IA Scholar Query: A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 30 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Conjunctive queries for logic-based information extraction
https://scholar.archive.org/work/wd2pb3qomzeb7lqcc3av3fepqq
This thesis offers two logic-based approaches to conjunctive queries in the context of information extraction. The first and main approach is the introduction of conjunctive query fragments of the logics FC and FC[REG], denoted as FC-CQ and FC[REG]-CQ respectively. FC is a first-order logic based on word equations, where the semantics are defined by limiting the universe to the factors of some finite input word. FC[REG] is FC extended with regular constraints. Our first results consider the comparative expressive power of FC[REG]-CQ in relation to document spanners (a formal framework for the query language AQL), and various fragments of FC[REG]-CQ – some of which coincide with well-known language generators, such as patterns and regular expressions. Then, we look at decision problems. We show that many decision problems for FC-CQ and FC[REG]-CQ (such as equivalence and regularity) are undecidable. The model checking problem for FC-CQ and FC[REG]-CQ is NP-complete even if the FC-CQ is acyclic – under the definition of acyclicity where each word equation in an FC-CQ is an atom. This leads us to look at the "decomposition" of an FC word equation into a conjunction of binary word equations (i.e., of the form x =˙ y · z). If a query consists of only binary word equations and the query is acyclic, then model checking is tractable and we can enumerate results efficiently. We give an algorithm that decomposes an FC-CQ into an acyclic FC-CQ consisting of binary word equations in polynomial time, or determines that this is not possible. The second approach is to consider the dynamic complexity of FC. This uses the common way of encoding words in a relational structure using a universe with a linear order along with symbol predicates. Then, each element of the universe can carry a symbol if the predicate for said symbol holds for that element. Instead of the "usual way" (looking at first-order logic over these structures), we study the dynamic complexity, where symbols can be modified. As each of these modifications only c [...]Sam M Thompsonwork_wd2pb3qomzeb7lqcc3av3fepqqWed, 30 Nov 2022 00:00:00 GMTDistribution-free joint independence testing and robust independent component analysis using optimal transport
https://scholar.archive.org/work/aly7wv7rirgpdkwoago6jz3yje
In this paper we study the problem of measuring and testing joint independence for a collection of multivariate random variables. Using the emerging theory of optimal transport (OT) based multivariate ranks, we propose a distribution-free test for multivariate joint independence. Towards this we introduce the notion of rank joint distance covariance (RJdCov), the higher-order rank analogue of the celebrated distance covariance measure, that captures the dependencies among all the subsets of the variables. The RJdCov can be easily estimated from the data without any moment assumptions and the associated test for joint independence is universally consistent. We can calibrate the test without any knowledge of the (unknown) marginal distributions (due to the distribution-free property), both asymptotically and in finite samples. In addition to being distribution-free and universally consistent, the proposed test is also statistically efficient, that is, it has non-trivial asymptotic (Pitman) efficiency. We demonstrate this by computing the limiting local power of the test for both mixture alternatives and joint Konijn alternatives. We also use the RJdCov measure to develop a method for independent component analysis (ICA) that is easy to implement and robust to outliers and contamination. Extensive simulations are performed to illustrate the efficacy of the proposed test in comparison to other existing methods. Finally, we apply the proposed test to learn the higher-order dependence structure among different US industries based on stock prices.Ziang Niu, Bhaswar B. Bhattacharyawork_aly7wv7rirgpdkwoago6jz3yjeWed, 30 Nov 2022 00:00:00 GMTHeterogeneous Graph Neural Network with Multi-view Representation Learning
https://scholar.archive.org/work/aibk4vwggbbulpv6acvcxjcqjm
