Machine Learning

Nota:

• Two definitions of Machine Learning are offered. Arthur Samuel described it as: "the field of study that gives computers the ability to learn without being explicitly programmed." This is an older, informal definition.
• Tom Mitchell provides a more modern definition: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E." Example: playing checkers. E = the experience of playing many games of checkers T = the task of playing checkers. P = the probability that the program will win the next game.

1. Supervised ML
   1. Regression:

      Nota:

      • In a regression problem, we are trying to predict results within a continuous output, meaning that we are trying to map input variables to some continuous function.
      • Example: Given data about the size of houses on the real estate market, try to predict their price. Price as a function of size is a continuous output, so this is a regression problem.
      1. Linear Regression with One Variable

         Nota:

         • Univariate linear regression is used when you want to predict a single output value from a single input value.
         1. Hypothesis function

            Nota:

            • h_{θ}(x)=θ_{0}+θ_{1}x
         2. Cost function

            Nota:

            • Measure the accuracy of our hypothesis function
            • This takes an average  of all the results of the hypothesis with inputs from x's compared to the actual output y's. J(θ_0,θ_1)=1/{2m}∑i=1mhθ(x(i))−y(i)2
   2. Classification

      Nota:

      • In a classification problem, we are instead trying to predict results in a discrete output. In other words, we are trying to map input variables into discrete categories.
      • Example: We could turn this example into a classification problem by instead making our output about whether the house "sells for more or less than the asking price." Here we are classifying the houses based on price  into two discrete categories.
2. Unsupervised ML

   Nota:

   • Unsupervised learning allows us to approach problems with little or no idea what our results should look like. We can derive structure from data where we don't necessarily know the effect of the variables.
   1. Clustering

      Nota:

      • Clustering: Take a collection of 1000 essays written on the US Economy, and find a way to automatically group these essays into a small number that are somehow similar or related by different variables, such as word frequency, sentence length, page count, and so on.
      • We can derive this structure by clustering the data based on relationships among the variables in the data.
   2. Associative Memory

      Nota:

      • Suppose a doctor over years of experience forms associations in his mind between patient characteristics and illnesses that they have. If a new patient shows up then based on this patient’s characteristics such as symptoms, family medical history, physical attributes, mental outlook, etc the doctor associates possible illness or illnesses based on what the doctor has seen before with similar patients. This is not the same as rule based reasoning as in expert systems. In this case we would like to estimate a mapping function from patient characteristics into illnesses.