1. of 19 June 15, 2015CUHK: Communication Amid Uncertainty1 Communication Amid Uncertainty Madhu Sudan Microsoft Research Based on joint works with Brendan Juba, Oded Goldreich, Adam Kalai, Sanjeev Khanna, Elad Haramaty, Jacob Leshno, Clement Canonne, Venkatesan Guruswami, Badih Ghazi, Pritish Kamath, Ilan Komargodski and Pravesh Kothari.

2. of 27 Context in Communication June 15, 2015CUHK: Communication Amid Uncertainty2

3. of 27 Communication Complexity Communication Complexity The model The model June 15, 2015CUHK: Communication Amid Uncertainty3 (with shared randomness) AliceAlice BobBob w.p. 2/3 Usually studied for lower bounds. This talk: CC as +ve model.

4. of 27 Modelling Shared Context + Imperfection 03/26/2015MSR Theory Day: ISR in Communication4 2 1 3

5. of 27 Part 1: Uncertain Compression June 15, 2015CUHK: Communication Amid Uncertainty5

6. of 27 Specific Motivation: Dictionary 10/31/2013Cornell: Uncertainty in Communication6

7. of 27 Context? In general complex notion … In general complex notion … What does sender know/believe What does sender know/believe What does receiver know/believe What does receiver know/believe Modifies as conversation progresses. Modifies as conversation progresses. Our abstraction: Our abstraction: Context = Probability distribution on potential “meanings”. Context = Probability distribution on potential “meanings”. Certainly part of what the context provides; and sufficient abstraction to highlight the problem. Certainly part of what the context provides; and sufficient abstraction to highlight the problem. 10/31/2013Cornell: Uncertainty in Communication7

8. of 27 The (Uncertain Compression) problem 10/31/2013Cornell: Uncertainty in Communication8

9. of 27 Closeness of distributions: 10/31/2013Cornell: Uncertainty in Communication9

10. of 27 Dictionary = Shared Randomness? 10/31/2013Cornell: Uncertainty in Communication10

11. of 27 Solution (variant of Arith. Coding) 10/31/2013Cornell: Uncertainty in Communication11

12. of 27 Performance 10/31/2013Cornell: Uncertainty in Communication12

13. of 27 Implications Reflects the tension between ambiguity resolution and compression. Reflects the tension between ambiguity resolution and compression. Larger the ((estimated) gap in context), larger the encoding length. Larger the ((estimated) gap in context), larger the encoding length. Entropy is still a valid measure! Entropy is still a valid measure! Coding scheme reflects the nature of human communication (extend messages till they feel unambiguous). Coding scheme reflects the nature of human communication (extend messages till they feel unambiguous). The “shared randomness’’ assumption The “shared randomness’’ assumption A convenient starting point for discussion A convenient starting point for discussion But is dictionary independent of context? But is dictionary independent of context? This is problematic. This is problematic. 10/31/2013Cornell: Uncertainty in Communication13

14. of 27 Deterministic Compression: Challenge 10/31/2013Cornell: Uncertainty in Communication14

15. of 27 Part 2: Imperfectly Shared Randomness June 15, 2015CUHK: Communication Amid Uncertainty15

16. of 27 Model: Imperfectly Shared Randomness 03/26/2015MSR Theory Day: ISR in Communication16

17. of 27 Imperfectly Shared Randomness: Results 03/26/2015MSR Theory Day: ISR in Communication17

18. of 27 Aside: Easy CC Problems 03/26/2015MSR Theory Day: ISR in Communication18 Thanks to Badih Ghazi and Pritish Kamath

19. of 27 Equality Testing (our proof) 03/26/2015MSR Theory Day: ISR in Communication19 GaussianProtocol

20. of 27 General One-Way Communication 03/26/2015MSR Theory Day: ISR in Communication20

21. of 27 General One-Way Communication 03/26/2015MSR Theory Day: ISR in Communication21

22. of 27 Two-way communication 03/26/2015MSR Theory Day: ISR in Communication22

23. of 27 Part 3: Uncertain Functionality June 15, 2015CUHK: Communication Amid Uncertainty23

24. of 27 Model June 15, 2015CUHK: Communication Amid Uncertainty24

25. of 27 Results June 15, 2015CUHK: Communication Amid Uncertainty25

26. of 27 Conclusions Context Important: Context Important: New layer of uncertainty. New layer of uncertainty. New notion of scale (context LARGE ) New notion of scale (context LARGE ) Many open directions+questions Many open directions+questions June 15, 2015CUHK: Communication Amid Uncertainty26

27. of 27 Thank You! June 15, 2015CUHK: Communication Amid Uncertainty27