arXiv subjects

Ilya Safro

Publications and source records attributed to Ilya Safro.

At least 73 records · Page 4Linked to original sources

arXiv2021

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that take advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depend partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations. We develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. In combination, these partitions are several orders of magnitude faster than the mesh-based partition. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

physics.comp-ph↗

arXiv2021

ELRUNA: Elimination Rule-based Network Alignment

Networks model a variety of complex phenomena across different domains. In many applications, one of the most essential tasks is to align two or more networks to infer the similarities between cross-network vertices and discover potential node-level correspondence. In this paper, we propose ELRUNA (Elimination rule-based network alignment), a novel network alignment algorithm that relies exclusively on the underlying graph structure. Under the guidance of the elimination rules that we defined, ELRUNA computes the similarity between a pair of cross-network vertices iteratively by accumulating the similarities between their selected neighbors. The resulting cross-network similarity matrix is then used to infer a permutation matrix that encodes the final alignment of cross-network vertices. In addition to the novel alignment algorithm, we also improve the performance of local search, a commonly used post-processing step for solving the network alignment problem, by introducing a novel selection method RAWSEM (Randomwalk based selection method) based on the propagation of the levels of mismatching (defined in the paper) of vertices across the networks. The key idea is to pass on the initial levels of mismatching of vertices throughout the entire network in a random-walk fashion. Through extensive numerical experiments on real networks, we demonstrate that ELRUNA significantly outperforms the state-of-the-art alignment methods in terms of alignment accuracy under lower or comparable running time. Moreover, ELRUNA is robust to network perturbations such that it can maintain a close to optimal objective value under a high level of noise added to the original networks. Finally, the proposed RAWSEM can further improve the alignment quality with a less number of iterations compared with the naive local search method.

cs.SI↗

arXiv2021

Coping with Mistreatment in Fair Algorithms

Machine learning actively impacts our everyday life in almost all endeavors and domains such as healthcare, finance, and energy. As our dependence on the machine learning increases, it is inevitable that these algorithms will be used to make decisions that will have a direct impact on the society spanning all resolutions from personal choices to world-wide policies. Hence, it is crucial to ensure that (un)intentional bias does not affect the machine learning algorithms especially when they are required to take decisions that may have unintended consequences. Algorithmic fairness techniques have found traction in the machine learning community and many methods and metrics have been proposed to ensure and evaluate fairness in algorithms and data collection. In this paper, we study the algorithmic fairness in a supervised learning setting and examine the effect of optimizing a classifier for the Equal Opportunity metric. We demonstrate that such a classifier has an increased false positive rate across sensitive groups and propose a conceptually simple method to mitigate this bias. We rigorously analyze the proposed method and evaluate it on several real world datasets demonstrating its efficacy.

cs.LG↗

arXiv2020

Leveraging Special-Purpose Hardware for Local Search Heuristics

As we approach the physical limits predicted by Moore's law, a variety of specialized hardware is emerging to tackle specialized tasks in different domains. Within combinatorial optimization, adiabatic quantum computers, CMOS annealers, and optical parametric oscillators are few of the emerging specialized hardware technology aimed at solving optimization problems. In terms of mathematical framework, the Ising optimization model unifies all of these emerging special-purpose hardware. In other words, they are all designed to solve optimization problems expressed in the Ising model or equivalently as a quadratic unconstrained binary optimization model. Due to variety of constraints specific to each type of hardware, they usually suffer from a major challenge: the number of variables that the hardware can manage to solve is very limited. Given that large-scale practical problems, including problems in operations research, combinatorial scientific computing, data science and network science require significantly more variables to model than these devices provide, we are likely to witness that cloud-based deployments of these devices will be available for parallel and shared access. Thus hybrid techniques in combination with both hardware and software must be developed to utilize these technologies. Local search meta-heuristics is one of the approaches to tackle large scale problems. However, a general optimization step within local search is not traditionally formulated in the Ising form. In this work, we propose a new meta-heuristic to model local search in the Ising form for the special-purpose hardware devices. As such, we demonstrate that our method takes the limitations of the Ising model and current hardware into account, utilizes a given hardware more efficiently compared to previous approaches, while also producing high quality solutions compared to other well-known meta-heuristics.

