingale theory, we prove that our variable penalization mechanism ensures FDR control. We further generalize the FDR-controlling framework by stating and proving a clear condition necessary for designing both graphical and non-graphical models that capture dependencies. Additionally, we formulate a fully integrated optimal calibration algorithm that concurrently determines the parameters of the graphical model and the T-Rex framework, such that the FDR is controlled while maximizing the number of selected variables. Numerical experiments and a breast cancer survival analysis use-case demonstrate that the proposed method is the only one among the state-of-the-art benchmark methods that controls the FDR and reliably detects genes that have been previously identified to be related to breast cancer. An open-source implementation is available within the R package TRexSelector on CRAN.

Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to tackle this issue: 1) restricting the number of possible representations by sorting the nodes, or 2) using permutation-invariant/equivariant functions, specifically Graph Neural Networks (GNNs). In this paper, we introduce a new framework named Discrete Graph Auto-Encoder (DGAE), which leverages the strengths of both strategies and mitigate their respective limitations. In essence, we propose a strategy in 2 steps. We first use a permutation-equivariant auto-encoder to convert graphs into sets of discrete latent node representations, each node being represented by a sequence of quantized vectors. In the second step, we sort the sets of discrete latent representations and learn their distribution with a specifically designed auto-regressive model based on the Transformer architecture. Through multiple experimental evaluations, we demonstrate the competitive performances of our model in comparison to the existing state-of-the-art across various datasets. Various ablation studies support the interest of our method.

For turbulent problems of industrial scale, computational cost may become prohibitive due to the stability constraints associated with explicit time discretization of the underlying conservation laws. On the other hand, implicit methods allow for larger time-step sizes but require exorbitant computational resources. Implicit-explicit (IMEX) formulations combine both temporal approaches, using an explicit method in nonstiff portions of the domain and implicit in stiff portions. While these methods can be shown to be orders of magnitude faster than typical explicit discretizations, they are still limited by their implicit discretization in terms of cost. Hybridization reduces the scaling of these systems to an effective lower dimension, which allows the system to be solved at significant speedup factors compared to standard implicit methods. This work proposes an IMEX scheme that combines hybridized and standard flux reconstriction (FR) methods to tackle geometry-induced stiffness. By using the so-called transmission conditions, an overall conservative formulation can be obtained after combining both explicit FR and hybridized implicit FR methods. We verify and apply our approach to a series of numerical examples, including a multi-element airfoil at Reynolds number 1.7 million. Results demonstrate speedup factors of four against standard IMEX formulations and at least 15 against standard explicit formulations for the same problem.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.