PPT-Local Linear Approximation

Math 200 Week 6 Friday Math 200 Goals Be able to compute the local linear approximation for a function of two or more variables at a given point Be able to use a local linear approximation to estimate a given quantity. . of Edit Distance. Robert Krauthgamer, . Weizmann Institute of Science. SPIRE 2013. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. Matt Weinberg. MIT .  Princeton  MSR. References: . . http. ://arxiv.org/abs/. 1305.4002. http. ://arxiv.org/abs/. 1405.5940. http. ://arxiv.org/abs/. 1305.4000. Recap. Costis. ’ Talk: . Optimal multi-dimensional mechanism: additive bidders, no constraints. Differentials and Linear Approximation. BC Calculus. Related Rates :. How . fast . is . y . changing as . x . is changing?. -. Differentials:. How . much. does . y . change as . x . changes?. M. Matsui.. Linear Cryptanalysis Method for DES Cipher. . EUROCRYPT 93, 1994. . The first experimental cryptanalysis of the Data Encryption Standard. . CRYPT0 94, 1994. . Linear Approximations. A function with one bit output is a linear function over if output is XOR of input bits.. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs (intern). Based on a paper at . ICALP’11. , joint with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Alexandr. . Andoni. . (Simons Institute). Robert . Krauthgamer. . (. Weizmann. . Institute). Ilya Razenshteyn . (CSAIL MIT). 1. Sketching. Compress a massive object to a . small. . sketch. Rich theories: . Sometimes we can handle NP problems with polynomial time algorithms which are guaranteed to return a solution within some specific bound of the optimal solution. within a constant . c. . of the optimal. Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. Local algebraic approximations. Variants on Taylor series. Local-Global approximations. Variants on “fudge factor”. Local algebraic approximations. Linear Taylor series. Intervening variables. Transformed approximation. . for Binary . Pairwise. Energies. Lena . Gorelick. . joint work with. . O. . Veksler. I. Ben . Ayed. A. Delong. . Y. . Boykov. Example of Simple Binary Energy. 2. Potts Model. Binary . Pairwise. How accurate is your estimate?. Differential Notation. The Linear Approximation to . y. = . f. (. x. ) is often written using the “differentials” . dx. and . dy. . In this notation, . dx. is used instead of . Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. LL8 Section 9. Salisbury Screen Absorber. (Janardan Nath). Top layer (a) 20 nm (b) 10 nm. Discontinuous!. Theory based on bulk Au permittivity. (d2 = 300 nm). Experiment. . Theory based on . effective.