cs.DS↗

arXiv2020

Accelerating Text Mining Using Domain-Specific Stop Word Lists

Text preprocessing is an essential step in text mining. Removing words that can negatively impact the quality of prediction algorithms or are not informative enough is a crucial storage-saving technique in text indexing and results in improved computational efficiency. Typically, a generic stop word list is applied to a dataset regardless of the domain. However, many common words are different from one domain to another but have no significance within a particular domain. Eliminating domain-specific common words in a corpus reduces the dimensionality of the feature space, and improves the performance of text mining tasks. In this paper, we present a novel mathematical approach for the automatic extraction of domain-specific words called the hyperplane-based approach. This new approach depends on the notion of low dimensional representation of the word in vector space and its distance from hyperplane. The hyperplane-based approach can significantly reduce text dimensionality by eliminating irrelevant features. We compare the hyperplane-based approach with other feature selection methods, namely \c{hi}2 and mutual information. An experimental study is performed on three different datasets and five classification algorithms, and measure the dimensionality reduction and the increase in the classification performance. Results indicate that the hyperplane-based approach can reduce the dimensionality of the corpus by 90% and outperforms mutual information. The computational time to identify the domain-specific words is significantly lower than mutual information.

cs.IR↗

arXiv2020

AML-SVM: Adaptive Multilevel Learning with Support Vector Machines

The support vector machines (SVM) is one of the most widely used and practical optimization based classification models in machine learning because of its interpretability and flexibility to produce high quality results. However, the big data imposes a certain difficulty to the most sophisticated but relatively slow versions of SVM, namely, the nonlinear SVM. The complexity of nonlinear SVM solvers and the number of elements in the kernel matrix quadratically increases with the number of samples in training data. Therefore, both runtime and memory requirements are negatively affected. Moreover, the parameter fitting has extra kernel parameters to tune, which exacerbate the runtime even further. This paper proposes an adaptive multilevel learning framework for the nonlinear SVM, which addresses these challenges, improves the classification quality across the refinement process, and leverages multi-threaded parallel processing for better performance. The integration of parameter fitting in the hierarchical learning framework and adaptive process to stop unnecessary computation significantly reduce the running time while increase the overall performance. The experimental results demonstrate reduced variance on prediction over validation and test data across levels in the hierarchy, and significant speedup compared to state-of-the-art nonlinear SVM libraries without a decrease in the classification quality. The code is accessible at https://github.com/esadr/amlsvm.

cs.LG↗

arXiv2020

Multilevel Combinatorial Optimization Across Quantum Architectures

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution.

quant-ph↗

arXiv2020

Hypergraph Partitioning With Embeddings

Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect any number of nodes. As a result, hypergraph partitioning is an NP-Hard problem to both solve or approximate. State-of-the-art algorithms that solve this problem follow the multilevel paradigm, which begins by iteratively "coarsening" the input hypergraph to smaller problem instances that share key structural features. Once identifying an approximate problem that is small enough to be solved directly, that solution can be interpolated and refined to the original problem. While this strategy represents an excellent trade off between quality and running time, it is sensitive to coarsening strategy. In this work we propose using graph embeddings of the initial hypergraph in order to ensure that coarsened problem instances retrain key structural features. Our approach prioritizes coarsening within self-similar regions within the input graph, and leads to significantly improved solution quality across a range of considered hypergraphs. Reproducibility: All source code, plots and experimental data are available at https://sybrandt.com/2019/partition.

cs.DS↗

arXiv2020

Unsupervised Hierarchical Graph Representation Learning by Mutual Information Maximization

Graph representation learning based on graph neural networks (GNNs) can greatly improve the performance of downstream tasks, such as node and graph classification. However, the general GNN models do not aggregate node information in a hierarchical manner, and can miss key higher-order structural features of many graphs. The hierarchical aggregation also enables the graph representations to be explainable. In addition, supervised graph representation learning requires labeled data, which is expensive and error-prone. To address these issues, we present an unsupervised graph representation learning method, Unsupervised Hierarchical Graph Representation (UHGR), which can generate hierarchical representations of graphs. Our method focuses on maximizing mutual information between "local" and high-level "global" representations, which enables us to learn the node embeddings and graph embeddings without any labeled data. To demonstrate the effectiveness of the proposed method, we perform the node and graph classification using the learned node and graph embeddings. The results show that the proposed method achieves comparable results to state-of-the-art supervised methods on several benchmarks. In addition, our visualization of hierarchical representations indicates that our method can capture meaningful and interpretable clusters.

