Center for Science of Information

1. Center forScience of Information NSF Center for Science of Information: Overview & Results National Science Foundation/Science & Technology Centers Program

2. Outline 1.Science of Information 2.Center Mission Integrated Research Education and Diversity Knowledge Transfer 3.Research Graph Compression Deinterleaving Markov Processes

3. Shannon Legacy The Information Revolution started in 1948, with the publication of: A Mathematical Theory of Communication. The digital age began. Claude Shannon: Shannon information quantifies the extent to which a recipient of data can reduce its statistical uncertainty. “semantic aspects of communication are irrelevant . . .” Fundamental Limits for Storage and Communication(Information Theory Field) Applications Enabler/Driver: CD, iPod, DVD, video games, Internet, Facebook, WiFi, mobile, Google, . . Design Driver: universal data compression, voiceband modems, CDMA, multiantenna, discrete denoising, space-time codes, cryptography, . . .

4. Post-Shannon Challenges Back from infinity: Extend Shannon findings to finite size data structures (i.e., sequences, graphs), that is, develop information theory of various data structures beyond first-order asymptotics. Science of Information: Extend Information Theory to meet new challenges in biology, massive data, communication, knowledge extraction, economics, … In order to accomplish it we must understand new aspects of information in: structure, time, space, and semantics, and dynamic information, limited resources, complexity, representation-invariant information, and cooperation & dependency.

5. Post-Shannon Challenges Structure: Measures are needed for quantifying information embodied in structures(e.g., information in material structures, nanostructures, biomolecules, gene regulatory networks, protein networks, social networks, financial transactions). Szpankowski & Choi : Information contained in unlabeled graphs & universal graphical compression.. Grama & Subramaniam: quantifying role of noise and incomplete data in biological network reconstruction. Neville: Outlining characteristics (e.g., weak dependence) sufficient for network models to be well-defined in the limit. Yu & Qi: Finding distributions of latent structures in social networks.

6. Post-Shannon Challenges Time: Classical Information Theoryis at its weakest in dealing with problems of delay (e.g., information Arriving late may be useless of has less value). Verdu & Polyanskiy: major breakthrough in extending Shannon capacity theorem to finite blocklengthinformation theory. Kumar: design reliable scheduling policies with delay constraints for wireless networks. Weissman: real time coding system to investigate the impact of delay on expected distortion. Subramaniam: reconstruct networks from dynamic biological data. Ramkrishna: quantify fluxes in biological networks by showing that enzyme metabolism is regulated by a survival strategy in controlling enzyme syntheses. Space: Bialek: explores transmission of information in making spatial patterns in developing embryos – relation to information capacity of a communication channel.

7. Post-Shannon Challenges Limited Resources: In many scenarios, information is limited by available computational resources (e.g., cell phone, living cell). Bialek works on structure of molecular networks that optimize information flow, subject to constraints on the total number of molecules being used. Verdu, Goldsmith investigates the minimum energy per bit as a function of data length in Gaussian channels. Semantics: Is there a way to account for the meaning or semantics of information? Sudan argues that the meaning of information becomes relevant whenever there is diversity across communicating parties and when parties themselves evolve over time.

8. Post-Shannon Challenges Representation-invariance: How to know whether two representations of the same information are information equivalent? Learnable Information (BigData): Data driven science focuses on extracting information from data. How much information can actually be extracted from a given data repository? How much knowledge is in Google's database? Atallah investigates how to enable the untrusted remote server to store and manipulate the client's confidential data. Clifton investigates differential privacy methods for graphs to determine conditions under which privacy is practically. Grama, Subramaniam and Szpankowskiwork on analysis of extreme-scale networks; such datasets are noisy and their analyses need fast probabilistic algorithms and compressed representations.

9. Cooperation & Dependency: How does cooperation impact information (nodes should cooperate in their own self-interest)? Cover initiates a theory of cooperation and coordination in networks, that is, they study the achievable joint distribution among network nodes, provided that the communication rates are given. Dependency and rational expectation are critical ingredients in Sims' work on modern dynamic economic theory. Coleman is studying statistical causality in neural systems by using Granger principles. Quantum Information: The flow of information in macroscopic systems and microscopic systems may posses different characteristics. Aaronson and Shor lead these investigations. Aaronson develops computational complexity of linear systems. Post-Shannon Challenges

10. Outline • Science of Information • Center Mission • Integrated Research • Education and Diversity • Knowledge Transfer 3. Research

11. Mission and Center Goals Advance science and technology through a new quantitative understanding of the representation, communication and processing of information in biological, physical, social and engineering systems. Some Specific Center’s Goals: • define core theoretical principles governing transfer of information, • develop metrics and methods for information, • apply to problems in physical and social sciences, and engineering, • offer a venue for multi-disciplinary long-term collaborations, • explore effective ways to educate students, • train the next generation of researchers, • broaden participation of underrepresented groups, • transfer advances in research to education and industry R E S E A R C H Education & Diversity Knowledge Transfer

