arXiv subjects

Mahantesh Halappanavar

Publications and source records attributed to Mahantesh Halappanavar.

At least 55 records · Page 3Linked to original sources

arXiv2022

HBMax: Optimizing Memory Efficiency for Parallel Influence Maximization on Multicore Architectures

Influence maximization aims to select k most-influential vertices or seeds in a network, where influence is defined by a given diffusion process. Although computing optimal seed set is NP-Hard, efficient approximation algorithms exist. However, even state-of-the-art parallel implementations are limited by a sampling step that incurs large memory footprints. This in turn limits the problem size reach and approximation quality. In this work, we study the memory footprint of the sampling process collecting reverse reachability information in the IMM (Influence Maximization via Martingales) algorithm over large real-world social networks. We present a memory-efficient optimization approach (called HBMax) based on Ripples, a state-of-the-art multi-threaded parallel influence maximization solution. Our approach, HBMax, uses a portion of the reverse reachable (RR) sets collected by the algorithm to learn the characteristics of the graph. Then, it compresses the intermediate reverse reachability information with Huffman coding or bitmap coding, and queries on the partially decoded data, or directly on the compressed data to preserve the memory savings obtained through compression. Considering a NUMA architecture, we scale up our solution on 64 CPU cores and reduce the memory footprint by up to 82.1% with average 6.3% speedup (encoding overhead is offset by performance gain from memory reduction) without loss of accuracy. For the largest tested graph Twitter7 (with 1.4 billion edges), HBMax achieves 5.9X compression ratio and 2.2X speedup.

cs.DC↗

arXiv2022

Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees based on control barrier functions. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model predictive control (MPC) problems. In DPC, the predictive control policy parametrized by a neural network is optimized offline via direct policy gradients obtained by automatic differentiation of the MPC problem. The proposed approach exploits a new form of sampled-data barrier function to enforce offline and online safety requirements in DPC settings while only interrupting the neural network-based controller near the boundary of the safe set. The effectiveness of the proposed approach is demonstrated in simulation.

eess.SY↗

arXiv2022

GraMeR: Graph Meta Reinforcement Learning for Multi-Objective Influence Maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of nodes called the seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, the uses are limited due to the computational complexity of current algorithms. Recently, learning heuristics for IM have been explored to ease the computational burden. However, there are serious limitations in current approaches such as: (1) IM formulations only consider influence via spread and ignore self activation; (2) scalability to large graphs; (3) generalizability across graph families; (4) low computational efficiency with a large running time to identify seed sets for every test network. In this work, we address each of these limitations through a unique approach that involves (1) formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2) employing double Q learning to estimate seed nodes; (3) ensuring scalability via sub-graph based representations; and (4) incorporating generalizability via meta-learning across graph families. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. The results indicate that GraMeR is multiple orders faster and generic than conventional approaches.

cs.LG↗

arXiv2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present a scalable alternative called stochastic parametric differentiable predictive control (SP-DPC) for unsupervised learning of neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the SP-DPC problem's value function is backpropagated through the closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy which allows for direct model-based policy optimization. We provide theoretical probabilistic guarantees for policies learned via the SP-DPC method on closed-loop stability and chance constraints satisfaction. Furthermore, we demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

cs.LG↗

arXiv2022

Neural Lyapunov Differentiable Predictive Control

We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.

eess.SY↗

arXiv2021

Gradient-based Novelty Detection Boosted by Self-supervised Binary Classification

