IA Scholar Query: Clique Partitions, Graph Compression and Speeding-Up Algorithms.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 31 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Computing Graph Neural Networks: A Survey from Algorithms to Accelerators
https://scholar.archive.org/work/7uww2lnxrbdpnnyvzsanojgnba
Graph Neural Networks (GNNs) have exploded onto the machine learning scene in recent years owing to their capability to model and learn from graph-structured data. Such an ability has strong implications in a wide variety of fields whose data are inherently relational, for which conventional neural networks do not perform well. Indeed, as recent reviews can attest, research in the area of GNNs has grown rapidly and has lead to the development of a variety of GNN algorithm variants as well as to the exploration of ground-breaking applications in chemistry, neurology, electronics, or communication networks, among others. At the current stage research, however, the efficient processing of GNNs is still an open challenge for several reasons. Besides of their novelty, GNNs are hard to compute due to their dependence on the input graph, their combination of dense and very sparse operations, or the need to scale to huge graphs in some applications. In this context, this article aims to make two main contributions. On the one hand, a review of the field of GNNs is presented from the perspective of computing. This includes a brief tutorial on the GNN fundamentals, an overview of the evolution of the field in the last decade, and a summary of operations carried out in the multiple phases of different GNN algorithm variants. On the other hand, an in-depth analysis of current software and hardware acceleration schemes is provided, from which a hardware-software, graph-aware, and communication-centric vision for GNN accelerators is distilled.Sergi Abadal, Akshay Jain, Robert Guirado, Jorge López-Alonso, Eduard Alarcónwork_7uww2lnxrbdpnnyvzsanojgnbaSat, 31 Dec 2022 00:00:00 GMTDescriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths
https://scholar.archive.org/work/7kx6vshwkjabhnaukqodb5j6ka
Community detection is one of the most important methodological fields of network science, and one which has attracted a significant amount of attention over the past decades. This area deals with the automated division of a network into fundamental building blocks, with the objective of providing a summary of its large-scale structure. Despite its importance and widespread adoption, there is a noticeable gap between what is arguably the state-of-the-art and the methods that are actually used in practice in a variety of fields. Here we attempt to address this discrepancy by dividing existing methods according to whether they have a "descriptive" or an "inferential" goal. While descriptive methods find patterns in networks based on context-dependent notions of community structure, inferential methods articulate generative models, and attempt to fit them to data. In this way, they are able to provide insights into the mechanisms of network formation, and separate structure from randomness in a manner supported by statistical evidence. We review how employing descriptive methods with inferential aims is riddled with pitfalls and misleading answers, and thus should be in general avoided. We argue that inferential methods are more typically aligned with clearer scientific questions, yield more robust results, and should be in many cases preferred. We attempt to dispel some myths and half-truths often believed when community detection is employed in practice, in an effort to improve both the use of such methods as well as the interpretation of their results.Tiago P. Peixotowork_7kx6vshwkjabhnaukqodb5j6kaMon, 26 Sep 2022 00:00:00 GMTComputing solution space properties of combinatorial optimization problems via generic tensor networks
https://scholar.archive.org/work/xee5elvwfjdvlmht37lzrjqc7m
We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the independent set problem as an example, we show how all these solution space properties can be computed in the unified approach of generic tensor networks. We demonstrate the versatility of this computational tool by applying it to several examples, including computing the entropy constant for hardcore lattice gases, studying the overlap gap properties, and analyzing the performance of quantum and classical algorithms for finding maximum independent sets.Jin-Guo Liu, Xun Gao, Madelyn Cain, Mikhail D. Lukin, Sheng-Tao Wangwork_xee5elvwfjdvlmht37lzrjqc7mFri, 23 Sep 2022 00:00:00 GMTParallel sampling of decomposable graphs using Markov chain on junction trees
https://scholar.archive.org/work/3cjqmshc7faxzda7ajknlj5yai
Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficultly in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a new parallel non-reversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph, where at every step, all edge perturbations within a partition are executed simultaneously. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current methods. The implementation of our work is available in a Python package.Mohamad Elmasriwork_3cjqmshc7faxzda7ajknlj5yaiThu, 22 Sep 2022 00:00:00 GMTObject-Based Dynamics: Applying Forman–Ricci Flow on a Multigraph to Assess the Impact of an Object on the Network Structure