cs.LG↗

arXiv2020

FOBE and HOBE: First- and High-Order Bipartite Embeddings

Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bipartite graphs that decompose edges into sets of indirect relationships between node neighborhoods. When sampling higher-order relationships, we reinforce similarities through algebraic distance on graphs. We also introduce ensemble embeddings to combine both into a "best of both worlds" embedding. The proposed methods are evaluated on link prediction and recommendation tasks and compared with other state-of-the-art embeddings. While being all highly beneficial in applications, we demonstrate that none of the considered embeddings is clearly superior (in contrast to what is claimed in many papers), and discuss the trade offs present among them. Reproducibility: Our code, data sets, and results are all publicly available online at: http://sybrandt.com/2020/fobe_hobe.

cs.LG↗

arXiv2020

Recent Advances in Scalable Network Generation

Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically spanning multiple areas of expertise. Challenges begin with the identification of relevant domain-specific network features, continue with the question of how to compile such features into a tractable model, and culminate in algorithmic details arising while implementing the pertaining model. In the present survey, we explore crucial aspects of random graph models with known scalable generators. We begin by briefly introducing network features considered by such models, and then discuss random graphs alongside with generation algorithms. Our focus lies on modelling techniques and algorithmic primitives that have proven successful in obtaining massive graphs. We consider concepts and graph models for various domains (such as social network, infrastructure, ecology, and numerical simulations), and discuss generators for different models of computation (including shared-memory parallelism, massive-parallel GPUs, and distributed systems).

cs.DS↗

arXiv2020

AGATHA: Automatic Graph-mining And Transformer based Hypothesis generation Approach

Medical research is risky and expensive. Drug discovery, as an example, requires that researchers efficiently winnow thousands of potential targets to a small candidate set for more thorough evaluation. However, research groups spend significant time and money to perform the experiments necessary to determine this candidate set long before seeing intermediate results. Hypothesis generation systems address this challenge by mining the wealth of publicly available scientific information to predict plausible research directions. We present AGATHA, a deep-learning hypothesis generation system that can introduce data-driven insights earlier in the discovery process. Through a learned ranking criteria, this system quickly prioritizes plausible term-pairs among entity sets, allowing us to recommend new research directions. We massively validate our system with a temporal holdout wherein we predict connections first introduced after 2015 using data published beforehand. We additionally explore biomedical sub-domains, and demonstrate AGATHA's predictive capacity across the twenty most popular relationship types. This system achieves best-in-class performance on an established benchmark, and demonstrates high recommendation scores across subdomains. Reproducibility: All code, experimental data, and pre-trained models are available online: sybrandt.com/2020/agatha

cs.LG↗

arXiv2020

CBAG: Conditional Biomedical Abstract Generation

Biomedical research papers use significantly different language and jargon when compared to typical English text, which reduces the utility of pre-trained NLP models in this domain. Meanwhile Medline, a database of biomedical abstracts, introduces nearly a million new documents per-year. Applications that could benefit from understanding this wealth of publicly available information, such as scientific writing assistants, chat-bots, or descriptive hypothesis generation systems, require new domain-centered approaches. A conditional language model, one that learns the probability of words given some a priori criteria, is a fundamental building block in many such applications. We propose a transformer-based conditional language model with a shallow encoder "condition" stack, and a deep "language model" stack of multi-headed attention blocks. The condition stack encodes metadata used to alter the output probability distribution of the language model stack. We sample this distribution in order to generate biomedical abstracts given only a proposed title, an intended publication year, and a set of keywords. Using typical natural language generation metrics, we demonstrate that this proposed approach is more capable of producing non-trivial relevant entities within the abstract body than the 1.5B parameter GPT-2 language model.

