Computing Research Repository

Schonsheck, Nikolas C.; Schonsheck, Stefan C.

doi: 10.1007/s41468-023-00141-wpmid: N/A

Abstract:We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization. We begin by computing the second-degree persistent cohomology of the filtered Vietoris-Rips (VR) complex of a data set $X$ and extract a cocycle $\alpha$ from any significant feature. From this cocycle, we define an associated map $\alpha: VR(X) \to S^2$ and use this map as an infeasible initialization for a variational model, which we show has a unique solution (up to rigid motion). We then employ an alternating gradient descent/Möbius transformation update method to solve the problem and generate a more suitable, i.e., smoother, representative of the homotopy class of $\alpha$, preserving the relevant topological feature. Finally, we conduct numerical experiments on both synthetic and real-world data sets to show the efficacy of our proposed approach.

Wu, Fangyu; Wang, Dequan; Hwang, Minjune; Hao, Chenhui; Lu, Jiawei; Zhang, Jiamu; Chou, Christopher; Darrell, Trevor; Bayen, Alexandre

doi: 10.48550/arxiv.2209.08763pmid: N/A

Abstract:A significant portion of roads, particularly in densely populated developing countries, lacks explicitly defined right-of-way rules. These understructured roads pose substantial challenges for autonomous vehicle motion planning, where efficient and safe navigation relies on understanding decentralized human coordination for collision avoidance. This coordination, often termed "social driving etiquette," remains underexplored due to limited open-source empirical data and suitable modeling frameworks. In this paper, we present a novel dataset and modeling framework designed to study motion planning in these understructured environments. The dataset includes 20 aerial videos of representative scenarios, an image dataset for training vehicle detection models, and a development kit for vehicle trajectory estimation. We demonstrate that a consensus-based modeling approach can effectively explain the emergence of priority orders observed in our dataset, and is therefore a viable framework for decentralized collision avoidance planning.

Li, Xixi; Yuan, Jingsong

doi: 10.48550/arxiv.2209.10587pmid: N/A

Abstract:The vector autoregressive (VAR) model has been used to describe the dependence within and across multiple time series. This is a model for stationary time series which can be extended to allow the presence of a deterministic trend in each series. Detrending the data either parametrically or nonparametrically before fitting the VAR model gives rise to more errors in the latter part. In this study, we propose a new approach called DeepVARwT that employs deep learning methodology for maximum likelihood estimation of the trend and the dependence structure at the same time. A Long Short-Term Memory (LSTM) network is used for this purpose. To ensure the stability of the model, we enforce the causality condition on the autoregressive coefficients using the transformation of Ansley & Kohn (1986). We provide a simulation study and an application to real data. In the simulation study, we use realistic trend functions generated from real data and compare the estimates with true function/parameter values. In the real data application, we compare the prediction performance of this model with state-of-the-art models in the literature.

Liberatore, Paolo

doi: 10.48550/arxiv.2209.12825pmid: N/A

Abstract:Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which maintains consequences rather than explanations. Differently from that, abductive forgetting from a propositional formula may not be expressed by any propositional formula. A necessary and sufficient condition tells when it is. Checking it is $\Pi^p_3$-complete. A way to guarantee expressibility of abductive forgetting is to switch from propositional to default logic. Another is to introduce new variables.

Barsamian, Yann; Chailloux, André

doi: 10.48550/arxiv.2209.02089pmid: N/A

Abstract:Inverted indexes allow to query large databases without needing to search in the database at each query. An important line of research is to construct the most efficient inverted indexes, both in terms of compression ratio and time efficiency. In this article, we show how to use trit encoding, combined with contextual methods for computing inverted indexes. We perform an extensive study of different variants of these methods and show that our method consistently outperforms the Binary Interpolative Method -- which is one of the golden standards in this topic -- with respect to compression size. We apply our methods to a variety of datasets and make available the source code that produced the results, together with all our datasets.

Liu, Zichuan; Zhu, Yuanyang; Wang, Zhi; Gao, Yang; Chen, Chunlin

doi: 10.48550/arxiv.2209.07225pmid: N/A

Abstract:While achieving tremendous success in various fields, existing multi-agent reinforcement learning (MARL) with a black-box neural network makes decisions in an opaque manner that hinders humans from understanding the learned knowledge and how input observations influence decisions. In contrast, existing interpretable approaches usually suffer from weak expressivity and low performance. To bridge this gap, we propose MIXing Recurrent soft decision Trees (MIXRTs), a novel interpretable architecture that can represent explicit decision processes via the root-to-leaf path and reflect each agent's contribution to the team. Specifically, we construct a novel soft decision tree using a recurrent structure and demonstrate which features influence the decision-making process. Then, based on the value decomposition framework, we linearly assign credit to each agent by explicitly mixing individual action values to estimate the joint action value using only local observations, providing new insights into interpreting the cooperation mechanism. Theoretical analysis confirms that MIXRTs guarantee additivity and monotonicity in the factorization of joint action values. Evaluations on complex tasks like Spread and StarCraft II demonstrate that MIXRTs compete with existing methods while providing clear explanations, paving the way for interpretable and high-performing MARL systems.