https://scholar.archive.org/work/iapmcy6vabarximgk64c5amaze
Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman–Ricci flow, we assess the object's impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman–Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist.Haim Cohen, Yinon Nachshon, Anat Maril, Paz M. Naim, Jürgen Jost, Emil Saucanwork_iapmcy6vabarximgk64c5amazeMon, 19 Sep 2022 00:00:00 GMTMathematical programming for stable control and safe operation of gas transport networks
https://scholar.archive.org/work/jbrpzy7fcrf4hccjg7q4udzdzm
The fight against climate change makes extreme but inevitable changes in the energy sector necessary. These in turn lead to novel and complex challenges for the transmission system operators (TSOs) of gas transport networks. In this thesis, we consider four different planning problems emerging from real-world operations and present mathematical programming models and solution approaches for all of them. Due to regulatory requirements and side effects of renewable energy production, controlling today's gas networks with their involved topologies is becoming increasingly difficult. Based on the network station modeling concept for approximating the technical capabilities of complex subnetworks, e.g., compressor stations, we introduce a tri-level MIP model to determine important global control decisions. Its goal is to avoid changes in the network elements' settings while deviations from future inflow pressures as well as supplies and demands are minimized. A sequential linear programming inspired post-processing routine is run to derive physically accurate solutions w.r.t. the transient gas flow in pipelines. Computational experiments based on real-world data show that meaningful solutions are quickly and reliably determined. Therefore, the algorithmic approach is used within KOMPASS, a decision support system for the transient network control that we developed together with the Open Grid Europe GmbH (OGE), one of Europe's largest natural gas TSOs. Anticipating future use cases, we adapt the aforementioned algorithmic approach for hydrogen transport. We investigate whether the natural gas infrastructure can be repurposed and how the network control changes when energy-equivalent amounts of hydrogen are transported. Besides proving the need for purpose-built compressors, we observe that, due to the reduced linepack, the network control becomes more dynamic, compression energy increases by 440% on average, and stricter regulatory rules regarding the balancing of supply and demand become necessary. Extreme load flows [...]Kai Hoppmann-Baum, Technische Universität Berlin, Thorsten Kochwork_jbrpzy7fcrf4hccjg7q4udzdzmWed, 14 Sep 2022 00:00:00 GMTSpace-Efficient Representations of Graphs
https://scholar.archive.org/work/vjtulzxmxnaunai4oh7eybsmkq
Computer science is no more about computers than astronomy is about telescopes. -Edsger Dijkstra To my sister, Tamara. . . Completing a Ph.D. is a long and arduous journey, and would have been neither possible nor worth doing without all the people that helped me along the way. I am immensely thankful to all those who have contributed either to my work or to my life during these past five years. First and foremost, I would like to express my gratitude to my advisor, Michael Kapralov, for his continued guidance, encouragement, and motivation throughout my time at EPFL. One could not ask for a better mentor. His apparent love of research, and his limitless energy made him a truly inspiring person to work with. It never ceased to amaze me how many projects he could juggle simultaneously while still being able to meet regularly on each of them, and come up with brilliant insights and helpful suggestions. I'm also grateful to the culture of collaboration he cultivated, always encouraging us to share, discuss, and work together on projects; this I think is one of the biggest reasons I found my work at EPFL so enjoyable. I would also like to thank my other jury members, Mika Göös, Sanjeev Khanna, Ola Svensson, and Luca Trevisan for their time and effort in reading this thesis, as well as their insightful questions and comments during the defense. Research is not a solo endeavor, and I could never have produced the quality and quantity of work that this thesis represents without my many collaborators. It is no accident that this is the only page of my thesis written in the singular first person. Both for directly contributing to the works contained in the following chapters, and perhaps more importantly, for shaping me as a researcher through our many discussions, I am indebted to my collaborators. For this reason, I would like to express my immense gratitude to MarwaJakab Tardoswork_vjtulzxmxnaunai4oh7eybsmkqMon, 12 Sep 2022 00:00:00 GMTVariational methods and its applications to computer vision
https://scholar.archive.org/work/dtthbdie4vf7nc4nxvyanwq7rq
Many computer vision applications such as image segmentation can be formulated in a "variational" way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Erika Pellegrino, Panagiota Stathakiwork_dtthbdie4vf7nc4nxvyanwq7rqWed, 07 Sep 2022 00:00:00 GMTCOVID-19 INFODEMIC IN THE TWITTERVERSE: CHARACTERIZATION OF MISINFORMATION SPREAD AND TWITTER BOT ACTIVITY BY CRITICAL MASS, ENERGY DECAY, ENTANGLEMENTS, AND NODE SYNCHRONIZATION USING MULTILAYER AND SPECTRAL GRAPH VISUALIZATIONS, KURAMOTO MODELING, SONIFICATION, AND WAVEFUNCTION SIMULATION