Graph neural networks for heterogeneous graph embedding is to project nodes into a low-dimensional space by exploring the heterogeneity and semantics of the heterogeneous graph. However, on the one hand, most of existing heterogeneous graph embedding methods either insufficiently model the local structure under specific semantic, or neglect the heterogeneity when aggregating information from it. On the other hand, representations from multiple semantics are not comprehensively integrated to obtain versatile node embeddings. To address the problem, we propose a Heterogeneous Graph Neural Network with Multi-View Representation Learning (named MV-HetGNN) for heterogeneous graph embedding by introducing the idea of multi-view representation learning. The proposed model consists of node feature transformation, view-specific ego graph encoding and auto multi-view fusion to thoroughly learn complex structural and semantic information for generating comprehensive node representations. Extensive experiments on three real-world heterogeneous graph datasets show that the proposed MV-HetGNN model consistently outperforms all the state-of-the-art GNN baselines in various downstream tasks, e.g., node classification, node clustering, and link prediction.Zezhi Shao, Yongjun Xu, Wei Wei, Fei Wang, Zhao Zhang, Feida Zhuwork_aibk4vwggbbulpv6acvcxjcqjmWed, 30 Nov 2022 00:00:00 GMTDr. Neurosymbolic, or: How I Learned to Stop Worrying and Accept Statistics
https://scholar.archive.org/work/o4q5lwow3nc5nmpl5rhwtm754m
The symbolic AI community is increasingly trying to embrace machine learning in neuro-symbolic architectures, yet is still struggling due to cultural barriers. To break the barrier, this rather opinionated personal memo attempts to explain and rectify the conventions in Statistics, Machine Learning, and Deep Learning from the viewpoint of outsiders. It provides a step-by-step protocol for designing a machine learning system that satisfies a minimum theoretical guarantee necessary for being taken seriously by the symbolic AI community, i.e., it discusses "in what condition we can stop worrying and accept statistical machine learning." Unlike most textbooks which are written for students trying to specialize in Stat/ML/DL and willing to accept jargons, this memo is written for experienced symbolic researchers that hear a lot of buzz but are still uncertain and skeptical. Information on Stat/ML/DL is currently too scattered or too noisy to invest in. This memo prioritizes compactness, citations to old papers (many in early 20th century), and concepts that resonate well with symbolic paradigms in order to offer time savings. It prioritizes general mathematical modeling and does not discuss any specific function approximator, such as neural networks (NNs), SVMs, decision trees, etc. Finally, it is open to corrections. Consider this memo as something similar to a blog post taking the form of a paper on Arxiv.Masataro Asaiwork_o4q5lwow3nc5nmpl5rhwtm754mTue, 29 Nov 2022 00:00:00 GMTVisual SLAM: What Are the Current Trends and What to Expect?
https://scholar.archive.org/work/ehqztjcdebgv3cx3xbbv273bb4
In recent years, Simultaneous Localization and Mapping (SLAM) systems have shown significant performance, accuracy, and efficiency gain. In this regard, Visual Simultaneous Localization and Mapping (VSLAM) methods refer to the SLAM approaches that employ cameras for pose estimation and map reconstruction and are preferred over Light Detection And Ranging (LiDAR)-based methods due to their lighter weight, lower acquisition costs, and richer environment representation. Hence, several VSLAM approaches have evolved using different camera types (e.g., monocular or stereo), and have been tested on various datasets (e.g., Technische Universität München (TUM) RGB-D or European Robotics Challenge (EuRoC)) and in different conditions (i.e., indoors and outdoors), and employ multiple methodologies to have a better understanding of their surroundings. The mentioned variations have made this topic popular for researchers and have resulted in various methods. In this regard, the primary intent of this paper is to assimilate the wide range of works in VSLAM and present their recent advances, along with discussing the existing challenges and trends. This survey is worthwhile to give a big picture of the current focuses in robotics and VSLAM fields based on the concentrated resolutions and objectives of the state-of-the-art. This paper provides an in-depth literature survey of fifty impactful articles published in the VSLAMs domain. The mentioned manuscripts have been classified by different characteristics, including the novelty domain, objectives, employed algorithms, and semantic level. The paper also discusses the current trends and contemporary directions of VSLAM techniques that may help researchers investigate them.Ali Tourani, Hriday Bavle, Jose Luis Sanchez-Lopez, Holger Vooswork_ehqztjcdebgv3cx3xbbv273bb4Tue, 29 Nov 2022 00:00:00 GMTOpen Source Variational Quantum Eigensolver Extension of the Quantum Learning Machine (QLM) for Quantum Chemistry