Hess, Philipp; Drüke, Markus; Petri, Stefan; Strnad, Felix M.; Boers, Niklas

doi: 10.48550/arxiv.2209.07568pmid: N/A

Abstract:Precipitation results from complex processes across many scales, making its accurate simulation in Earth system models (ESMs) challenging. Existing post-processing methods can improve ESM simulations locally, but cannot correct errors in modelled spatial patterns. Here we propose a framework based on physically constrained generative adversarial networks (GANs) to improve local distributions and spatial structure simultaneously. We apply our approach to the computationally efficient ESM CM2Mc-LPJmL. Our method outperforms existing ones in correcting local distributions, and leads to strongly improved spatial patterns especially regarding the intermittency of daily precipitation. Notably, a double-peaked Intertropical Convergence Zone, a common problem in ESMs, is removed. Enforcing a physical constraint to preserve global precipitation sums, the GAN can generalize to future climate scenarios unseen during training. Feature attribution shows that the GAN identifies regions where the ESM exhibits strong biases. Our method constitutes a general framework for correcting ESM variables and enables realistic simulations at a fraction of the computational costs.

Yongacoglu, Bora; Arslan, Gürdal; Yüksel, Serdar

doi: 10.48550/arxiv.2209.05703pmid: N/A

Abstract:Independent learners are agents that employ single-agent algorithms in multi-agent systems, intentionally ignoring the effect of other strategic agents. This paper studies mean-field games from a decentralized learning perspective, with two primary objectives: (i) to identify structure that can guide algorithm design, and (ii) to understand the emergent behaviour in systems of independent learners. We study a new model of partially observed mean-field games with finitely many players, local action observability, and a general observation channel for partial observations of the global state. Specific observation channels considered include (a) global observability, (b) local and mean-field observability, (c) local and compressed mean-field observability, and (d) only local observability. We establish conditions under which the control problem of a given agent is equivalent to a fully observed MDP, as well as conditions under which the control problem is equivalent only to a POMDP. Building on the connection to MDPs, we prove the existence of perfect equilibrium among memoryless stationary policies under mean-field observability. Leveraging the connection to POMDPs, we prove convergence of learning iterates obtained by independent learning agents under any of the aforementioned observation channels. We interpret the limiting values as subjective value functions, which an agent believes to be relevant to its control problem. These subjective value functions are then used to propose subjective Q-equilibrium, a new solution concept for partially observed n-player mean-field games, whose existence is proved under mean-field or global observability. We provide a decentralized learning algorithm for partially observed n-player mean-field games, and we show that it drives play to subjective Q-equilibrium by adapting the recently developed theory of satisficing paths to allow for subjectivity.

Levonian, Zachary; Zent, Matthew; Nguyen, Ngan; McNamara, Matthew; Terveen, Loren; Yarosh, Svetlana

doi: 10.1145/3711044pmid: N/A

Abstract:Online health communities (OHCs) offer the promise of connecting with supportive peers. Forming these connections first requires finding relevant peers - a process that can be time-consuming. Peer recommendation systems are a computational approach to make finding peers easier during a health journey. By encouraging OHC users to alter their online social networks, peer recommendations could increase available support. But these benefits are hypothetical and based on mixed, observational evidence. To experimentally evaluate the effect of peer recommendations, we conceptualize these systems as health interventions designed to increase specific beneficial connection behaviors. In this paper, we designed a peer recommendation intervention to increase two behaviors: reading about peer experiences and interacting with peers. We conducted an initial feasibility assessment of this intervention by conducting a 12-week field study in which 79 users of CaringBridge received weekly peer recommendations via email. Our results support the usefulness and demand for peer recommendation and suggest benefits to evaluating larger peer recommendation interventions. Our contributions include practical guidance on the development and evaluation of peer recommendation interventions for OHCs.

Costabal, Francisco Sahli; Pezzuto, Simone; Perdikaris, Paris

doi: 10.1016/j.engappai.2023.107324pmid: N/A

Abstract:Physics-informed neural networks (PINNs) have demonstrated promise in solving forward and inverse problems involving partial differential equations. Despite recent progress on expanding the class of problems that can be tackled by PINNs, most of existing use-cases involve simple geometric domains. To date, there is no clear way to inform PINNs about the topology of the domain where the problem is being solved. In this work, we propose a novel positional encoding mechanism for PINNs based on the eigenfunctions of the Laplace-Beltrami operator. This technique allows to create an input space for the neural network that represents the geometry of a given object. We approximate the eigenfunctions as well as the operators involved in the partial differential equations with finite elements. We extensively test and compare the proposed methodology against traditional PINNs in complex shapes, such as a coil, a heat sink and a bunny, with different physics, such as the Eikonal equation and heat transfer. We also study the sensitivity of our method to the number of eigenfunctions used, as well as the discretization used for the eigenfunctions and the underlying operators. Our results show excellent agreement with the ground truth data in cases where traditional PINNs fail to produce a meaningful solution. We envision this new technique will expand the effectiveness of PINNs to more realistic applications.