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https://stanford.edu/~shervine CS 229 – Machine Learning VIP Cheatsheet: Supervised Learning r Cost function – The cost function J is commonly used to assess the performance of a model, and is defined with the loss function L as follows: J(θ) = Afshine Amidi and Shervine Amidi m X L(hθ (x(i) ), y (i) ) i=1 August 23, 2018 r Gradient descent – By noting α ∈ R the learning rate, the update rule for gradient descent is expressed with the learning rate and the cost function J as follows: θ ←− θ − α∇J(θ) Introduction to Supervised Learning Given a set of data points {x(1) , ..., x(m) } associated to a set of outcomes {y (1) , ..., y (m) }, we want to build a classifier that learns how to predict y from x. r Type of prediction – The different types of predictive models are summed up in the table below: Model Outcome Examples Regression Continuous Linear regression Classifier Class Logistic regression, SVM, Naive Bayes Remark: Stochastic gradient descent (SGD) is updating the parameter based on each training example, and batch gradient descent is on a batch of training examples. r Type of model – The different models are summed up in the table below: Model Goal Examples Discriminative Estimate P (y|x) Regressions, SVMs Generative Estimate P (x|y) Used to deduce P (y|x) GDA, Naive Bayes r Likelihood – The likelihood of a model L(θ) given parameters θ is used to find the optimal parameters θ through maximizing the likelihood. In practice, we use the log-likelihood `(θ) = log(L(θ)) which is easier to optimize. We have: θopt = arg max L(θ) θ r Newton’s algorithm – The Newton’s algorithm is a numerical method that finds θ such that `0 (θ) = 0. Its update rule is as follows: Notations and general concepts r Hypothesis – The hypothesis is noted hθ and is the model that we choose. For a given input data x(i) , the model prediction output is hθ (x(i) ). θ←θ− r Loss function – A loss function is a function L : (z,y) ∈ R × Y 7−→ L(z,y) ∈ R that takes a

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