Novelty detection aims to automatically identify out-of-distribution (OOD) data, without any prior knowledge of them. It is a critical step in data monitoring, behavior analysis and other applications, helping enable continual learning in the field. Conventional methods of OOD detection perform multi-variate analysis on an ensemble of data or features, and usually resort to the supervision with OOD data to improve the accuracy. In reality, such supervision is impractical as one cannot anticipate the anomalous data. In this paper, we propose a novel, self-supervised approach that does not rely on any pre-defined OOD data: (1) The new method evaluates the Mahalanobis distance of the gradients between the in-distribution and OOD data. (2) It is assisted by a self-supervised binary classifier to guide the label selection to generate the gradients, and maximize the Mahalanobis distance. In the evaluation with multiple datasets, such as CIFAR-10, CIFAR-100, SVHN and TinyImageNet, the proposed approach consistently outperforms state-of-the-art supervised and unsupervised methods in the area under the receiver operating characteristic (AUROC) and area under the precision-recall curve (AUPR) metrics. We further demonstrate that this detector is able to accurately learn one OOD class in continual learning.

cs.LG↗

arXiv2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

cs.LG↗

arXiv2021

A Parallel Approximation Algorithm for Maximizing Submodular $b$-Matching

We design new serial and parallel approximation algorithms for computing a maximum weight $b$-matching in an edge-weighted graph with a submodular objective function. This problem is NP-hard; the new algorithms have approximation ratio $1/3$, and are relaxations of the Greedy algorithm that rely only on local information in the graph, making them parallelizable. We have designed and implemented Local Lazy Greedy algorithms for both serial and parallel computers. We have applied the approximate submodular $b$-matching algorithm to assign tasks to processors in the computation of Fock matrices in quantum chemistry on parallel computers. The assignment seeks to reduce the run time by balancing the computational load on the processors and bounding the number of messages that each processor sends. We show that the new assignment of tasks to processors provides a four fold speedup over the currently used assignment in the NWChemEx software on $8000$ processors on the Summit supercomputer at Oak Ridge National Lab.

cs.DS↗

arXiv2021

V2W-BERT: A Framework for Effective Hierarchical Multiclass Classification of Software Vulnerabilities

Weaknesses in computer systems such as faults, bugs and errors in the architecture, design or implementation of software provide vulnerabilities that can be exploited by attackers to compromise the security of a system. Common Weakness Enumerations (CWE) are a hierarchically designed dictionary of software weaknesses that provide a means to understand software flaws, potential impact of their exploitation, and means to mitigate these flaws. Common Vulnerabilities and Exposures (CVE) are brief low-level descriptions that uniquely identify vulnerabilities in a specific product or protocol. Classifying or mapping of CVEs to CWEs provides a means to understand the impact and mitigate the vulnerabilities. Since manual mapping of CVEs is not a viable option, automated approaches are desirable but challenging. We present a novel Transformer-based learning framework (V2W-BERT) in this paper. By using ideas from natural language processing, link prediction and transfer learning, our method outperforms previous approaches not only for CWE instances with abundant data to train, but also rare CWE classes with little or no data to train. Our approach also shows significant improvements in using historical data to predict links for future instances of CVEs, and therefore, provides a viable approach for practical applications. Using data from MITRE and National Vulnerability Database, we achieve up to 97% prediction accuracy for randomly partitioned data and up to 94% prediction accuracy in temporally partitioned data. We believe that our work will influence the design of better methods and training models, as well as applications to solve increasingly harder problems in cybersecurity.

cs.LG↗

arXiv2018

A 2/3-Approximation Algorithm for Vertex-weighted Matching in Bipartite Graphs

We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, the weight of a matching is the sum of the weights of the matched vertices, and we are required to compute a matching of maximum weight. We describe an exact algorithm for MVM with $O(|V|\, |E|)$ time complexity, and then we design a $2/3$-approximation algorithm for MVM on bipartite graphs by restricting the length of augmenting paths to at most three. The latter algorithm has time complexity $O(|E| + |V| \log |V|)$. The approximation algorithm solves two MVM problems on bipartite graphs, each with weights only on one vertex part, and then finds a matching from these two matchings using the Mendelsohn-Dulmage Theorem. The approximation ratio of the algorithm is obtained by considering failed vertices, i.e., vertices that the approximation algorithm fails to match but the exact algorithm does. We show that at every step of the algorithm there are two distinct heavier vertices that we can charge each failed vertex to. We have implemented the $2/3$-approximation algorithm for MVM and compare it with four other algorithms: an exact MEM algorithm, the exact MVM algorithm, a $1/2$-approximation algorithm for MVM, and a scaling-based $(1-ε)$-approximation algorithm for MEM. We also show that MVM problems should not be first transformed to MEM problems and solved using exact algorithms for the latter, since this transformation can increase runtimes by several orders of magnitude.