12. STC Team Wojciech Szpankowski, Purdue Bryn Mawr College: D. Kumar Howard University: C. Liu, L. Burge MIT: P. Shor (co-PI), M. Sudan (Microsoft) Purdue University:(lead): W. Szpankowski (PI) Princeton University: S. Verdu (co-PI) Stanford University: A. Goldsmith (co-PI) Texas A&M:P.R. Kumar University of California, Berkeley: Bin Yu (co-PI) University of California, San Diego: S. Subramaniam UIUC: O. Milenkovic. Andrea Goldsmith,Stanford Peter Shor,MIT Sergio Verdú,Princeton R. Aguilar, M. Atallah, C. Clifton, S. Datta, A. Grama, S. Jagannathan, A. Mathur, J. Neville, D. Ramkrishna, J. Rice, Z. Pizlo, L. Si, V. Rego, A. Qi, M. Ward, D. Blank, D. Xu, C. Liu, L. Burge, M. Garuba, S. Aaronson, N. Lynch, R. Rivest, Y. Polyanskiy, W. Bialek, S. Kulkarni, C. Sims, G. Bejerano, T. Cover, T. Weissman, V. Anantharam, J. Gallant, C. Kaufman, D. Tse,T.Coleman. Bin Yu, U.C. Berkeley

13. Center Participant Awards • Nobel Prize (Economics): Chris Sims • National Academies (NAS/NAE) – Bialek, Cover, Datta, Lynch, Kumar, Ramkrishna, Rice, Rivest, Shor, Sims, Verdu. • Turing award winner -- Rivest. • Shannon award winners -- Cover and Verdu. • Nevanlinna Prize (outstanding contributions in Mathematical Aspects of Information Sciences) -- Sudan and Shor. • Richard W. Hamming Medal –Cover and Verdu. • Humboldt Research Award -- Szpankowski.

14. STC Staff Bob Brown Managing Director Director– WojciechSzpankowski Managing Director – Bob Brown Education Director – Brent Ladd Diversity Director– Barbara Gibson Multimedia Specialist – Mike Atwell Administrative Asst. – Kiya Smith Brent Ladd Education Director Barbara Gibson, Diversity Director Mike Atwell Multimedia Specialist Kiya Smith Administrative Asst.

15. Integrated Research Create a shared intellectual space, integral to the Center’s activities, providing a collaborative research environment that crosses disciplinary and institutional boundaries. S. Subramaniam A. Grama • Research Thrusts: • 1.Life Sciences • 2.Communication • 3.Knowledge Management(BigData) David TseT. Weissman S. Kulkarni M. Atallah

16. Opportunistic Research Workshops • Kickoff Workshop – Chicago, IL – October 6-7, 2010 (28 STC participants and students) • 1. Allerton Workshop, IL – September 28, 2010 • 2. Stanford Workshop – Palo Alto, CA – January 24, 2011 (Princeton – Stanford –Berkeley) • 3. UC San Diego Workshop – February 11, 2011 (Berkeley – UCSD) • 4. Princeton Workshop – May 13, 2011 (Princeton – Purdue) • 5. Purdue Workshop – September 9, 2011 (Berkeley – UCSD – Purdue) • 6. Allerton Workshop – September 27, 2011 (Purdue –UIUC) • 7. UCSD Workshop on Neuroscience, February 2012 (UCSD – Berkeley) • 8. Princeton Grand & Petit Challenges Workshop, March 2012 (Center-wide) • 9. Maui Workshop (ICC), (Industrial Round-Table), May, 2012 (Center-wide) • 10. MIT Workshop, July 2012.

17. Grand and Petits Challenges • Data Representation and Analysis • Succinct Data Structures (compressed structures that lend themselves to operations efficiently) • Metrics: tradeoff storage efficiency and query cost • Validations on specific data (sequences, networks, structures, high dim. sets) • Streaming Data (correlation and anomaly detection, semantics, association) • Generative Models for data (dynamic model generations) • Identifying statistically correlated graph modules (e.g., given a graph with edges weighted by node correlations and a generative model for graphs, identify the most statistically significantly correlated sun-networks) • Information theoretic methods for inference of causality from data and modeling of agents. • Complexity of flux models/networks

18. Grand and Petits Challenges 2. Challenges in Life Science • Sequence Analysis • Reconstructing sequences for emerging nano-pore sequencers. • Optimal error correction of NGS reads. • Genome-wide associations • Rigorous approach to associations while accurately quantifying the prior in data • Darwin Channel and Repetitive Channel • Semantic and syntactic integration of data from different datasets (with same or different abstractions) • Construction of flux models guided measures of information theoretic complexity of models • Quantification of query response quality in the presence of noise • Rethinking interactions and signals from fMRI • Develop in-vivo system to monitor 3D of animal brain (will allow to see the interaction between different cells in cortex – flow of information, structural relations)

19. Grand and Petits Challenges 3. Challenges in Economics • To study the impact of information flow on dynamics of economic systems • Impact of finite rate feedback and delay on system behavior • Impact of agents with widely differing capabilities (information and computation) on overall system state, and on the state of individual agents. • Choosing portfolios in the presence of information constraints.

