Citadel–styleQuant ResearcherQuantitative ResearchQuestion #52
Why is regularization important, for example using ridge or lasso regression compared to ordinary least squares (OLS), even when the number of samples is greater than the number of parameters?
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Explain the difference between Lasso and Ridge regression.Given three variables x, y, and z, where x is distributed as N(0,1), z is distributed as N(0, sigma^2), and y = x + z, with x independent of z: For a given observed value of y, what is the conditional distribution of x given y, i.e., p(x|y)?What is an O(n log n) sorting algorithm? Give an example and briefly explain how it works.Suppose you want to predict y and you have predictor vectors, each with known accuracy, variance, and sample length. How do you combine these predictors to minimize the residual standard error (RSE)?There are three random variables, X, Y, Z. The correlations between each pair of variables are the same, i.e., ρ = Corr(X,Y) = Corr(Y,Z) = Corr(Z,X). What is the tightest bound you can give for ρ? How about the general case for n random variables?
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