arXiv subjects

Vikram Krishnamurthy

Publications and source records attributed to Vikram Krishnamurthy.

At least 127 records · Page 7Linked to original sources

arXiv2015

Sequential Detection of Market shocks using Risk-averse Agent Based Models

This paper considers a statistical signal processing problem involving agent based models of financial markets which at a micro-level are driven by socially aware and risk- averse trading agents. These agents trade (buy or sell) stocks by exploiting information about the decisions of previous agents (social learning) via an order book in addition to a private (noisy) signal they receive on the value of the stock. We are interested in the following: (1) Modelling the dynamics of these risk averse agents, (2) Sequential detection of a market shock based on the behaviour of these agents. Structural results which characterize social learning under a risk measure, CVaR (Conditional Value-at-risk), are presented and formulation of the Bayesian change point detection problem is provided. The structural results exhibit two interesting prop- erties: (i) Risk averse agents herd more often than risk neutral agents (ii) The stopping set in the sequential detection problem is non-convex. The framework is validated on data from the Yahoo! Tech Buzz game dataset.

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arXiv2015

Online Reputation and Polling Systems: Data Incest, Social Learning and Revealed Preferences

This paper considers online reputation and polling systems where individuals make recommendations based on their private observations and recommendations of friends. Such interaction of individuals and their social influence is modelled as social learning on a directed acyclic graph. Data incest (misinformation propagation) occurs due to unintentional re-use of identical actions in the for- mation of public belief in social learning; the information gathered by each agent is mistakenly considered to be independent. This results in overconfidence and bias in estimates of the state. Necessary and sufficient conditions are given on the structure of information exchange graph to mitigate data incest. Incest removal algorithms are presented. Experimental results on human subjects are presented to illustrate the effect of social influence and data incest on decision making. These experimental results indicate that social learning protocols require careful design to handle and mitigate data incest. The incest removal algorithms are illustrated in an expectation polling system where participants in a poll respond with a summary of their friends' beliefs. Finally, the principle of revealed preferences arising in micro-economics theory is used to parse Twitter datasets to determine if social sensors are utility maximizers and then determine their utility functions.

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arXiv2014

Reinforcement Learning and Nonparametric Detection of Game-Theoretic Equilibrium Play in Social Networks

This paper studies two important signal processing aspects of equilibrium behavior in non-cooperative games arising in social networks, namely, reinforcement learning and detection of equilibrium play. The first part of the paper presents a reinforcement learning (adaptive filtering) algorithm that facilitates learning an equilibrium by resorting to diffusion cooperation strategies in a social network. Agents form homophilic social groups, within which they exchange past experiences over an undirected graph. It is shown that, if all agents follow the proposed algorithm, their global behavior is attracted to the correlated equilibria set of the game. The second part of the paper provides a test to detect if the actions of agents are consistent with play from the equilibrium of a concave potential game. The theory of revealed preference from microeconomics is used to construct a non-parametric decision test and statistical test which only require the probe and associated actions of agents. A stochastic gradient algorithm is given to optimize the probe in real time to minimize the Type-II error probabilities of the detection test subject to specified Type-I error probability. We provide a real-world example using the energy market, and a numerical example to detect malicious agents in an online social network.

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arXiv2014

Social Learning in a Human Society: An Experimental Study

This paper presents an experimental study to investigate the learning and decision making behavior of individuals in a human society. Social learning is used as the mathematical basis for modelling interaction of individuals that aim to perform a perceptual task interactively. A psychology experiment was conducted on a group of undergraduate students at the University of British Columbia to examine whether the decision (action) of one individual affects the decision of the subsequent individuals. The major experimental observation that stands out here is that the participants of the experiment (agents) were affected by decisions of their partners in a relatively large fraction (60%) of trials. We fit a social learning model that mimics the interactions between participants of the psychology experiment. Misinformation propagation (also known as data incest) within the society under study is further investigated in this paper.

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arXiv2014

Boundary value problems in consensus networks

This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such networks and show that in contrast to standard consensus networks, the network estimate converges to a general harmonic function on the graph. Furthermore, the final value depends only on the value at the boundary nodes. This has important implications in consensus networks -- for example, we show that consensus networks are extremely sensitive to the existence of a single malicious node or consistent errors in a single node. We also discuss applications of this result in social and sensor networks. We investigate the existence of boundary nodes in human social networks via an experimental study involving human subjects. Finally, the paper is concluded with the numerical studies of the boundary value problems in consensus networks.

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arXiv2014

Reduced Complexity Filtering with Stochastic Dominance Bounds: A Convex Optimization Approach

This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. Given a HMM, by using convex optimization methods for nuclear norm minimization with copositive constraints, we construct low rank stochastic marices so that the optimal filters using these matrices provably lower and upper bound (with respect to a partially ordered set) the true filtered distribution at each time instant. Since these matrices are low rank (say R), the computational cost of evaluating the filtering bounds is O(XR) instead of O(X2). A Monte-Carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior. Finally, using the Dobrushin coefficient, explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds.