20. Grand and Petits Challenges 4. Challenges in Communications • Coordination over networks • Game theoretic solution concept for coordination over networks • Applications in control. • Relearning information theory in non-asymptotic regimes • Modeling energy, computational power, feedback, sampling, and delay • Point to point communication with delay and/or finite rate feedback • Back from Infinity (analytic and non-asymptotic information theory) • Information and computation • Quantifying fundamental limits of in-network computation, and the computing capacity of networks for different functions • Complexity of distributed computation in wireless and wired networks • Information theoretic study of aggregation for scalable query processing

21. Prestige Lecture Series

22. Outline • Science of Information • Center Mission • Integrated Research • Education and Diversity • Knowledge Transfer • Research Graph Compression Deinterleaving Markov Processes

23. Structural Information Information Theory of Data Structures: Following Ziv (1997) we propose to explore finite size information theory of data structures (i.e., sequences, graphs), that is, to develop information theory of various data structures beyond first-order asymptotics. We focus here on information of graphical structures (unlabeled graphs). F. Brooks, jr.(JACM, 50, 2003, “Three Great Challenges for . . .CS”): We have no theorythat gives us a metric for the Information embodied in structure. This is the most fundamental gap in the theoretical underpinnings of information science and of computer science. Networks (Internet, protein-protein interactions, and collaboration network) and Matter (chemicals and proteins) have structures. They can be abstracted by (unlabeled) graphs. (Y. Choi, W.S., IEEE Trans. Info.Th., 58, 2012)

24. Graph and Structural Entropy Information Content of Unlabeled Graphs: A structure model Sof a graph G is defined for an unlabeled version. Some labeled graphs have the same structure. Graph Entropyvs Structural Entropy: The probability of a structure Sis: P(S) = N(S) · P(G) where N(S) is the number of different labeled graphs having the same structure. 24

25. Relationship between and

26. Erdös-RényiGraph Model

27. Structural Entropy

28. Compression Algorithm called Structural zipin short SZIP – Demo Structural Zip (SZIP) Algorithm

29. Asymptotic Optimality of SZIP

30. Outline • Science of Information • Center Mission • Integrated Research • Education and Diversity • Knowledge Transfer • Research Graph Compression Deinterleaving Markov Processes

31. Interleaved Streams • User 1 output: • aababbaaababaabbbbababbabaaaabbb • User 2 output: • ABCABCABCABCABCABCABCABCABCAB • But only one log file is available, with no correlation between users: • aABacbAabbBaCaABababCaABCAabBbc • Questions: • Can we detect the existence of two users? • Can we de-interleave the two streams? (G. Seroussi, W.S., M. Weinberger, IEEE Trans. Info. Th., 2012.)

32. Probabilistic Model

33. Problem Statement Given a sampleof,infer the partition(s) ( w.h.p. as ) Some Observations: • Is there a unique solution? (Not always!) • Any partition of induces a representation of , but • may not have finite memory or ‘s may not be independent • (switch) may not be memoryless(Markov) • For the problem was studied by Batu et al. (2004) • an approach to identify one valid IMP presentation of w.h.p. • greedy, very partial use of statistics slow convergence • but simple and fast • We propose an MDLapproachfor unknown • much better results, finds all partitions compatible with • Complex if implemented via exhaustive search, but randomized gradient descentapproximation achieves virtually the same results

34. Uniqueness of Representation • Clearly, if is memorylessand then any re-partitioning of leads to another partition compatible with • canonical partition (w.r.t. ): one in which such ‘s are singletons • canonical version of (both compatible with ) • Theorem: If compatible with , then compatable with iff • IMP presentation unique up to re-partitioning of “memoryless alphabets” • Proof idea (warm-up): :any string over with • : sub-string “projected” over • : a -tuple over with • (there’s always one) • independent of • independent of ,

35. Finding via Penalized ML

36. Main Result = argmin Theorem: Let and . For in the penalization we have Proof Ideas: P is a FSM process. If P’ is the ``wrong’’ process (partition), then either one of the underlying process or switch process will not be of finite order, or some of the independence assumptions will be violated. The penalty for P’ will only increase. Rigorous proofs use large deviations results and Pinsker’s inequality over the underlying state space.

37. Experimental Results

38. Generalizationand Future Work • A different Markov order can be estimated for each , as well as more general tree models • Switch with memory • can be solved with similar tools • Future work: intersecting sub-alphabets • much more challenging!