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notes

college

• yale s&ds 669 (statistical learning theory)
  • course notes
  • final presentation
• yale math 330 (measure-theoretic probability)
  • proof of randomly indexed clt
• cornell/bard measure theory
  • solutions to “lebesgue measure”
  • solutions to “introduction to the lebesgue integral”
  • solutions to “introduction to probability theory (with measures)”
• columbia ieor e4706
  • solutions to “a brief introduction to stochastic calculus”
• yale s&ds 242
  • sandwich asymptotic variance
• solutions to zach furman’s singular learning theory exercises

random

• berkeley eecs 126 (probability & random processes)
  • reversible markov chains & poisson processes
• berkeley eecs 127 (optimization models)
  • line convexity, convex duality, & farkas lemma
• uc davis sta 141c (big data & hpc)
  • k-means & hierarchical clustering

doodles

• derivation of black-scholes-merton pde under risk-neutral probability measure
• informal proof: itô process is a martingale ⇒ itô process is driftless
• proof of cauchy-schwarz inequality for expectations
• proof of triangle inequality for expectations
• informal proof of optional stopping theorem for martingales
• expected # of visits to transient state in an absorbing markov chain
• proof of perceptron mistake bound
• asymptotic normality of sample quantiles
• asymptotic normality of m-estimators
• derivation for two-sided ockham’s razor bound
• l2 regularization: gaussian prior on weights for linear regression
• l1 regularization: laplace prior on weights for linear regression
• ridge regression closed form solution