https://scholar.archive.org/work/gk6ei767mfgdpiyf4hohftjhau
No communication framework for "infodemiology" or investigative techniques within the discipline of communication have covered measurement of Twitter bots' "virality" and (massive) "misinformation spread" by energy with mass and energy equivalence because these are relegated to quantum mechanics. To posit infodemical measurements, this study of "COVID-19 infodemic" on Twitter characterizes misinformation spread and Twitter bot activity by critical mass, energy decay, entanglements, and node synchronization using multilayer and spectral graph visualizations, Kuramoto modeling, sonification, and wavefunction simulation. The Python-based analytics pipeline was developed based on fundamental conceptualizations of 7 communication theories and quantum mechanics. Simulation and (stochastic) modeling were implemented to investigate the intra- and interlayer relationships between bots, humans, and tweets. This study endeavored on: (1) theorizing "virality" and bot activity, (2) data mining using Hoaxy® and bot detection set at ≥.43 using Botometer®, and (3) comprehensive analysis using state-of-the-art techniques and statistics. Misinformation spreads more frequently with user replies than with retweets and faster through interlayer edges. Super spreaders were detected using centrality-based metrics. Bots that had high betweenness and eigenvector centralities, random walk score, and PageRank score were false human accounts. Bot cliques emerged inconsistently by edge entanglement with humans. False human accounts were central spreaders and were detectable by an increase in percolation centrality, random walk and PageRank scores. Spammers were peripheral spreaders with scores decreased or unchanged whenever indirectly connected to human hubs. False human accounts connect by power-law distribution. Many cross-links were shown between bots and humans. Overall, bots (re)produce the intrinsic "virality" of tweets with human users. Bots synchronized (partially) around 400 seconds (6.67 minutes) at peak befo [...]JOANNES PAULUS TOLENTINO HERNANDEZ, SERLIE BARROGA-JAMIASwork_gk6ei767mfgdpiyf4hohftjhauFri, 02 Sep 2022 00:00:00 GMTSearch-Space Reduction via Essential Vertices
https://scholar.archive.org/work/g424tiquefftzgb65fute7ctia
We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total instance size, our focus is on finding a non-empty vertex set that belongs to an optimal solution. This decreases the size of the remaining part of the solution which still has to be found, and therefore shrinks the search space of fixed-parameter tractable algorithms for parameterizations based on the solution size. We introduce the notion of a c-essential vertex as one that is contained in all c-approximate solutions. For several classic combinatorial problems such as Odd Cycle Transversal and Directed Feedback Vertex Set, we show that under mild conditions a polynomial-time preprocessing algorithm can find a subset of an optimal solution that contains all 2-essential vertices, by exploiting packing/covering duality. This leads to FPT algorithms to solve these problems where the exponential term in the running time depends only on the number of non-essential vertices in the solution.Benjamin Merlin Bumpus, Bart M. P. Jansen, Jari J. H. de Kroon, Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Hermanwork_g424tiquefftzgb65fute7ctiaThu, 01 Sep 2022 00:00:00 GMTProbGraph: High-Performance and High-Accuracy Graph Mining with Probabilistic Set Representations
https://scholar.archive.org/work/kjqvqijal5dfjg26wx46rkku4q
Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with strong theoretical guarantees on work, depth, and result accuracy. The key idea is to represent sets of vertices using probabilistic set representations such as Bloom filters. These representations are much faster to process than the original vertex sets thanks to vectorizability and small size. We use these representations as building blocks in important parallel graph mining algorithms such as Clique Counting or Clustering. When enhanced with ProbGraph, these algorithms significantly outperform tuned parallel exact baselines (up to nearly 50x on 32 cores) while ensuring accuracy of more than 90% for many input graph datasets. Our novel bounds and algorithms based on probabilistic set representations with desirable statistical properties are of separate interest for the data analytics community.Maciej Besta, Cesare Miglioli, Paolo Sylos Labini, Jakub Tětek, Patrick Iff, Raghavendra Kanakagiri, Saleh Ashkboos, Kacper Janda, Michal Podstawski, Grzegorz Kwasniewski, Niels Gleinig, Flavio Vella, Onur Mutlu, Torsten Hoeflerwork_kjqvqijal5dfjg26wx46rkku4qFri, 26 Aug 2022 00:00:00 GMTExplaining news spreading phenomena in social networks
https://scholar.archive.org/work/bd277sxfsnh5rphpi3hzoscplu
