Question

1 Prostate Cancer The data come from a study by Stamey et al. (1989). They examined the correlation between the level of prostate-specific antigen and a number of clinical measures in men who were about to receive a radical prostatectomy. The variables are log cancer volume (lcavol), log prostate weight (lweight), age, log of the amount of benign prostatic hyperplasia (lbph), seminal vesicle invasion (svi), log of capsular penetration (lcp), Gleason score (gleason), and percent of Gleason scores 4 or 5 (pgg45). i. (10 pts) Fit a linear model to the log of prostate-specific antigen, lpsa, after first standardizing the predictors to have unit variance. ii. (60 pts) Using the standardized predictors, fit a LASSO model producing the estimates using the: (a) subgradient method (b) proximal gradient method (c) accelerated proximal gradient method iii. (10 pts) Discuss your choice of the regularization parameter in each case. iv. (5 pts) Show the convergence rates of the methods in part ii.

          1 Prostate Cancer
The data come from a study by Stamey et al. (1989). They examined the correlation between
the level of prostate-specific antigen and a number of clinical measures in men who were about to
receive a radical prostatectomy. The variables are log cancer volume (lcavol), log prostate weight
(lweight), age, log of the amount of benign prostatic hyperplasia (lbph), seminal vesicle invasion
(svi), log of capsular penetration (lcp), Gleason score (gleason), and percent of Gleason scores 4 or
5 (pgg45).
i. (10 pts) Fit a linear model to the log of prostate-specific antigen, lpsa, after first standardizing
the predictors to have unit variance.
ii. (60 pts) Using the standardized predictors, fit a LASSO model producing the estimates using
the:
(a) subgradient method
(b) proximal gradient method
(c) accelerated proximal gradient method
iii. (10 pts) Discuss your choice of the regularization parameter in each case.
iv. (5 pts) Show the convergence rates of the methods in part ii.

1 Prostate Cancer
The data come from a study by Stamey et al. (1989). They examined the correlation between
the level of prostate-specific antigen and a number of clinical measures in men who were about to
receive a radical prostatectomy. The variables are log cancer volume (lcavol), log prostate weight
(lweight), age, log of the amount of benign prostatic hyperplasia (lbph), seminal vesicle invasion
(svi), log of capsular penetration (lcp), Gleason score (gleason), and percent of Gleason scores 4 or
5 (pgg45).
i. (10 pts) Fit a linear model to the log of prostate-specific antigen, lpsa, after first standardizing
the predictors to have unit variance.
ii. (60 pts) Using the standardized predictors, fit a LASSO model producing the estimates using
the:
(a) subgradient method
(b) proximal gradient method
(c) accelerated proximal gradient method
iii. (10 pts) Discuss your choice of the regularization parameter in each case.
iv. (5 pts) Show the convergence rates of the methods in part ii.

Added by Martin R.

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