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CSC2515 Fall 2007  Introduction to Machine Learning Lecture 1: What is Machine Learning? All lecture slides will be available as .ppt, .ps, & .htm at www.cs.toronto.edu/~hinton Many of the figures are provided by Chris Bishop  from his textbook: ”Pattern Recognition and Machine Learning”
What is Machine Learning? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A classic example of a task that requires machine learning: It is very hard to say what makes a 2
Some more examples of tasks that are best solved by using a learning algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Some web-based examples of machine learning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Displaying the structure of a set of documents  using Latent Semantic Analysis   (a  form of PCA) Each document is converted to a vector of word counts. This vector is then mapped to two coordinates and displayed as a colored dot. The colors represent the hand-labeled classes.  When the documents are laid out in 2-D, the classes are not used. So we can judge how good the algorithm is by seeing if the classes are separated.
Displaying the structure of a set of documents  using a deep neural network
Machine Learning & Symbolic AI ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Machine Learning & Statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A spectrum of machine learning tasks ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Statistics--- --- --- --- --- --- --- Artificial Intelligence
Types of learning task ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Hypothesis Space ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Searching a hypothesis space ,[object Object],[object Object],[object Object],[object Object]
Some Loss Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Generalization ,[object Object],[object Object],[object Object],[object Object],[object Object]
Trading off the goodness of fit against  the complexity of the model ,[object Object],[object Object],[object Object],[object Object]
A sampling assumption ,[object Object],[object Object],[object Object],[object Object],[object Object]
The probabilistic guarantee ,[object Object],[object Object],[object Object],[object Object],[object Object]
A simple example: Fitting a polynomial ,[object Object],[object Object],[object Object],from Bishop
Some fits to the data: which is best? from Bishop
A simple way to reduce model complexity ,[object Object],regularization parameter target value penalized loss function from Bishop
Regularization:  vs.
Polynomial Coefficients
Using a validation set ,[object Object],[object Object],[object Object],[object Object],[object Object]
The Bayesian framework ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A coin tossing example ,[object Object],[object Object],[object Object],probability of a particular sequence
Some problems with picking the parameters that are most likely to generate the data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Using a distribution over parameter values ,[object Object],[object Object],[object Object],probability density p area=1 area=1 0 1 1 1 2 probability density probability density
Lets do it again: Suppose we get a tail ,[object Object],[object Object],[object Object],probability density p area=1 area=1 0 1 1 2
Lets do it another 98 times ,[object Object],probability density p area=1 0 1 1 2
Bayes Theorem Prior probability of weight vector W Posterior probability of weight vector W given training data D Probability of observed data given W joint probability conditional probability
A cheap trick to avoid computing the posterior probabilities of all weight vectors ,[object Object],[object Object],[object Object]
Why we maximize sums of log probs ,[object Object],[object Object],[object Object]
A even cheaper trick ,[object Object],[object Object],[object Object],[object Object]
Supervised Maximum Likelihood Learning ,[object Object],d =  the correct answer y =  model’s estimate of most probable value
Supervised Maximum Likelihood Learning ,[object Object],[object Object],[object Object]

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notes as .ppt

  • 1. CSC2515 Fall 2007 Introduction to Machine Learning Lecture 1: What is Machine Learning? All lecture slides will be available as .ppt, .ps, & .htm at www.cs.toronto.edu/~hinton Many of the figures are provided by Chris Bishop from his textbook: ”Pattern Recognition and Machine Learning”
  • 2.
  • 3. A classic example of a task that requires machine learning: It is very hard to say what makes a 2
  • 4.
  • 5.
  • 6. Displaying the structure of a set of documents using Latent Semantic Analysis (a form of PCA) Each document is converted to a vector of word counts. This vector is then mapped to two coordinates and displayed as a colored dot. The colors represent the hand-labeled classes. When the documents are laid out in 2-D, the classes are not used. So we can judge how good the algorithm is by seeing if the classes are separated.
  • 7. Displaying the structure of a set of documents using a deep neural network
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20. Some fits to the data: which is best? from Bishop
  • 21.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31. Bayes Theorem Prior probability of weight vector W Posterior probability of weight vector W given training data D Probability of observed data given W joint probability conditional probability
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.