Hands-On Learning Theory Fall 2017, Lecture 4

Hands-On Learning Theory Fall 2017, Lecture 8

Hands-On Learning Theory Fall 2016, Lecture 3

A basic property of the entropy of a discrete random variable x is that: 0 ≤ H(x) ≤ log |X | In fact, the entropy is maximal for the discrete uniform distribution. That is, (∀x ∈ X ) p(x) = 1/|X |, in which case H(x) = log |X |. Definition 3.2 (Conditional entropy). The conditional entropy of y given x is defined as: H(y|x) = ∑ v∈X px(v)H(y|x = v) = − ∑ v∈X px(v) ∑ y∈Y py|x(y|v) log py|x(y|v) =...

Hands-On Learning Theory Fall 2017, Lecture 6

Recall that in Theorem 2.1, we analyzed empirical risk minimization with a finite hypothesis class F , i.e., |F| < +∞. Here as in Theorem 4.1, we will prove results for a possibly infinite hypothesis class F . We will make a generalization with respect to the previous results. In this lecture, we have z ∈ Z and we use a hypothesis (∀h ∈ F) h : Z → R. This setting is more general than for predic...

Hands-On Learning Theory Fall 2016, Lecture 4

Recall that in Theorem 2.1, we analyzed empirical risk minimization with a finite hypothesis class F , i.e., |F| < +∞. Here, we will prove results for possibly infinite hypothesis classes. Although the PAC-Bayes framework is far more general, we will concentrate of the prediction problem as before, i.e., (∀f ∈ F) f : X → Y. Also, note that Theorem 2.1 could have been stated in a more general fa...

Improving Students’ Learning Outcomes in Safety Education through Interdepartmental Collaboration

It is critical to learn the theory to work safely. However, it is also important to learn how to apply such theories into the workplace. In addition, adults learn best when they are active partners in the learning process. The authors emphasize not to lecture adult learners but rather, get them involved in discussions, problem solving and hands-on activities. To assist this effort, Purdue Unive...