When a high-ranking British politician was falsely accused of child abuse by the BBC in November 2012, a wave of short messages followed on the online social network Twitter leading to considerable damage to his reputation. However, not only did the politician's image suffer considerable damage, moreover, he was also able to sue the BBC for £185,000 in damages. On the relatively new media of the internet and specifically in online social networks, digital wildfires, i.e., fast spreading, counterfactual or even intentionally misleading information occur on a regular basis and lead to severe repercussions. Although the example of the British politician is a simple digital wildfire that only damaged the reputation of a single person, there are more complex digital wildfires whose consequences are more far-reaching. This thesis deals with the capture, automatic processing, and investigation of a complex digital wildfire, namely, the Corona and 5G misinformtionsevent - the idea that the COVID-19 outbreak is somehow connected to the introduction of the 5G wireless technology. In this context, we present a system whose application allows us to acquire large amounts of data from the online social network Twitter and thus create the database from which we extract the digital wildfire in its entirety. Furthermore, we present a framework that provides the playing field for investigating the spread of digital wildfires. The main findings that emerge from the study of the 5G and corona misinformation event can be summarised as follows. Although published work suggests that a purely structure-based analysis of the information spread allows for early detection, there is no way of predictively labelling spreading information as probably leading to a digital wildfire. Digital wildfires do not emerge out of nowhere but find their origin in a multitude of already existing ideas and narratives that are reinterpreted and recomposed in the light of a new situation. It does not matter if ideas and explanations contradict each other. On [...]Daniel Thilo Schroeder, Technische Universität Berlin, Odej Kao, Johannes Langguth, Pål Halvorsenwork_bd277sxfsnh5rphpi3hzoscpluWed, 24 Aug 2022 00:00:00 GMTDagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issue
https://scholar.archive.org/work/scntyrlsivecdcac4psbic4qzy
Dagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issuework_scntyrlsivecdcac4psbic4qzyTue, 23 Aug 2022 00:00:00 GMTExponential Speedup Over Locality in MPC with Optimal Memory
https://scholar.archive.org/work/wwivgubbm5cnvc672rxwqall4u
Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal independent set, and coloring problems. A successful line of research has been studying the complexities of LCL problems on paths/cycles, trees, and general graphs, providing many interesting results for the LOCAL model of distributed computing. In this work, we initiate the study of LCL problems in the low-space Massively Parallel Computation (MPC) model. In particular, on forests, we provide a method that, given the complexity of an LCL problem in the LOCAL model, automatically provides an exponentially faster algorithm for the low-space MPC setting that uses optimal global memory, that is, truly linear. While restricting to forests may seem to weaken the result, we emphasize that all known (conditional) lower bounds for the MPC setting are obtained by lifting lower bounds obtained in the distributed setting in tree-like networks (either forests or high girth graphs), and hence the problems that we study are challenging already on forests. Moreover, the most important technical feature of our algorithms is that they use optimal global memory, that is, memory linear in the number of edges of the graph. In contrast, most of the state-of-the-art algorithms use more than linear global memory. Further, they typically start with a dense graph, sparsify it, and then solve the problem on the residual graph, exploiting the relative increase in global memory. On forests, this is not possible, because the given graph is already as sparse as it can be, and using optimal memory requires new solutions.Alkida Balliu, Sebastian Brandt, Manuela Fischer, Rustam Latypov, Yannic Maus, Dennis Olivetti, Jara Uittowork_wwivgubbm5cnvc672rxwqall4uFri, 19 Aug 2022 00:00:00 GMTAlmost Consistent Systems of Linear Equations
https://scholar.archive.org/work/4ktke6denbdqbmcnglhojd3t7e
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied equations. This problem is NP-hard and UGC-hard to approximate within any constant even for two-variable equations over the two-element field. We study this problem from the point of view of parameterized complexity, with the parameter being the number of unsatisfied equations. We consider equations defined over Euclidean domains - a family of commutative rings that generalize finite and infinite fields including the rationals, the ring of integers, and many other structures. We show that if every equation contains at most two variables, the problem is fixed-parameter tractable. This generalizes many eminent graph separation problems such as Bipartization, Multiway Cut and Multicut parameterized by the size of the cutset. To complement this, we show that the problem is W[1]-hard when three or more variables are allowed in an equation, as well as for many commutative rings that are not Euclidean domains. On the technical side, we introduce the notion of important balanced subgraphs, generalizing important separators of Marx [Theor. Comput. Sci. 2006] to the setting of biased graphs. Furthermore, we use recent results on parameterized MinCSP [Kim et al., SODA 2021] to efficiently solve a generalization of Multicut with disjunctive cut requests.Konrad K. Dabrowski, Peter Jonsson, Sebastian Ordyniak, George Osipov, Magnus Wahlströmwork_4ktke6denbdqbmcnglhojd3t7eThu, 04 Aug 2022 00:00:00 GMTAdaptive solver behavior in mixed-integer programming