cs.DS↗

arXiv2018

A generative graph model for electrical infrastructure networks

We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the model design, we analyze the properties of power grid graphs derived from the U.S. Eastern Interconnection, Texas Interconnection, and Poland transmission system power grids. Across these datasets, we find subgraphs induced by nodes of the same voltage level exhibit shared structural properties atypical to small-world networks, including low local clustering, large diameter, and large average distance. On the other hand, we find subgraphs induced by transformer edges linking nodes of different voltage types contain a more limited structure, consisting mainly of small, disjoint star graphs. The goal of our proposed model is to match both these inter and intra-network properties by proceeding in two phases: the first phase adapts the Chung-Lu random graph model, taking desired vertex degrees and desired diameter as inputs, while the second phase of the model is based on a simpler random star graph generation process. We test the model's performance by comparing its output across many runs to the aforementioned real data. In nearly all categories tested, we find our model is more accurate in reproducing the unusual mixture of properties apparent in the data than the Chung-Lu model. We also include graph visualization comparisons, a brief analysis of edge-deletion resiliency, and guidelines for artificially generating the model inputs in the absence of real data.

physics.soc-ph↗

arXiv2017

Comparative Study of Clustering Techniques for Real-Time Dynamic Model Reduction

Dynamic model reduction in power systems is necessary for improving computational efficiency. Traditional model reduction using linearized models or online analysis is not adequate to capture dynamic behaviors of the power system, especially with the new mix of intermittent generation and intelligent consumption making the power system more dynamic and non-linear. Real-time dynamic model reduction has emerged to fill this important need. This paper explores using clustering techniques to analyze real-time phasor measurements to identify groups of generators with similar behavior, as well as a representative generator from each group for dynamic model reduction. Two clustering techniques -- graph clustering and k-means -- are considered. These techniques are compared with a previously developed dynamic model reduction approach using Singular Value Decomposition. Two sample power grid data sets are used to test these different model reduction techniques. Based on the algorithms' relative performance, recommendations are provided for practical use.

physics.soc-ph↗

arXiv2017

Exploring the Role of Intrinsic Nodal Activation on the Spread of Influence in Complex Networks

In many complex networked systems, such as online social networks, activity originates at certain nodes and subsequently spreads on the network through influence. In this work, we consider the problem of modeling the spread of influence and the identification of influential entities in a complex network when nodal activation can happen via two different mechanisms. The first mechanism of activation stems from factors that are intrinsic to the node. The second mechanism comes from the influence of connected neighbors. After introducing the model, we provide an algorithm to mine for the influential nodes in such a scenario by modifying the well-known influence maximization algorithm to work with our model that incorporates both forms of activation. Our model can be considered as a variation of the independent cascade diffusion model. We provide small motivating examples to facilitate an intuitive understanding of the effect of including the intrinsic activation mechanism. We sketch a proof of the submodularity of the influence function under the new formulation and demonstrate the same on larger graphs. Based on the model, we explain how influential content creators can drive engagement on social media platforms. Using additional experiments on a Twitter dataset, we then show how the formulation can be applied to real-world social media datasets. Finally, we derive a centrality metric that takes into account, both the mechanisms of activation and provides for an accurate, computationally efficient, alternate approach to the problem of identifying influencers under intrinsic activation.

