STATS 231

Homework 0 solutions CS229T/STATS231 1. Linear algebra (0 points) a (dual norm of L1 norm) The L1 norm k · k1 of a vector v 2 Rn is defined as kvk1 = nX i =1 jvij: (1) The dual norm k · k∗ of a norm k · k is defined as kvk∗ = sup kwk≤1 (v · w): (2) Compute the dual norm of the L1 norm. (Here v · w denotes the inner product between v and w: v · w , Pn i=1 viwi) Solution: We will prove that sup kwk1≤1 (v · w) = max i2[n] vi = kvk1 (3) which implies that the dua...

Homework 1 solutions CS229T/STATS231 (Fall) 1. Value of labeled data (11 points) In many applications, labeled data is expensive and therefore limited, while unlabeled data is cheap and therefore abundant. For example, there are tons of images on the web, but getting labeled images is much harder. What is the statistical value of having labeled data versus unlabeled data? This problem will explore this formally using asymptotics. Specifically, suppose we have an exponential family mod...

Homework 1 solutions CS229T/STATS231 (Fall) 1. Value of labeled data (11 points) In many applications, labeled data is expensive and therefore limited, while unlabeled data is cheap and therefore abundant. For example, there are tons of images on the web, but getting labeled images is much harder. What is the statistical value of having labeled data versus unlabeled data? This problem will explore this formally using asymptotics. Specifically, suppose we have an exponential family mod...

Homework 1 solutions CS229T/STATS231 (Fall) 1. Value of labeled data (11 points) In many applications, labeled data is expensive and therefore limited, while unlabeled data is cheap and therefore abundant. For example, there are tons of images on the web, but getting labeled images is much harder. What is the statistical value of having labeled data versus unlabeled data? This problem will explore this formally using asymptotics. Specifically, suppose we have an exponential family mod...