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Information theory has been traditionally studied in the context of communication theory and statistical physics. However, it has also had important applications in other fields such as computer science, economics, mathematics, and statistics. This talk is very much in the spirit of discovering applications of information theory in other fields. We will discuss three such recent applications:
Statistics: The Hirschfeld-Gebelein-Rényi maximal correlation is an important tool in statistics that has found numerous applications from correspondence analysis, to detection of non-linear patterns in data. We will describe a simple information-theoretic proof of a fundamental result on maximal correlation due to Dembo, Kagan, and Shepp (2001).
Computer Science: Boolean functions are one of the most basic objects of study in theoretical computer science. We show how information-theoretic tools can aid Fourier analytic tools in this quest. Specifically, we will consider the problem of correlation between Boolean functions on a noisy hypercube graph.
Mathematics: Hypercontractivity and Reverse Hypercontractivity are very useful tools for studying concentration of measure, and extremal questions in the geometry of high-dimensional spaces, both discrete and continuous. In this talk, we will describe a recent result by Chandra Nair characterizing hypercontractivity using information measures. We will extend this result to reverse hypercontractivity, and we will discuss implications of these results.
The title of this presentation is derived from two measures of correlation - the maximal correlation and the so-called strong data processing constant - that will be key concepts used throughout. This talk is based on joint work with Venkat Anantharam, Amin Gohari, and Chandra Nair.
Recent studies have examined racial disparities in stop-and-frisk, a widely employed but controversial policing tactic. The statistical evidence, though, has been limited and contradictory. We investigate by analyzing three million stops in New York City over five years, focusing on cases where officers suspected the stopped individual of criminal possession of a weapon (CPW). For each CPW stop, we estimate the ex-ante probability that the detained suspect would have a weapon. We find that in 44% of cases, the likelihood of finding a weapon was less than 1%, raising concerns that the legal requirement of "reasonable suspicion" was often not met. We further find that blacks and Hispanics were disproportionately stopped in these low hit rate contexts, a phenomenon largely attributable to lower thresholds for stopping individuals in high-crime, predominately minority areas, particularly public housing. Even after adjusting for location effects, however, we find that stopped blacks and Hispanics were still less likely than similarly situated whites to possess weapons, indicative of racial bias in stop decisions. We demonstrate that by conducting only the 6% ex-ante highest hit rate stops, one can both recover the majority of weapons and mitigate racial disparities. Finally, we develop stop heuristics that can be implemented as a simple scoring rule, and have comparable accuracy to our full statistical models.
This work is joint with Justin Rao (Microsoft) and Ravi Shroff (NYU).A draft of the paper can be downloaded here: https://5harad.com/papers/frisky.pdf
In this talk we will present a simple and fundamental problem: communicating via a memoryless binary erasure channel with feedback without consecutive 1's.
First, we will present the problem as a puzzle and provide a simple solution. We will prove its optimality using only counting, logics and basic probability arguments. Then we will show how we obtained the solution using information theory tools (such as the Directed information) and optimization tools (such as Dynamic Programing).
The talk will be given mostly on a whiteboard.
Based on Joint work with Oron Sabag from Ben-Gurion University and Navin Kashyap from Indian Institute of Science.
Recently, there has been a lot of work on decentralized control (team) problems -- problems in which multiple agents having different information act, perhaps in a dynamic environment, to minimize a common objective function. Such scenarios naturally occur, for example, in large-scale control systems, communication systems, organizations, and networks. However, very few team problems were known to admit optimal solutions.
In this talk, we discuss some recent results on this topic and show that a class of dynamic LQG teams with no observation sharing information structures admit team-optimal solutions. This result provides the first unified proof of existence of optimal solutions in several different classes of stochastic teams, including the celebrated Witsenhausen's counterexample, the Gaussian test channel, the Gaussian relay channel and their non-scalar extensions.