Machine Learning|Andrew Ng|Coursera 吴恩达机器学习笔记

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Week1:

Machine Learning:

 

  • 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.

 

  • Supervised Learning:We already know what our correct output should look like.
  1. Regression:Try to map input variables to some continuous function.
  2. Classification:Try to map input variables into discrete categories.
  • Unsupervised Learning:We only have little or no idea what our results should look like.
  1. Clustering:Find a way to automatically group data into groups that are somehow similar or related by different variables.
  2. Non-clustering:Find structure in a chaotic environment,like the "Cocktail Party Algorithm".

Model Representation:

 

  • x(i):Input features
  • y(i):Target variable
  • (x(i),y(i)):Training example
  • (x(i),y(i));i=1,...,m:Training set
  • m:Number of training examples
  • h(x):Hypothesis,θ0+θ1x1
Cost Function:
  • This takes an average difference of all the results of the hypothesis with inputs from x‘s and the actual output y‘s.
  • Algorithm:技术分享图片(The mean is halved 1/2 as a convenience for the computation of the gradient descent, as the derivative term of the square function will cancel out the 1/2 term.)
  • We use contour plot to show how to minimize the cost function.
技术分享图片技术分享图片
 
Gradient Descent:
  • Help us to estimate the parameters in the hypothesis function.
  • Algorithm:技术分享图片(repeat until convergence)
  • j=0,1:Feature index numbe
  • α:Learning rate or the size of each step.If α is too small,gradient descent can be slow.If α is too large,gradient descent can overshoot the minimum.
  • Partial Derivative of J:Direction of each step
  • At each iteration j, one should simultaneously update all of the parameters.
Gradient Descent For Linear Regression:
  • Algorithm:技术分享图片
  • This method looks at every example in the entire training set on every step, and is calledbatch gradient descent.
Linear Algebra:
  • I have learned liner algebra in my college so I will skip this part in my note.
 
Week2:
Mutiple Features:
  • n:number of features
  • x(i):input of ith training example
  • x(i)j:value of feature j in ith training example
  • hθ(x):θ0x0+θ1x1+θ2x2+θ3x3+?+θnxn=技术分享图片(assume x0 = 1)
Gradient Descent for Multiple Variables:
  • Algorithm:技术分享图片
  • Feature Scaling:
  1. Feature Scaling:Dividing the input values by the range (max - min) of the input variable.Get every feature into approximately  a -1 <= xi <= 1 range.
  2. Mean Normalization:Subtracting the average value for an input variable from the values for that input variable resulting in a new average value for the input variable of just zero.
  3. 技术分享图片Where μi is the average of all the values for feature i and si is the range of values (max - min), or si is the standard deviation.
  • Learning Rate:Make a plot with number of iterations on the x-axis. and J(θ) on the y-axis.If J(θ) ever increases, then you probably need to decrease α.It has been proven that if learning rate α is sufficiently small, then J(θ) will decrease on every iteration.To choose α,try 0.001,0.003,0.01......
  • Features and Polynomial Regression:We can improve our features and the form of our hypothesis function in a couple different ways
  1. We can combine multiple features into one.We can get a new feature x3 by taking x1 * x2
  2. We can change the behavior or curve of our hypothesis function by making it a quadratic, cubic or square root function (or any other form).
  3. if you choose your features this way then feature scaling becomes very important.
Normal Equation:
  • