PPT-Randomized Algorithms

CS648 Lecture 22 Chebyshev Inequality Method of Bounded Difference 1 Chernoff Bound Theorem Suppose be independent Bernoulli random variables with parameters that is . Randomiza tion if done properly can keep study groups as similar as possible at the outset so that the investigators can isolate and quantify the effect of the interventions they are studying No other study design gives us the power to balance unkno 005 p0005 p0005 p0013 p0013 p0013 25 25 25 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 5 5 5 01 01 01 2345678 2345678 2345678 Change in UDysRS Score LS Mean SE Change in UDysRS Score LS Mean SE Change in UDysRS Score LS Mean SE Weeks Weeks Weeks Placeb Impact Evaluation Methods for Policy Makers. This material constitutes supporting material for the "Impact Evaluation in Practice" book. This additional material is made freely but please acknowledge its use as follows: . CS648. . Lecture 15. Randomized Incremental Construction . (building the background). 1. Partition Theorem. A set of events . ,…,. . defined over a probability space (. ,. P. ) is said to induce a partition of . 1. , Dragi Kocev. 2. , . Suzana Lo. skovska. 1. , . Sašo Džeroski. 2. 1. Faculty of Electrical Engineering and Information Technologies, Department of Computer Science, Skopje, Macedonia. . 2. . CS648. . Lecture 17. Miscellaneous applications of . Backward analysis. 1. Minimum spanning tree. 2. Minimum spanning tree. . 3. b. a. c. d. h. x. y. u. v. 18. 7. 1. 19. 22. 10. 3. 12. 3. 15. 11. 5. CS648. . Lecture . 25. Derandomization. using conditional expectation. A probability gem. 1. Derandomization. using . conditional expectation. 2. Problem 1. : Large cut in a graph. Problem:. Let . CS648. . Lecture 4. Linearity of Expectation with applications. (Most important tool for analyzing randomized algorithms). 1. RECAP from the last lecture. 2. Random variable. Definition. :. . A random variable defined over a probability space (. Data Collection: . Experiments and Observational Studies. 1/23/12. Association. versus Causation. Confounding Variables. Observational Studies . vs. Experiments. Randomized Experiments. Section 1.3. Neighborhood. Hill Climbing. : Sample p points randomly in the neighborhood of the currently best . solution; determine the best solution of the n sampled points. If it is better than the . current solution, make it the new current solution and continue the search; otherwise, . James . Aspnes. , Yale. Keren Censor-Hillel, Technion. 1. Snapshot Objects. p. 1. p. 2. p. n. …. …. update(. v. ). scan. 2. update your location. r. ead all locations. Model. 3. System of . n. . Holger Thiele, . MD. o. n behalf of the CULPRIT-SHOCK Investigators. Disclosure Statement of Financial Interest. Grant/Research . Support. Consulting Fees/Honoraria. Major Stock Shareholder/Equity. Royalty Income. Problem - a well defined task.. Sort a list of numbers.. Find a particular item in a list.. Find a winning chess move.. Algorithms. A series of precise steps, known to stop eventually, that solve a problem.. Wendy . Parulekar. MD, FRCP(C). Wei Tu PhD. Objectives. To review the classification of randomized phase II trial designs. To propose and critique potential  randomized phase II trials designs for a concept in head and neck cancer (case scenario to be presented).