https://scholar.archive.org/work/774zvmkbbvcxxbd3iknlxytuky
Quantum Chemistry (QC) is one of the most promising applications of Quantum Computing. However, present quantum processing units (QPUs) are still subject to large errors. Therefore, noisy intermediate-scale quantum (NISQ) hardware is limited in terms of qubits counts and circuit depths. Specific algorithms such as Variational Quantum Eigensolvers (VQEs) can potentially overcome such issues. We introduce here a novel open-source QC package, denoted Open-VQE, providing tools for using and developing chemically-inspired adaptive methods derived from Unitary Coupled Cluster (UCC). It facilitates the development and testing of VQE algorithms. It is able to use the Atos Quantum Learning Machine (QLM), a general quantum programming framework enabling to write, optimize and simulate quantum computing programs. Along with Open-VQE, we introduce myQLM-Fermion, a new open-source module (that includes the key QLM ressources that are important for QC developments (fermionic second quantization tools etc...). The Open-VQE package extends therefore QLM to QC providing: (i) the functions to generate the different types of excitations beyond the commonly used UCCSD ansätz;(ii) a new implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE), written in simple class structure python codes. Interoperability with other major quantum programming frameworks is ensured thanks to myQLM, which allows users to easily build their own code and execute it on existing QPUs. The combined Open-VQE/myQLM-Fermion quantum simulator facilitates the implementation, tests and developments of variational quantum algorithms towards choosing the best compromise to run QC computations on present quantum computers while offering the possibility to test large molecules. We provide extensive benchmarks for several molecules associated to qubit counts ranging from 4 up to 24.Mohammad Haidar, Marko J. Rančić, Thomas Ayral, Yvon Maday, Jean-Philip Piquemalwork_774zvmkbbvcxxbd3iknlxytukyMon, 28 Nov 2022 00:00:00 GMTSimulation Intelligence: Towards a New Generation of Scientific Methods
https://scholar.archive.org/work/rfujm43y4ngcnml5emnvjksbjy
The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of Simulation Intelligence", a roadmap for the development and integration of the essential algorithms necessary for a merger of scientific computing, scientific simulation, and artificial intelligence. We call this merger simulation intelligence (SI), for short. We argue the motifs of simulation intelligence are interconnected and interdependent, much like the components within the layers of an operating system. Using this metaphor, we explore the nature of each layer of the simulation intelligence operating system stack (SI-stack) and the motifs therein: (1) Multi-physics and multi-scale modeling; (2) Surrogate modeling and emulation; (3) Simulation-based inference; (4) Causal modeling and inference; (5) Agent-based modeling; (6) Probabilistic programming; (7) Differentiable programming; (8) Open-ended optimization; (9) Machine programming. We believe coordinated efforts between motifs offers immense opportunity to accelerate scientific discovery, from solving inverse problems in synthetic biology and climate science, to directing nuclear energy experiments and predicting emergent behavior in socioeconomic settings. We elaborate on each layer of the SI-stack, detailing the state-of-art methods, presenting examples to highlight challenges and opportunities, and advocating for specific ways to advance the motifs and the synergies from their combinations. Advancing and integrating these technologies can enable a robust and efficient hypothesis-simulation-analysis type of scientific method, which we introduce with several use-cases for human-machine teaming and automated science.Alexander Lavin, David Krakauer, Hector Zenil, Justin Gottschlich, Tim Mattson, Johann Brehmer, Anima Anandkumar, Sanjay Choudry, Kamil Rocki, Atılım Güneş Baydin, Carina Prunkl, Brooks Paige, Olexandr Isayev, Erik Peterson, Peter L. McMahon, Jakob Macke, Kyle Cranmer, Jiaxin Zhang, Haruko Wainwright, Adi Hanuka, Manuela Veloso, Samuel Assefa, Stephan Zheng, Avi Pfefferwork_rfujm43y4ngcnml5emnvjksbjySun, 27 Nov 2022 00:00:00 GMTInformation Geometry of Dynamics on Graphs and Hypergraphs
https://scholar.archive.org/work/zzobax2mnngiljvk6zetumgap4