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arXiv2014

Interactive Sensing and Decision Making in Social Networks

The proliferation of social media such as real time microblogging and online reputation systems facilitate real time sensing of social patterns and behavior. In the last decade, sensing and decision making in social networks have witnessed significant progress in the electrical engineering, computer science, economics, finance, and sociology research communities. Research in this area involves the interaction of dynamic random graphs, socio-economic analysis, and statistical inference algorithms. This monograph provides a survey, tutorial development, and discussion of four highly stylized examples: social learning for interactive sensing; tracking the degree distribution of social networks; sensing and information diffusion; and coordination of decision making via game-theoretic learning. Each of the four examples is motivated by practical examples, and comprises of a literature survey together with careful problem formulation and mathematical analysis. Despite being highly stylized, these examples provide a rich variety of models, algorithms and analysis tools that are readily accessible to a signal processing, control/systems theory, and applied mathematics audience.

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arXiv2014

Adaptive Search Algorithms for Discrete Stochastic Optimization: A Smooth Best-Response Approach

This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose an adaptive simulation-based search algorithm that uses a smooth best-response sampling strategy and tracks the set of global optima, yet distributes the search so that most of the effort is spent on simulating the system performance at the global optima. The algorithm converges weakly to the set of global optima even when the observation data is correlated (as long as a weak law of large numbers holds). Numerical examples show that the proposed scheme yields a faster convergence for finite sample lengths compared with several existing random search and pure exploration methods in the literature.

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arXiv2013

Interactive Sensing in Social Networks

This paper presents models and algorithms for interactive sensing in social networks where individuals act as sensors and the information exchange between individuals is exploited to optimize sensing. Social learning is used to model the interaction between individuals that aim to estimate an underlying state of nature. In this context the following questions are addressed: How can self-interested agents that interact via social learning achieve a tradeoff between individual privacy and reputation of the social group? How can protocols be designed to prevent data incest in online reputation blogs where individuals make recommendations? How can sensing by individuals that interact with each other be used by a global decision maker to detect changes in the underlying state of nature? When individual agents possess limited sensing, computation and communication capabilities, can a network of agents achieve sophisticated global behavior? Social and game theoretic learning are natural settings for addressing these questions. This article presents an overview, insights and discussion of social learning models in the context of data incest propagation, change detection and coordination of decision making.

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arXiv2013

Removal of Data Incest in Multi-agent Social Learning in Social Networks

Motivated by online reputation systems, we investigate social learning in a network where agents interact on a time dependent graph to estimate an underlying state of nature. Agents record their own private observations, then update their private beliefs about the state of nature using Bayes' rule. Based on their belief, each agent then chooses an action (rating) from a finite set and transmits this action over the social network. An important consequence of such social learning over a network is the ruinous multiple re-use of information known as data incest (or mis-information propagation). In this paper, the data incest management problem in social learning context is formulated on a directed acyclic graph. We give necessary and sufficient conditions on the graph topology of social interactions to eliminate data incest. A data incest removal algorithm is proposed such that the public belief of social learning (and hence the actions of agents) is not affected by data incest propagation. This results in an online reputation system with a higher trust rating. Numerical examples are provided to illustrate the performance of the proposed optimal data incest removal algorithm.

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arXiv2013

Tracking the Empirical Distribution of a Markov-modulated Duplication-Deletion Random Graph

This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite state Markov chain. The paper comprises of 2 results. First, motivated by social network applications, we analyze the asymptotic behavior of the degree distribution of the Markov-modulated random graph. Using the asymptotic degree distribution, an expression is obtained for the delay in searching such graphs. Second, a stochastic approximation algorithm is presented to track empirical degree distribution as it evolves over time. The tracking performance of the algorithm is analyzed in terms of mean square error and a functional central limit theorem is presented for the asymptotic tracking error.

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arXiv2012

When to look at a noisy Markov chain in sequential decision making if measurements are costly?

A decision maker records measurements of a finite-state Markov chain corrupted by noise. The goal is to decide when the Markov chain hits a specific target state. The decision maker can choose from a finite set of sampling intervals to pick the next time to look at the Markov chain. The aim is to optimize an objective comprising of false alarm, delay cost and cumulative measurement sampling cost. Taking more frequent measurements yields accurate estimates but incurs a higher measurement cost. Making an erroneous decision too soon incurs a false alarm penalty. Waiting too long to declare the target state incurs a delay penalty. What is the optimal sequential strategy for the decision maker? The paper shows that under reasonable conditions, the optimal strategy has the following intuitive structure: when the Bayesian estimate (posterior distribution) of the Markov chain is away from the target state, look less frequently; while if the posterior is close to the target state, look more frequently. Bounds are derived for the optimal strategy. Also the achievable optimal cost of the sequential detector as a function of transition dynamics and observation distribution is analyzed. The sensitivity of the optimal achievable cost to parameter variations is bounded in terms of the Kullback divergence. To prove the results in this paper, novel stochastic dominance results on the Bayesian filtering recursion are derived. The formulation in this paper generalizes quickest time change detection to consider optimal sampling and also yields useful results in sensor scheduling (active sensing).