cs.SI↗

arXiv2017

AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids

We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform N - k contingency analysis, i.e., determine the state of the system when exactly k links from N fail. Our algorithms augment the matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and vectors to accelerate the overall computation. We analyze the time complexity of both algorithms, and show that it is bounded by the number of nonzeros in a subset of the columns of the Cholesky factor that are selected by the nonzeros in the sparse right-hand-side vector. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing N - k contingency analysis on a 778 thousand bus grid, updating a solution with k = 20 elements in 16 milliseconds on an Intel Xeon processor.

cs.CE↗

arXiv2015

A Network-of-Networks Model for Electrical Infrastructure Networks

Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to solve these problems, but are subject to several limitations. One of the limitations is the ability to model a heterogeneous system in a consistent manner using the standard graph-theoretic formulation. In this paper, we propose a {\em network-of-networks} approach for modeling power transmission networks in order to explicitly incorporate heterogeneity in the model. This model distinguishes between different components of the network that operate at different voltage ratings, and also captures the intra and inter-network connectivity patterns. By building the graph in this fashion we present a novel, and fundamentally different, perspective of power transmission networks. Consequently, this novel approach will have a significant impact on the graph-theoretic modeling of power grids that we believe will lead to a better understanding of transmission networks.

physics.soc-ph↗

arXiv2014

Parallel Heuristics for Scalable Community Detection

Community detection has become a fundamental operation in numerous graph-theoretic applications. It is used to reveal natural divisions that exist within real world networks without imposing prior size or cardinality constraints on the set of communities. Despite its potential for application, there is only limited support for community detection on large-scale parallel computers, largely owing to the irregular and inherently sequential nature of the underlying heuristics. In this paper, we present parallelization heuristics for fast community detection using the Louvain method as the serial template. The Louvain method is an iterative heuristic for modularity optimization. Originally developed by Blondel et al. in 2008, the method has become increasingly popular owing to its ability to detect high modularity community partitions in a fast and memory-efficient manner. However, the method is also inherently sequential, thereby limiting its scalability. Here, we observe certain key properties of this method that present challenges for its parallelization, and consequently propose heuristics that are designed to break the sequential barrier. For evaluation purposes, we implemented our heuristics using OpenMP multithreading, and tested them over real world graphs derived from multiple application domains (e.g., internet, citation, biological). Compared to the serial Louvain implementation, our parallel implementation is able to produce community outputs with a higher modularity for most of the inputs tested, in comparable number or fewer iterations, while providing absolute speedups of up to 16x using 32 threads.

cs.SI↗

arXiv2013

Towards a Networks-of-Networks Framework for Cyber Security

Networks-of-networks (NoN) is a graph-theoretic model of interdependent networks that have distinct dynamics at each network (layer). By adding special edges to represent relationships between nodes in different layers, NoN provides a unified mechanism to study interdependent systems intertwined in a complex relationship. While NoN based models have been proposed for cyber-physical systems, in this position paper we build towards a three-layered NoN model for an enterprise cyber system. Each layer captures a different facet of a cyber system. We present in-depth discussion for four major graph- theoretic applications to demonstrate how the three-layered NoN model can be leveraged for continuous system monitoring and mission assurance.

cs.CR↗

arXiv2012

Feature Clustering for Accelerating Parallel Coordinate Descent

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building upon previous work on coordinate descent algorithms for L1-regularized problems, we introduce a novel family of algorithms called block-greedy coordinate descent that includes, as special cases, several existing algorithms such as SCD, Greedy CD, Shotgun, and Thread-Greedy. We give a unified convergence analysis for the family of block-greedy algorithms. The analysis suggests that block-greedy coordinate descent can better exploit parallelism if features are clustered so that the maximum inner product between features in different blocks is small. Our theoretical convergence analysis is supported with experimental re- sults using data from diverse real-world applications. We hope that algorithmic approaches and convergence analysis we provide will not only advance the field, but will also encourage researchers to systematically explore the design space of algorithms for solving large-scale L1-regularization problems.

stat.ML↗