We introduce a new information-geometric structure of dynamics on discrete objects such as graphs and hypergraphs. The setup consists of two dually flat structures built on the vertex and edge spaces, respectively. The former is the conventional duality between density and potential, e.g., the probability density and its logarithmic form induced by a convex thermodynamic function. The latter is the duality between flux and force induced by a convex and symmetric dissipation function, which drives the dynamics on the manifold. These two are connected topologically by the homological algebraic relation induced by the underlying discrete objects. The generalized gradient flow in this doubly dual flat structure is an extension of the gradient flows on Riemannian manifolds, which include Markov jump processes and nonlinear chemical reaction dynamics as well as the natural gradient and mirror descent. The information-geometric projections on this doubly dual flat structure lead to the information-geometric generalizations of Helmholtz-Hodge-Kodaira decomposition and Otto structure in L^2 Wasserstein geometry. The structure can be extended to non-gradient nonequilibrium flow, from which we also obtain the induced dually flat structure on cycle spaces. This abstract but general framework can extend the applicability of information geometry to various problems of linear and nonlinear dynamics.Tetsuya J. Kobayashi, Dimitri Loutchko, Atsushi Kamimura, Shuhei Horiguchi, Yuki Sughiyamawork_zzobax2mnngiljvk6zetumgap4Sat, 26 Nov 2022 00:00:00 GMTThe distribution of syntactic dependency distances
https://scholar.archive.org/work/npj5lb5qirbctlvctkja7zkp6y
The syntactic structure of a sentence can be represented as a graph where vertices are words and edges indicate syntactic dependencies between them. In this setting, the distance between two syntactically linked words can be defined as the difference between their positions. Here we want to contribute to the characterization of the actual distribution of syntactic dependency distances, and unveil its relationship with short-term memory limitations. We propose a new double-exponential model in which decay in probability is allowed to change after a break-point. This transition could mirror the transition from the processing of words chunks to higher-level structures. We find that a two-regime model -- where the first regime follows either an exponential or a power-law decay -- is the most likely one in all 20 languages we considered, independently of sentence length and annotation style. Moreover, the break-point is fairly stable across languages and averages values of 4-5 words, suggesting that the amount of words that can be simultaneously processed abstracts from the specific language to a high degree. Finally, we give an account of the relation between the best estimated model and the closeness of syntactic dependencies, as measured by a recently introduced optimality score.Sonia Petrini, Ramon Ferrer-i-Canchowork_npj5lb5qirbctlvctkja7zkp6ySat, 26 Nov 2022 00:00:00 GMTMolecular Joint Representation Learning via Multi-modal Information
https://scholar.archive.org/work/m5uibp4h25gbbew7bcw6efxom4
In recent years, artificial intelligence has played an important role on accelerating the whole process of drug discovery. Various of molecular representation schemes of different modals (e.g. textual sequence or graph) are developed. By digitally encoding them, different chemical information can be learned through corresponding network structures. Molecular graphs and Simplified Molecular Input Line Entry System (SMILES) are popular means for molecular representation learning in current. Previous works have done attempts by combining both of them to solve the problem of specific information loss in single-modal representation on various tasks. To further fusing such multi-modal imformation, the correspondence between learned chemical feature from different representation should be considered. To realize this, we propose a novel framework of molecular joint representation learning via Multi-Modal information of SMILES and molecular Graphs, called MMSG. We improve the self-attention mechanism by introducing bond level graph representation as attention bias in Transformer to reinforce feature correspondence between multi-modal information. We further propose a Bidirectional Message Communication Graph Neural Network (BMC GNN) to strengthen the information flow aggregated from graphs for further combination. Numerous experiments on public property prediction datasets have demonstrated the effectiveness of our model.Tianyu Wu, Yang Tang, Qiyu Sun, Luolin Xiongwork_m5uibp4h25gbbew7bcw6efxom4Fri, 25 Nov 2022 00:00:00 GMTIgneous: Distributed dense 3D segmentation meshing, neuron skeletonization, and hierarchical downsampling
