Centre for Networked Intelligence

Dear All, Networks Seminar, supported by the Centre for Networked Intelligence, is a technical discussion forum in topics including but not limited to computer networks, machine learning, signal processing, and information theory. The seminar series has a webpage hosted at https://cni.iisc.ac.in/seminars/. You are invited to the following seminar held as part of this series. Title: Asymptotics of the Number of Labelled Connected Sparse Multitype Graphs Speaker: Prof. Luisa Andreis, Professor, University of Turin Time: 4:00 PM - 5:00 PM (IST) Date: 14 September 2026 Venue: Online on Zoom Zoom link: https://us06web.zoom.us/j/83388976389?pwd=XcpO3GhLxsR14a7SVbPx33HQQa1jbt.1 Zoom Meeting ID: 833 8897 6389, Pass Code: NSSIISc YouTube: https://www.youtube.com/watch?v=Wu8MynsrO0Q&list=PLNN9TCnjABcY5RBvFXAghzQ6HMsNX8GeF Webpage Link: https://cni.iisc.ac.in/seminars/2026-09-14/ <https://cni.iisc.ac.in/seminars/2026-09-14/> Abstract: We consider the enumeration of connected multitype (colored) graphs with prescribed vertex profile and edge matrix, in the sparse regime where the number of edges and the excess are proportional to the size of the graph. This extends the classical result of Bender, Canfield, and McKay for connected sparse graphs to the multitype setting. Our approach is probabilistic: we establish that a connected multitype graph with prescribed statistics can be identified, with high probability, as the giant component of an appropriately tuned supercritical inhomogeneous random graph. Combining this correspondence with large-deviation estimates for the connectivity probability of inhomogeneous random graphs, we derive the leading exponential asymptotics of the corresponding enumeration problem. We will outline the proof strategy and discuss the connectivity constraints that arise specifically in the multitype setting. This is a joint work with M. Veshaj (WIAS- Berlin). Bio: Luisa Andreis is Associate Professor at the Department of Mathematics "Giuseppe Peano," University of Torino, in Italy. She received her PhD from the University of Padova, and held positions as a postdoc at the Weierstrass Institute in Berlin and as Assistant Professor at the University of Florence and Politecnico di Milano. Her research focuses on probability theory, with an emphasis on random graphs, large deviations, and interacting particle systems, and, most recently, on mathematical models for artificial intelligence. More Details: https://sites.google.com/view/luisaandreis/home ALL ARE WELCOME. Thank you, CNI Seminar Series Organizing Committee.

Dear All, Networks Seminar, supported by the Centre for Networked Intelligence, is a technical discussion forum in topics including but not limited to computer networks, machine learning, signal processing, and information theory. The seminar series has a webpage hosted at https://cni.iisc.ac.in/seminars/. You are invited to the following seminar held as part of this series. Title: Beyond KL Divergence: Divergence Tests for Universal Hypothesis Testing Speaker: Prof. Jithin Ravi, Assistant Professor, IIT Kharagpur Time: 4:00 PM - 5:00 PM (IST) Date: 21 September 2026 Venue: GJ Hall and Online on Zoom Tea/Coffee: 5:00 PM Zoom link: https://us06web.zoom.us/j/83388976389?pwd=XcpO3GhLxsR14a7SVbPx33HQQa1jbt.1 Zoom Meeting ID: 833 8897 6389, Pass Code: NSSIISc YouTube: https://www.youtube.com/watch?v=Wu8MynsrO0Q&list=PLNN9TCnjABcY5RBvFXAghzQ6HMsNX8GeF Webpage Link: https://cni.iisc.ac.in/seminars/2026-09-21/ <https://cni.iisc.ac.in/seminars/2026-09-21/> Abstract: We study divergence-based tests for statistical hypothesis testing in settings where the underlying distributions are only partially known. First, we consider a one-sample binary hypothesis testing problem in which the observations are i.i.d. according to either a known distribution (P) or an unknown alternative (Q). The classical test for this problem is the Hoeffding test which accepts the null hypothesis when the Kullback–Leibler (KL) divergence between the empirical distribution and (P) is below a prescribed threshold. We generalize the Hoeffding test by replacing the KL divergence with an arbitrary divergence which we refer to as the divergence test. We characterise the first- and second-order asymptotics of the type-II error probability for a fixed type-I error probability. We show that, irrespective of the divergence, divergence tests achieve the optimal first-order exponent of the Neyman–Pearson test, while their second-order performance is generally inferior. Divergence tests based on invariant divergences attain the same second-order term as the Hoeffding test, whereas suitably chosen non-invariant divergences can outperform it for certain alternatives. We further extend this framework to two-sample testing, where one observes two independent sequences of i.i.d. random variables distributed according to (P_1) and (P_2), respectively, and wishes to determine whether (P_1=P_2) (null hypothesis) or (P_1\ eq P_2) (alternative hypothesis). We generalise the Gutman test, which is designed for two-sample testing, by replacing the Jensen–Shannon divergence with an arbitrary divergence. We show that divergence tests achieve the optimal first-order exponent and that tests based on invariant divergences have the same second-order asymptotics as the Gutman test. These results provide a unified perspective on divergence-based universal hypothesis testing and establish connections between two-sample testing and robust goodness-of-fit testing. Bio: Jithin Ravi received the M.Tech. and Ph.D. degrees in electrical engineering from Indian Institute of Technology Bombay, Mumbai, in 2017. He completed his first postdoctoral fellowship at the Tata Institute of Fundamental Research, Mumbai, in 2017, followed by a second post-doctoral position at the Signal Theory and Communications Department, Universidad Carlos III de Madrid, Leganes, Spain, from 2018 to 2021. He is currently an Assistant Professor with the Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology Kharagpur. His research interests include information theory, wireless communications, information-theoretic security, and statistical inference. More Details: https://sites.google.com/view/rjithin/home ALL ARE WELCOME. Thank you, CNI Seminar Series Organizing Committee.