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nhaliday : mit   77

Cilk Hub
looks like this is run by Billy Moses and Leiserson (the L in CLRS)
mit  tools  programming  pls  plt  systems  c(pp)  libraries  compilers  performance  homepage  concurrency 
may 2019 by nhaliday
Section 10 Chi-squared goodness-of-fit test.
- pf that chi-squared statistic for Pearson's test (multinomial goodness-of-fit) actually has chi-squared distribution asymptotically
- the gotcha: terms Z_j in sum aren't independent
- solution:
- compute the covariance matrix of the terms to be E[Z_iZ_j] = -sqrt(p_ip_j)
- note that an equivalent way of sampling the Z_j is to take a random standard Gaussian and project onto the plane orthogonal to (sqrt(p_1), sqrt(p_2), ..., sqrt(p_r))
- that is equivalent to just sampling a Gaussian w/ 1 less dimension (hence df=r-1)
QED
pdf  nibble  lecture-notes  mit  stats  hypothesis-testing  acm  probability  methodology  proofs  iidness  distribution  limits  identity  direction  lifts-projections 
october 2017 by nhaliday
6.896: Essential Coding Theory
- probabilistic method and Chernoff bound for Shannon coding
- probabilistic method for asymptotically good Hamming codes (Gilbert coding)
- sparsity used for LDPC codes
mit  course  yoga  tcs  complexity  coding-theory  math.AG  fields  polynomials  pigeonhole-markov  linear-algebra  probabilistic-method  lecture-notes  bits  sparsity  concentration-of-measure  linear-programming  linearity  expanders  hamming  pseudorandomness  crypto  rigorous-crypto  communication-complexity  no-go  madhu-sudan  shannon  unit  p:**  quixotic  advanced 
february 2017 by nhaliday

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