cs.LG↗

arXiv2019

Scalable Dynamic Topic Modeling with Clustered Latent Dirichlet Allocation (CLDA)

Topic modeling, a method for extracting the underlying themes from a collection of documents, is an increasingly important component of the design of intelligent systems enabling the sense-making of highly dynamic and diverse streams of text data. Traditional methods such as Dynamic Topic Modeling (DTM) do not lend themselves well to direct parallelization because of dependencies from one time step to another. In this paper, we introduce and empirically analyze Clustered Latent Dirichlet Allocation (CLDA), a method for extracting dynamic latent topics from a collection of documents. Our approach is based on data decomposition in which the data is partitioned into segments, followed by topic modeling on the individual segments. The resulting local models are then combined into a global solution using clustering. The decomposition and resulting parallelization leads to very fast runtime even on very large datasets. Our approach furthermore provides insight into how the composition of topics changes over time and can also be applied using other data partitioning strategies over any discrete features of the data, such as geographic features or classes of users. In this paper CLDA is applied successfully to seventeen years of NIPS conference papers (2,484 documents and 3,280,697 words), seventeen years of computer science journal abstracts (533,560 documents and 32,551,540 words), and to forty years of the PubMed corpus (4,025,978 documents and 273,853,980 words).

cs.IR↗

arXiv2019

Multistart Methods for Quantum Approximate Optimization

Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical applications. Such algorithms are often implemented in a variational form, combining classical optimization methods with a quantum machine to find parameters to maximize performance. The quality of the QAOA solution depends heavily on quality of the parameters produced by the classical optimizer. Moreover, the presence of multiple local optima in the space of parameters makes it harder for the classical optimizer. In this paper we study the use of a multistart optimization approach within a QAOA framework to improve the performance of quantum machines on important graph clustering problems. We also demonstrate that reusing the optimal parameters from similar problems can improve the performance of classical optimization methods, expanding on similar results for MAXCUT.

quant-ph↗

arXiv2019

Network Community Detection On Small Quantum Computers

In recent years a number of quantum computing devices with small numbers of qubits became available. We present a hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size. The proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. We demonstrate it to solve the 2-community detection problem on graphs of size up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. Our results demonstrate that QLS perform similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.

quant-ph↗

arXiv2019

Multiscale Planar Graph Generation

The study of network representations of physical, biological, and social phenomena can help us better understand the structural and functional dynamics of their networks and formulate predictive models of these phenomena. However, due to the scarcity of real-world network data owing to factors such as cost and effort required in collection of network data and the sensitivity of this data towards theft and misuse, engineers and researchers often rely on synthetic data for simulations, hypothesis testing, decision making, and algorithm engineering. An important characteristic of infrastructure networks such as roads, water distribution and other utility systems is that they can be embedded in a plane, therefore to simulate these system we need realistic networks which are also planar. While the currently-available synthetic network generators can model networks that exhibit realism, they do not guarantee or achieve planarity. Therefore, in this paper we present a flexible algorithm that can synthesize realistic networks that are planar. The method follows a multi-scale randomized editing approach generating a hierarchy of coarsened networks of a given planar graph and introducing edits at various levels in the hierarchy. The method preserves the structural properties with minimal bias including the planarity of the network, while introducing realistic variability at multiple scales.

cs.SI↗

arXiv2019

Centralities for Networks with Consumable Resources

Identification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic and spreading processes in networks. As a result, a number of centrality measures have been proposed and used across different application domains. At the heart of many of these measures, lies an assumption describing the manner in which traffic (of information, social actors, particles, etc.) flows through the network. For example, some measures only count shortest paths while others consider random walks. This paper considers a spreading process in which a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error correcting nodes, and consumption of ammunition of military troops while moving. We propose generalizations of the well-known measures of betweenness, random walk betweenness, and Katz centralities to take such a spreading process with consumable resources into account. In order to validate the results, experiments on real-world networks are carried out by developing simulations based on well-known models such as Susceptible-Infected-Recovered and congestion with respect to particle hopping from vehicular flow theory. The simulation-based models are shown to be highly correlated to the proposed centrality measures.

cs.SI↗