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Number of Connected Components in a Graph: Estimation via Counting Patterns [article]

Ashish Khetan, Harshay Shah, Sewoong Oh
2018 arXiv   pre-print
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such a sampled subgraph is of a fundamental interest. In this work, we focus on estimating the number of connected components. It is a challenging problem and, for general graphs,
more » ... le is known about the connection between the observed subgraph and the number of connected components of the original graph. In order to make this connection, we propose a highly redundant and large-dimensional representation of the subgraph, which at first glance seems counter-intuitive. A subgraph is represented by the counts of patterns, known as network motifs. This representation is crucial in introducing a novel estimator for the number of connected components for general graphs, under the knowledge of the spectral gap of the original graph. The connection is made precise via the Schatten k-norms of the graph Laplacian and the spectral representation of the number of connected components. We provide a guarantee on the resulting mean squared error that characterizes the bias variance tradeoff. Experiments on synthetic and real-world graphs suggest that we improve upon competing algorithms for graphs with spectral gaps bounded away from zero.
arXiv:1812.00139v1 fatcat:olmz3cwckfc3fh7r2qpgeaib6a

Do Input Gradients Highlight Discriminative Features? [article]

Harshay Shah, Prateek Jain, Praneeth Netrapalli
2021 arXiv   pre-print
believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at https://github.com/harshays  ... 
arXiv:2102.12781v3 fatcat:kujienpo5jawxpapkzmt2dqu5e

The Pitfalls of Simplicity Bias in Neural Networks [article]

Harshay Shah, Kaustav Tamuly, Aditi Raghunathan, Prateek Jain, Praneeth Netrapalli
2020 arXiv   pre-print
Note that all code and datasets are available at the following repository: https://github.com/harshays/simplicitybiaspitfalls.  ... 
arXiv:2006.07710v2 fatcat:7waalb434zdu7a2va7gkrcatle

Growing Attributed Networks through Local Processes [article]

Harshay Shah, Suhansanu Kumar, Hari Sundaram
2019 arXiv   pre-print
This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain the emergence of rich structural properties found in real-world networks. We make three contributions. First, we propose a parsimonious and accurate model of attributed network growth that jointly explains the emergence of in-degree distributions, local
more » ... ng, clustering-degree relationship and attribute mixing patterns. Second, our model is based on biased random walks and uses local processes to form edges without recourse to global network information. Third, we account for multiple sociological phenomena: bounded rationality, structural constraints, triadic closure, attribute homophily, and preferential attachment. Our experiments indicate that the proposed Attributed Random Walk (ARW) model accurately preserves network structure and attribute mixing patterns of six real-world networks; it improves upon the performance of eight state-of-the-art models by a statistically significant margin of 2.5-10x.
arXiv:1712.10195v4 fatcat:cqnkgkr4mncc5pennkrrvp5gri

Model for Generating Scale-Free Artificial Social Networks Using Small-World Networks

Farhan Amin, Gyu Sang Choi
2022 Computers Materials & Continua  
Fig. 11 demonstrates the accuracy of growth models by comparing our model with the baseline Harshay shah et al. [6] Random walk (RW) model.  ...  On the other hand, the green line indicates the Harshay shah RW model. In this figure, we can see that our model preserves degree distribution compared to the RW model.  ... 
doi:10.32604/cmc.2022.029927 fatcat:nqr2vykiqbckvkd5av76islssq

Signal Strength and Noise Drive Feature Preference in CNN Image Classifiers [article]

Max Wolff, Stuart Wolff
2022 arXiv   pre-print
Harshay Shah, Kaustav Tamuly, Aditi Raghunathan, Prateek Jain, and Praneeth Netrapalli. The Pitfalls of Simplicity Bias in Neural Networks. arXiv e-prints, art. arXiv:2006.07710, June 2020.  ...  Another machine bias was identified by Shah et al. (2020)-simplicity bias-which they described as the tendency for neural network classifiers trained with gradient descent to form the "simple" decision  ... 
arXiv:2201.08893v1 fatcat:kdacquljnvbirptwqb5df3tw3y

Better Safe Than Sorry: Preventing Delusive Adversaries with Adversarial Training [article]

Lue Tao, Lei Feng, Jinfeng Yi, Sheng-Jun Huang, Songcan Chen
2021 arXiv   pre-print
Following Shah et al.  ...  For overcoming simplicity bias on MNIST-CIFAR, we modify the original -ball used in Shah et al.  ... 
arXiv:2102.04716v4 fatcat:dzm4rfswabbstckbmgybp6sr6q

Wide-minima Density Hypothesis and the Explore-Exploit Learning Rate Schedule [article]

Nikhil Iyer, V Thejas, Nipun Kwatra, Ramachandran Ramjee, Muthian Sivathanu
2021 arXiv   pre-print
Shah for helpful discussions.  ...  same test accuracy as the baseline when trained with a much shorter budget. 7 ACKNOWLEDGEMENT We would like to thank Sanjith Athlur for his help in setting up VM cluster for large training runs and Harshay  ... 
arXiv:2003.03977v5 fatcat:k5sjeuy35fahfi7senmh6adn3u

Understanding the Failure Modes of Out-of-Distribution Generalization [article]

Vaishnavh Nagarajan, Anders Andreassen, Behnam Neyshabur
2021 arXiv   pre-print
Harshay Shah, Kaustav Tamuly, Aditi Raghunathan, Prateek Jain, and Praneeth Netrapalli. The pitfalls of simplicity bias in neural networks.  ...  ., 2019; Shah et al., 2020) provide valuable answers to this question through concrete theoretical examples; however, their examples critically rely on certain factors to make the task difficult enough  ... 
arXiv:2010.15775v2 fatcat:3rc2s7gutrf3tg7i3dcrgqdoaa

Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization [article]

Jivat Neet Kaur, Emre Kiciman, Amit Sharma
2022 arXiv   pre-print
ArXiv, abs/2007.01434, 2021. [32] Harshay Shah, Kaustav Tamuly, Aditi Raghunathan, Prateek Jain, and Praneeth Netrapalli. The pitfalls of simplicity bias in neural networks.  ... 
arXiv:2206.07837v1 fatcat:b7tm7j4vgvepzax3rw2pwvc7ci