indrajit saha | Indian Institute of Technology Bombay (original) (raw)

Papers by indrajit saha

arXiv (Cornell University), Sep 4, 2020

The spread of fake news on online social networks (OSNs) has become a matter of concern. These pl... more The spread of fake news on online social networks (OSNs) has become a matter of concern. These platforms are also used for propagating important authentic information. Thus, there is a need for mitigating fake news without significantly influencing the spread of real news. We leverage users' inherent capabilities of identifying fake news and propose a warning-based control mechanism to curb this spread. Warnings are based on previous users' responses that indicate the authenticity of the news. We use population-size dependent continuous-time multi-type branching processes to describe the spreading under the warning mechanism. We also have new results towards these branching processes. The (time) asymptotic proportions of the individual populations are derived using stochastic approximation tools. Using these, relevant type 1, type 2 performances are derived and an appropriate optimization problem is solved. The proposed mechanism effectively controls fake news, with negligible influence on the propagation of authentic news. We validate performance measures using Monte Carlo simulations on network connections provided by Twitter data. 1 visits OSN, opens his timeline and reads the news/post.

arXiv (Cornell University), Jul 18, 2018

Many systems require frequent and regular updates of a certain information. These updates have to... more Many systems require frequent and regular updates of a certain information. These updates have to be transferred regularly from the source to the destination. We consider scenarios in which an old packet becomes completely obsolete, in the presence of a new packet. In this context, if a new packet arrives at the source while it is transferring a packet, one needs to decide the packet to be dropped. New packet has recent information, but might require more time to transfer. Thus it is not clear as to which packet to be discarded, and this is the main focus of the paper. Recently introduced performance metrics, called average age of information (AAoI) and peak age of information (PAoI) of the information available at the destination, are the relevant performance measures. These type of systems do not require storage buffers, of size more than one, at the source queue. We consider single source / multiple sources regularly updating information to a single destination possibly over wireless channels to derive optimal drop policies that optimize the AAoI. We showed that the state independent (static) policies like dropping always the old packets or dropping always the new packets is optimal in many scenarios, among an appropriate set of stationary Markov policies. We consider relevant games when multiple sources compete. In many scenarios, the non-cooperative solution 'almost' minimizes the social objective, the sum of AAoIs of all the sources.

arXiv (Cornell University), Feb 20, 2020

We consider a random financial network with a large number of agents. The agents connect through ... more We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at the end of the contract period can be expressed as solutions of random fixed point equations. Our first step is to derive these solutions (asymptotically), using a recent result on random fixed point equations. We consider a large population in which the agents adapt one of the two available strategies, risky or risk-free investments, with an aim to maximize their expected returns (or surplus). We aim to study the emerging strategies when different types of replicator dynamics capture inter-agent interactions. We theoretically reduced the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). We proved that the equilibrium strategies converge almost surely to that of an attractor of the ODE. We also derived the conditions under which a mixed evolutionary stable strategy (ESS) emerges; in these scenarios the replicator dynamics converges to an equilibrium at which the expected returns of both the populations are equal. Further the average dynamics (choices based on large observation sample) always averts systemic risk events (events with large fraction of defaults). We verified through Monte Carlo simulations that the equilibrium suggested by the ODE method indeed represents the limit of the dynamics.

Annals of Operations Research, Dec 24, 2022

We consider a large random network, in which the performance of a node depends upon that of its n... more We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional spaces, and our aim is to study their almost-sure solutions. An underlying directed random graph defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i-th FP equation depends on the j-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random 'neighbour' components. We obtain finite dimensional limit FP equations in a much smaller dimensional space, whose solutions aid to approximate the solution of FP equations for almost all realizations, as the number of nodes increases. We use Maximum theorem for non-compact sets to prove this convergence. We apply the results to study systemic risk in an example financial network with large number of heterogeneous entities. We utilized the simplified limit system to analyse trends of default probability (probability that an entity fails to clear its liabilities) and expected surplus (expected-revenue after clearing liabilities) with varying degrees of interconnections between two diverse groups. We illustrated the accuracy of the approximation using exhaustive Monte-Carlo simulations. Our approach can be utilized for a variety of financial networks (and others); the developed methodology provides approximate small-dimensional solutions to large-dimensional FP equations that represent the clearing vectors in case of financial networks.

Dynamic Games and Applications

We consider a financial network represented at any time instance by a random liability graph whic... more We consider a financial network represented at any time instance by a random liability graph which evolves over time. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liability edges. These random edges are modified (locally) by the agents over time, as they learn from their experiences and (possibly imperfect) observations. The settlement of the liabilities of various agents at the end of the contract period (at any time instance) can be expressed as solutions of random fixed point equations. Our first step is to derive the solutions of these equations (asymptotically and one for each time instance), using a recent result on random fixed point equations. The agents, at any time instance, adapt one of the two available strategies, risky or less risky investments, with an aim to maximize their returns. We aim to study the emerging strategies of such replicator dynamics that drives the financial network. We theoretically reduce the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). Using the attractors of the resulting ODE we show that the replicator dynamics converges to one of the two pure evolutionary stable strategies (all risky or all less risky agents); one can have mixed limit only when the observations are imperfect. We verify our theoretical findings using exhaustive Monte Carlo simulations. The dynamics avoid the emergence of the systemic-risk regime (where majority default). However, if all the agents blindly adapt risky strategy it can lead to systemic risk regime.

2018 IEEE Conference on Decision and Control (CDC), 2018

We consider vector fixed point (FP) equations in large dimensional spaces involving random variab... more We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i-th FP equation depends on the j-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random 'neighbour' components. We obtain finite dimensional limit FP equations (in a much smaller dimensional space), whose solutions approximate the solution of the random FP equations for almost all realizations, in the asymptotic limit (number of components increase). Our techniques are different from the traditional mean-field methods, which deal with stochastic FP equations in the space of distributions to describe the stationary distributions of the systems. In contrast our focus is on realization-wise FP solutions. We apply the results to study systemic risk in a large financial heterogeneous network with many small institutions and one big institution, and demonstrate some interesting phenomenon.