https://scholar.archive.org/work/6gjp5nfr75eddg7vgj2sb7boni
Three-dimensional electron microscopy images of brain tissue and their dense segmentations are now petascale and growing. These volumes require the mass production of dense segmentation-derived neuron skeletons, multi-resolution meshes, image hierarchies (for both modalities) for visualization and analysis, and tools to manage the large amount of data. However, open tools for large-scale meshing, skeletonization, and data management have been missing. Igneous is a Python-based distributed computing framework that enables economical meshing, skeletonization, image hierarchy creation, and data management using cloud or cluster computing that has been proven to scale horizontally. We sketch Igneous's computing framework, show how to use it, and characterize its performance and data storage.William Silversmith, Aleksandar Zlateski, J. Alexander Bae, Ignacio Tartavull, Nico Kemnitz, Jingpeng Wu, H. Sebastian Seungwork_6gjp5nfr75eddg7vgj2sb7boniFri, 25 Nov 2022 00:00:00 GMTGeodesic Models with Convexity Shape Prior
https://scholar.archive.org/work/tj3amvw57ngmtbc3gw6zvdqdee
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.Da Chen and Jean-Marie Mirebeau and Minglei Shu and Xuecheng Tai and Laurent D. Cohenwork_tj3amvw57ngmtbc3gw6zvdqdeeFri, 25 Nov 2022 00:00:00 GMTA-Optimal Active Learning
https://scholar.archive.org/work/bljdajrfqjblhmodgspu62sbt4
In this work we discuss the problem of active learning. We present an approach that is based on A-optimal experimental design of ill-posed problems and show how one can optimally label a data set by partially probing it, and use it to train a deep network. We present two approaches that make different assumptions on the data set. The first is based on a Bayesian interpretation of the semi-supervised learning problem with the graph Laplacian that is used for the prior distribution and the second is based on a frequentist approach, that updates the estimation of the bias term based on the recovery of the labels. We demonstrate that this approach can be highly efficient for estimating labels and training a deep network.Tue Boesen, Eldad Haberwork_bljdajrfqjblhmodgspu62sbt4Fri, 25 Nov 2022 00:00:00 GMTEngineered bioinspired natural dynamics and their synergy with control and learning in legged robots
https://scholar.archive.org/work/lcibfeusxrduxakyiexfabapua
The performance of legged locomotion relies on the successful mitigation of unstructured, rough terrain in the presence of sparse information and neurosensory delays. Bioinspired walking systems benefit from carefully engineered passive compliant behavior that models the inherent elastic behavior of muscle-tendon structures in animals. To leverage the passive behavior that provides energy efficiency, passive stability as well as simplified control and learning tasks to the system, locomotion control and learning algorithms have to be designed and coordinated with the natural system dynamics in mind to achieve similar locomotion behavior we see in animals. The major contribution of this thesis is the synergy of a bio-inspired leg design with biarticular muscle-tendon structures, a wearable force and pressure sensor design for closed-loop control in legged locomotion, a biologically inspired closed-loop central pattern generator with reflex-like feedback and a learning approach that enables the locomotion controller to leverage the carefully engineered natural dynamics of the robot to learn convincing locomotion skills and increase energy efficiency. The first contribution is a biologically inspired leg design focusing on the biarticular lower leg muscle-tendon structure in vertebrate animals. The biarticular elasticity provides two-dimensional passive impedance to the leg and allows the storage of energy orthogonal to the leg axis direction. The leg blueprint is characterized in its capability to store and release elastic energy in the biarticular structure. The stored energy can be recuperated back into the system and increases the energy efficiency of the leg. This leg design achieves the lowest relative cost of transport documented for all dynamically hopping and running robots. The second contribution introduces the concept of training wheels, temporary mechanical modifications to the system dynamics that shape the learning reward landscape and simplify learning locomotion directly in hardware. Through deliber [...]Felix Ruppert, Universität Stuttgartwork_lcibfeusxrduxakyiexfabapuaThu, 24 Nov 2022 00:00:00 GMTProtein structure generation via folding diffusion
