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# Discontinuities Demo

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### Discontinuities Demo

1. 1. Discontinuities Demo Shrayes Ramesh, PhD. Data Tactics Corporation Thursday, November 14, 13
2. 2. Challenges • how do you decide which variables capture what happened? • /when/ did an event happen • what's the effect of the event on the variables • Can we construct a UI and algorithm to tackle all three problem simultaneously? Thursday, November 14, 13
3. 3. Goals • The goal is to feed in raw data as the sole input, and obtain answers to all three questions: • (1) when did an event likely occur • (2) what variables can we use to measure the event • (3) what was the effect of the event on those variables Thursday, November 14, 13
4. 4. variable outcome Simple example effect event Thursday, November 14, 13 time
5. 5. Scaled up Thursday, November 14, 13
6. 6. With limited insight… • if we know timing and the important variables, we can measure the effect of the shock on the variables. (standard regression techniques) • if we know the set of important variables and track variables over time, we can identify timing of shocks. • if we know timing and have a long history of variable evolution, we can cluster variables by their behavior at the important point in time (relative to other points in time) Thursday, November 14, 13
7. 7. estimated effect Methodology correct effect correct timing Thursday, November 14, 13
8. 8. Methodology • For every time T and variable K, run an OLS, under the hypothesis that a shock occurred at time T to variable K • Sample is restricted to variables for a neighborhood around t, i.e. [t-bandwith , t +bandwidth]: Y(K,t) = A(K,T) + B(K,T)S(t) + e(K,t) with S(t) = 1(t>T) is an indicator with T as the time to test • Results are stored as the matrix of coefficients B(K,T) • OLS estimates of B(K,T) are biased towards zero to the extent that S(t) is misspeciﬁed. • In other words, B(K,T) will be maximally different from zero (and unbiased) at the true break T Thursday, November 14, 13
9. 9. Methodology Thursday, November 14, 13
10. 10. Answers • when did an event likely occur? – aggregate (sum) effects across all variables • what variables can we use to measure the event? – which variables had the largest effect at time point? • what was the effect of the event on those variables? – we just measured that • what variables move together often across time? – show similar variables Thursday, November 14, 13
11. 11. Example 1: Super Bowl tweets • Twitter streaming API (every tweet) • Sample of data selected from Sunday, February 3, 1600-2210 hours • Binned into minute-by-minute word counts • Out of 651k 1-grams, kept 1035 least sparse (> 30% sparse) words. • Input data is 371x1035 matrix Thursday, November 14, 13
12. 12. SUPERBOWL SHINY Thursday, November 14, 13
13. 13. Network graph of variables with correlations > .95 Halftime show Power outage Thursday, November 14, 13
14. 14. Deployable and Repeatable • The model only requires data to be transformed to a KxT matrix. – K variables – T time periods We could use this model on many other data sets! • minute-by-minute word count in twitter • stock prices • chatter on social media forums Thursday, November 14, 13
15. 15. Network graph of forums with correlations > .27 Hezbollah Thursday, November 14, 13
16. 16. Future improvements • OLS is simple and efficient, but other models may be more accurate at estimating effects in some cases • exploring different approaches to choosing which variables to consider and approach to aggregating variable effects. • massively parallel on all 630k words simultaneously? • real-time analytics on streaming data Thursday, November 14, 13