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arXiv2012

Quickest Detection with Social Learning: Interaction of local and global decision makers

We consider how local and global decision policies interact in stopping time problems such as quickest time change detection. Individual agents make myopic local decisions via social learning, that is, each agent records a private observation of a noisy underlying state process, selfishly optimizes its local utility and then broadcasts its local decision. Given these local decisions, how can a global decision maker achieve quickest time change detection when the underlying state changes according to a phase-type distribution? The paper presents four results. First, using Blackwell dominance of measures, it is shown that the optimal cost incurred in social learning based quickest detection is always larger than that of classical quickest detection. Second, it is shown that in general the optimal decision policy for social learning based quickest detection is characterized by multiple thresholds within the space of Bayesian distributions. Third, using lattice programming and stochastic dominance, sufficient conditions are given for the optimal decision policy to consist of a single linear hyperplane, or, more generally, a threshold curve. Estimation of the optimal linear approximation to this threshold curve is formulated as a simulation-based stochastic optimization problem. Finally, the paper shows that in multi-agent sensor management with quickest detection, where each agent views the world according to its prior, the optimal policy has a similar structure to social learning.

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arXiv2011

Sequential Detection with Mutual Information Stopping Cost

This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar.

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arXiv2011

Biosensor Arrays for Estimating Molecular Concentration in Fluid Flows

This paper constructs dynamical models and estimation algorithms for the concentration of target molecules in a fluid flow using an array of novel biosensors. Each biosensor is constructed out of protein molecules embedded in a synthetic cell membrane. The concentration evolves according to an advection-diffusion partial differential equation which is coupled with chemical reaction equations on the biosensor surface. By using averaging theory methods and the divergence theorem, an approximate model is constructed that describes the asymptotic behaviour of the concentration as a system of ordinary differential equations. The estimate of target molecules is then obtained by solving a nonlinear least squares problem. It is shown that the estimator is strongly consistent and asymptotically normal. An explicit expression is obtained for the asymptotic variance of the estimation error. As an example, the results are illustrated for a novel biosensor built out of protein molecules.

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arXiv2011

Average-Consensus Algorithms in a Deterministic Framework

We consider the average-consensus problem in a multi-node network of finite size. Communication between nodes is modeled by a sequence of directed signals with arbitrary communication delays. Four distributed algorithms that achieve average-consensus are proposed. Necessary and sufficient communication conditions are given for each algorithm to achieve average-consensus. Resource costs for each algorithm are derived based on the number of scalar values that are required for communication and storage at each node. Numerical examples are provided to illustrate the empirical convergence rate of the four algorithms in comparison with a well-known "gossip" algorithm as well as a randomized information spreading algorithm when assuming a fully connected random graph with instantaneous communication.

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arXiv2011

Bayesian Sequential Detection with Phase-Distributed Change Time and Nonlinear Penalty -- A POMDP Approach

We show that the optimal decision policy for several types of Bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions. This is established by using lattice programming and stochastic orders in a partially observed Markov decision process (POMDP) framework. A stochastic gradient algorithm is presented to estimate the optimal linear approximation to this threshold curve. We illustrate these results by first considering quickest time detection with phase-type distributed change time and a variance stopping penalty. Then it is proved that the threshold switching curve also arises in several other Bayesian decision problems such as quickest transient detection, exponential delay (risk-sensitive) penalties, stopping time problems in social learning, and multi-agent scheduling in a changing world. Using Blackwell dominance, it is shown that for dynamic decision making problems, the optimal decision policy is lower bounded by a myopic policy. Finally, it is shown how the achievable cost of the optimal decision policy varies with change time distribution by imposing a partial order on transition matrices.

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arXiv2011

Quickest Time Herding and Detection for Optimal Social Learning

This paper considers social learning amongst rational agents (for example, sensors in a network). We consider three models of social learning in increasing order of sophistication. In the first model, based on its private observation of a noisy underlying state process, each agent selfishly optimizes its local utility and broadcasts its action. This protocol leads to a herding behavior where the agents eventually choose the same action irrespective of their observations. We then formulate a second more general model where each agent is benevolent and chooses its sensor-mode to optimize a social welfare function to facilitate social learning. Using lattice programming and stochastic orders, it is shown that the optimal decision each agent makes is characterized by a switching curve on the space of Bayesian distributions. We then present a third more general model where social learning takes place to achieve quickest time change detection. Both geometric and phase-type change time distributions are considered. It is proved that the optimal decision is again characterized by a switching curve We present a stochastic approximation (adaptive filtering) algorithms to estimate this switching curve. Finally, we present extensions of the social learning model in a changing world (Markovian target) where agents learn in multiple iterations. By using Blackwell stochastic dominance, we give conditions under which myopic decisions are optimal. We also analyze the effect of target dynamics on the social welfare cost.

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