https://scholar.archive.org/work/r5yiiovzsva77k73qcsfgimlem
The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction, directly generating diverse, novel protein structures from neural networks remains difficult. In this work, we present a new diffusion-based generative model that designs protein backbone structures via a procedure that mirrors the native folding process. We describe protein backbone structure as a series of consecutive angles capturing the relative orientation of the constituent amino acid residues, and generate new structures by denoising from a random, unfolded state towards a stable folded structure. Not only does this mirror how proteins biologically twist into energetically favorable conformations, the inherent shift and rotational invariance of this representation crucially alleviates the need for complex equivariant networks. We train a denoising diffusion probabilistic model with a simple transformer backbone and demonstrate that our resulting model unconditionally generates highly realistic protein structures with complexity and structural patterns akin to those of naturally-occurring proteins. As a useful resource, we release the first open-source codebase and trained models for protein structure diffusion.Kevin E. Wu, Kevin K. Yang, Rianne van den Berg, James Y. Zou, Alex X. Lu, Ava P. Aminiwork_r5yiiovzsva77k73qcsfgimlemThu, 24 Nov 2022 00:00:00 GMTEquality on all #CSP Instances Yields Constraint Function Isomorphism via Interpolation and Intertwiners
https://scholar.archive.org/work/cgpsw5qrrnakperzatup652qmm
A fundamental result in the study of graph homomorphisms is Lovász's theorem that two graphs are isomorphic if and only if they admit the same number of homomorphisms from every graph. A line of work extending Lovász's result to more general types of graphs was recently capped by Cai and Govorov, who showed that it holds for graphs with vertex and edge weights from an arbitrary field of characteristic 0. In this work, we generalize from graph homomorphism – a special case of #CSP with a single binary function – to general #CSP by showing that two sets ℱ and 𝒢 of arbitrary constraint functions are isomorphic if and only if the partition function of any #CSP instance is unchanged when we replace the functions in ℱ with those in 𝒢. We give two very different proofs of this result. First, we demonstrate the power of the simple Vandermonde interpolation technique of Cai and Govorov by extending it to general #CSP. Second, we give a proof using the intertwiners of the automorphism group of a constraint function set, a concept from the representation theory of compact groups. This proof is a generalization of a classical version of the recent proof of the Lovász-type result by Mančinska and Roberson relating quantum isomorphism and homomorphisms from planar graphs.Ben Youngwork_cgpsw5qrrnakperzatup652qmmThu, 24 Nov 2022 00:00:00 GMTCross-Sectional Dynamics Under Network Structure: Theory and Macroeconomic Applications
https://scholar.archive.org/work/pkkirnlwijbwvhucwybfeahu5i
Many environments in economics feature a cross-section of agents or units linked by a network of bilateral ties. I develop a framework to study dynamics in these cases. It consists of a vector autoregression in which innovations transmit cross-sectionally via bilateral links and which can accommodate general patterns of how network effects of higher order accumulate over time. In a first application, I take the supply chain network of the US economy as given and document how it drives the dynamics of sectoral prices. By estimating the time profile of network effects, the model allows me to go beyond steady state comparisons and study transition dynamics induced by granular shocks. As a result of different positions in the input-output network, sectors differ in both the strength and the timing of their impact on aggregates. In a second application, I discuss how to approximate cross-sectional processes by assuming that dynamics are driven by a network and in turn estimating the latter. The proposed framework offers a sparse, yet flexible and interpretable method for doing so, owing to networks' ability to summarize complex relations among units by relatively few non-zero bilateral links. Modeling industrial production growth across 44 countries, I obtain reductions in out-of-sample mean squared errors of up to 20% relative to a principal components factor model.Marko Mlikotawork_pkkirnlwijbwvhucwybfeahu5iThu, 24 Nov 2022 00:00:00 GMTOn the Complexity of Counterfactual Reasoning
https://scholar.archive.org/work/4knyczjsbrgg3ljeo5zsrzlxni