https://scholar.archive.org/work/esijys24zrg6vk7tfl54dbcsdy
This thesis addresses general-purpose solution techniques for mixed-integer programs (MIPs), a paradigm which captures formulations of countless real-world optimization problems. Most state-of-the-art MIP solvers employ a version of the branch-and-bound (B&B) algorithm to solve a MIP instance to proven optimality, supported by numerous auxiliary components that contribute new solutions or improve the dual convergence. One cannot expect that all such components are equally effective on all possible instances from the tremendous range of MIP applications. Ideally, a solver adapts to a given MIP instance by concentrating the available computational budget on those components that work best. In this thesis, we develop adaptive algorithmic behavior for several such MIP solver components solver as well as the B&B search itself. We develop new notions of pseudo-cost reliability, namely relative-error reliability and hypothesis reliability, by computing confidence intervals and pairwise t-tests on branching candidates to dynamically decide if strong branching is necessary. We develop two heuristic frameworks, adaptive large neighborhood search and adaptive diving that learn the most effective primal heuristics inspired by selection strategies for the multi-armed bandit problem. The presented ideas are transferred to adaptive LP pricing to maximize LP throughout by learning the pricing strategy for the dual simplex algorithms online during the search. Our proposed adaptive algorithmic behavior extends beyond individual solving components to the B&B search as a whole. To this end, we partition the B&B search into a feasibility phase, an improvement phase, and a heuristically detected proof phase. We improve solver performance by emphasizing different components and search strategies in each phase. We propose new estimation techniques for the progress of the B&B search based on forecasting and machine learning techniques. We turn this tree-size estimation into a novel restart strategy of the B&B algo [...]Gregor Christian Hendel, Technische Universität Berlin, Thorsten Kochwork_esijys24zrg6vk7tfl54dbcsdyTue, 02 Aug 2022 00:00:00 GMTEquivariant Hypergraph Diffusion Neural Operators
https://scholar.archive.org/work/ujuqbipxlffhlego2twrcnbpi4
Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2%↑ in prediction accuracy over four datasets therein.Peihao Wang, Shenghao Yang, Yunyu Liu, Zhangyang Wang, Pan Liwork_ujuqbipxlffhlego2twrcnbpi4Fri, 22 Jul 2022 00:00:00 GMTAn Introduction to Modern Statistical Learning
https://scholar.archive.org/work/5lgf33wamrbsva3zmwtwjvfude
This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet resources that explain this or that new machine-learning algorithm in isolation, but they do not (and cannot, in so brief a space) connect these algorithms with each other or with the classical literature on statistical models, out of which the modern algorithms emerged. Also conspicuously lacking is a single notational system which, although unfazing to those already familiar with the material (like the authors of these posts), raises a significant barrier to the novice's entry. Likewise, I have aimed to assimilate the various models, wherever possible, to a single framework for inference and learning, showing how (and why) to change one model into another with minimal alteration (some of them novel, others from the literature). Some background is of course necessary. I have assumed the reader is familiar with basic multivariable calculus, probability and statistics, and linear algebra. The goal of this book is certainly not completeness, but rather to draw a more or less straight-line path from the basics to the extremely powerful new models of the last decade. The goal then is to complement, not replace, such comprehensive texts as Bishop's Pattern Recognition and Machine Learning, which is now 15 years old.Joseph G. Makinwork_5lgf33wamrbsva3zmwtwjvfudeWed, 20 Jul 2022 00:00:00 GMTAlgorithm and System Co-design for Efficient Subgraph-based Graph Representation Learning
https://scholar.archive.org/work/hmgz5binlzh3hpdrbqwmy6lak4
Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from scalability issues since they require extracting subgraphs for each training or test query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over six homogeneous, heterogeneous and higher-order graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10× speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50Haoteng Yin, Muhan Zhang, Yanbang Wang, Jianguo Wang, Pan Liwork_hmgz5binlzh3hpdrbqwmy6lak4Mon, 18 Jul 2022 00:00:00 GMTQuantum machine learning for chemistry and physics
https://scholar.archive.org/work/ts35ancqmvay5fhyqya6degva4
Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.Manas Sajjan, Junxu Li, Raja Selvarajan, Shree Hari Sureshbabu, Sumit Suresh Kale, Rishabh Gupta, Vinit Singh, Sabre Kaiswork_ts35ancqmvay5fhyqya6degva4Mon, 18 Jul 2022 00:00:00 GMT