ML: Lecture 8

This week

in Witten: Finish Chapter 4, start Chapter 5
Test on Thursday
Hw 3 will be due in Week 6 and will be based on Lab 4
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Was Lab 4 too tedious?
What is upper division credit?
You do need to turn in all hw and labs; however, you don't have to complete everything 
on all of them.  Some weeks you may have too much to do.  Or each week you focus on a 
different aspect.  However, for ML upper division 
work you should do a very good job on some of the homework or labs to demonstrate your
level of understanding, e.g. doing some optional parts.  Also, your project is important for 
upper division credit.  

Spend a reasonable amount of time on each lab or homework -- not too little and not
too much.

Bayesian Probability

The basic formula P(A | B) * P(B) = P(A ∩ B)

                  P(A | B) * P(B)
    P(B | A) = ---------------------
                     P(A)

The other piece is P(A) = P(A ∩ B) + P(A – B)

Lastly, assuming independence, if A = A₁∩…∩A_n, then we have

  P(A | B) = P(A₁∩...∩A_n | B) = 
  P(A₁ | B) *... * P( A_n | B)

The Laplace estimator for dealing with very low probabilities.

Linear Models

Remember the exercise to find a line that separates one species of iris from another?
That is a particular approach to linear modeling:
```
    ∑ w_i⋅a_i 
    w₀ + w₁⋅a₁ + ... +w_k⋅a_k
  
```
A decision is made based on whether this expression is positive or negative. (linear
separation)
We can also formulate the problem as approximating the function, which is 0 or 1
```
xⁱ =  w₀ + w₁⋅a₁ⁱ + ... +w_k⋅a_kⁱ    
  
```
What is multi-response linear regression?
logistic regression
Perceptron model and learning rule.
Winnow rule.

Instance-based models

The basic idea is to use the instances themselves as the model for a class or cluster.
This leads to ideas like k-nearest neighbors and k-means.

We need a distance function, e.g. Euclidean distance

In order to make this efficient, we can turn to data structures for some ideas:
k-D trees and Ball trees.

Practice the algorithm for constructing a 2-D tree. Can you state it?
Some optimizations. Which axis to pick, which point to pick? Do you use median or mean? Why?

How do you access a Ball Tree? How do you construct one?

Review

Decision Trees: divide-and-conquer

How do you apply the formula to the following set of sets:

  {yes, yes, yes, no, no}, {yes, yes}, {yes, no, no, no}

Gain ratio: information with classes / information ignoring classes.

Rule Sets: separate and conquer

coverage vs accuracy: false negatives vs false positives. If the coverage
is 80%, what is the false negative rate? If you are a supermarket manager, what
does this mean in practice? Note that accuracy is what is meant by confidence in Weka.
What is the relationship between information and accuracy and coverage?
Rules vs Trees: for decision trees, you choose one attribute at a time and make
a decision node for that attribute. For decision rules, you choose one class at a
time and make a list of rules for that class.
Choose an attribute-value pair that maximizes the accuracy and then coverage,
the probability of the desired classification. PRISM?
rules vs decision lists: rule sets can be executed in any order, decision lists are
ordered

Association Rules

threshold on coverage.
An item is an attribute-value pair.
An item set is a set of items [with no duplicate attributes].
An efficient algorithm starts with 1-item sets, then 2-item sets, etc.
Each pass through the large amount of data has a significant time penalty.
Ideally, you would only look at each datum once. However, coverage is a global property, so you can’t just process one datum at a time and then never look at it again.