We study the computational complexity of counterfactual reasoning in relation to the complexity of associational and interventional reasoning on structural causal models (SCMs). We show that counterfactual reasoning is no harder than associational or interventional reasoning on fully specified SCMs in the context of two computational frameworks. The first framework is based on the notion of treewidth and includes the classical variable elimination and jointree algorithms. The second framework is based on the more recent and refined notion of causal treewidth which is directed towards models with functional dependencies such as SCMs. Our results are constructive and based on bounding the (causal) treewidth of twin networks -- used in standard counterfactual reasoning that contemplates two worlds, real and imaginary -- to the (causal) treewidth of the underlying SCM structure. In particular, we show that the latter (causal) treewidth is no more than twice the former plus one. Hence, if associational or interventional reasoning is tractable on a fully specified SCM then counterfactual reasoning is tractable too. We extend our results to general counterfactual reasoning that requires contemplating more than two worlds and discuss applications of our results to counterfactual reasoning with a partially specified SCM that is coupled with data. We finally present empirical results that measure the gap between the complexities of counterfactual reasoning and associational/interventional reasoning on random SCMs.Yunqiu Han, Yizuo Chen, Adnan Darwichework_4knyczjsbrgg3ljeo5zsrzlxniThu, 24 Nov 2022 00:00:00 GMTBridging the Gap Between Tree and Connectivity Augmentation: Unified and Stronger Approaches
https://scholar.archive.org/work/qcee6uiqbvcr3jaapa27atl3uy
We consider the Connectivity Augmentation Problem (CAP), a classical problem in the area of Survivable Network Design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a k-edge-connected graph G=(V,E) and a set of extra edges, the task is to find a minimum cardinality subset of extra edges whose addition to G makes the graph (k+1)-edge-connected. If k is odd, the problem is known to reduce to the Tree Augmentation Problem (TAP) – i.e., G is a spanning tree – for which significant progress has been achieved recently, leading to approximation factors below 1.5 (the currently best factor is 1.458). However, advances on TAP did not carry over to CAP so far. Indeed, only very recently, Byrka, Grandoni, and Ameli (STOC 2020) managed to obtain the first approximation factor below 2 for CAP by presenting a 1.91-approximation algorithm based on a method that is disjoint from recent advances for TAP. We first bridge the gap between TAP and CAP, by presenting techniques that allow for leveraging insights and methods from TAP to approach CAP. We then introduce a new way to get approximation factors below 1.5, based on a new analysis technique. Through these ingredients, we obtain a 1.393-approximation algorithm for CAP, and therefore also TAP. This leads to the currently best approximation result for both problems in a unified way, by significantly improving on the above-mentioned 1.91-approximation for CAP and also the previously best approximation factor of 1.458 for TAP by Grandoni, Kalaitzis, and Zenklusen (STOC 2018). Additionally, a feature we inherit from recent TAP advances is that our approach can deal with the weighted setting when the ratio between the largest to smallest cost on extra links is bounded, in which case we obtain approximation factors below 1.5.Federica Cecchetto and Vera Traub and Rico Zenklusenwork_qcee6uiqbvcr3jaapa27atl3uyWed, 23 Nov 2022 00:00:00 GMTA Data-Driven Simulation-Based Method for Transportation Network Design
https://scholar.archive.org/work/3fh62t5g7vbuhewnblirj6g6ty
This research develops a data-driven simulation-based method, which integrates high-resolution simulators and machine learning techniques, to model and solve the NDP. Three major tasks are tackled: a) developing a computable traffic flow model for representing traffic dynamics in interrupted multimodal environments, b) developing a generic data-driven simulation-based approach for NDP with a specific focus on network topology, by establishing a simulation-based bi-level model and a solution algorithm based on Bayesian optimization, c) incorporating practical and political constraints into the optimization of the network capacity analysis. The proposed framework can serve as a decision-making tool for transport planners and traffic engineers.RUYANG YINwork_3fh62t5g7vbuhewnblirj6g6tyWed, 23 Nov 2022 00:00:00 GMT