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normal equation: Method to solve for θ\theta analytically. one step to get the optimal value. θ=(XTX)−1XTy\theta=(X^TX)^{-1}X^Ty Octave: pinv(X'*X)*X'*yGradient Descent - Need to choose α\alpha

function [U, S] = pca(X)%PCA Run principal component analysis on the dataset X% [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X% Returns the eigenvectors U, the eigenvalues

Once we have done some trouble shooting for errors in our predictions by:Getting more training examplesTrying smaller sets of features Trying additional features Trying polynomial features Incr

Learning curvesfunction [error_train, error_val] = ... learningCurve(X, y, Xval, yval, lambda)%LEARNINGCURVE Generates the train and cross validation set errors needed %to plot a learning curve%

recommender system problem formulation—a content based recommendationsNotations Algorithm(with linear regression) featuring learning—Collaborative Filtering (Low rank matrix fractorization)iterati

Before learning with large datasets, plot a learning curve with a much small datasets, and to see if it appears to be have high bias.Stochastic Gradient Decent (taking linear regression for example)

build a model for the probability of x—p(x) a small threshold— ϵ\epsilon Gaussian(Normal) Distributionx~N(μ,σ2\mu,\sigma^2) p(x; μ,σ2\mu,\sigma^2) Parameter estimationif x(i)x^{(i)}~N(μ,σ2)N(\mu,\s

Estimating parameters for a Gaussianfunction [mu sigma2] = estimateGaussian(X)%ESTIMATEGAUSSIAN This function estimates the parameters of a %Gaussian distribution using the data in X% [mu sigma2] =

Two ways to eliminate extra zero onesidx = find(R(i, :)==1) Thetatemp = Theta(idx,:) Ytemp = Y(i,idx) Xgrad(i,:) = (X(i,:)∗ThetaTtemp −Ytemp)∗Thetatemp.R .* M sum(sum(R.*M))function [J, grad] = c

Neural Networks —a much better way to learn complex hypotheses even when n is large,compared to algorithm above.Neuron model Logistic unit x0x_0 calls bias unit Sigmoid(logistic) activation funct

Photo OCRSlide Windows Two things are recommended: 1.Plot Learning Curves. 2.Get 10x Data Set which actually takes much less time than we expect.Ceiling AnalysisWhen there’s a pipeline with seve

m=Number of training examples h(hypothesis)=output function Linear regression with one variable. Univariate linear regression.Idea: Choose θ0,θ1\theta_0,\theta_1 so that hθ(x)h_\theta(x)is close to

K-means% Initialize centroids centroids = kMeansInitCentroids(X, K); for iter = 1:iterations % Cluster assignment step: Assign each data point to the % closest centroid. idx(i) corresponds to cˆ(i),

% comment ~= not equal PS1(‘>> ”); ; suppress the print output a ——a=? disp(a) ——value of a disp(sprintf(‘2 decimals: %0.2f’,a)) ——2 decimals: 3.14 format long a ——a=?? matrix or vector:

ML is the field of study that gives computer the ability to learn without being explicitly programmed. ML——E=T+P A computer program is said to learn from with respect to some class of tasks T,and pe

(or large margin classifiers) C=1λ\frac{1}{\lambda} (C is very large) KernelsUsing Kernels and SVM to define extra features with landmarks and similarity functions to learn more complex nonlinear

Most SVM software packages (including svmTrain.m) automatically add the extra featurex0 = 1 for you and automatically take care of learning the intercept term ✓0. So when passing your training data to

Gradient descentX = [ones(m, 1), data(:,1)]; % Add a column of ones to xtheta = zeros(2, 1); % initialize fitting parameters% Some gradient descent settingsiterations = 1500;alpha = 0.01;1.Computin

underfitting or high bias—hypothesis function h maps poorly to the trend of the data. usually caused by a function that is too simple or uses too few features.overfitting or high variance—fits the ava

Visualizing the data %Find Indices of Positive and Negative Examplespos = find(y==1); neg = find(y == 0);% Plot Examplesplot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2, ...'MarkerSize', 7);plot(X(

classification problems ——where the variable y that you want to predict is valued. negative class-positive class “-“-“+” y(i)->the label for the training example way1: linear regression thres

Skewed Classes—the ratio of positive to negative examples is very close to one of two extremes. In that case, it becomes much harder to use just classification accuracy.It’s not clear that the decreas

improve the accuracy of certain algorithm - Collect lots of data - Develop sophisticated features - Develop algorithms to process your input in different waysThe recommended approach to solving m

cluster centroid distortion cost function —using that to make sure k-means is converging and working properly.cluster assignment step move centroids steprandom initialization(also for global optima)

Dimensionality Reduction ——allows us to compress the data and have it therefore use up less computer memory or disk space, but it will also allow us to speed up our learning algorithms. ——to visuali

choosing your features defining new features you might actually get a better model 1. combine multiple features into one. to predict the price of a house there’s two features: the fron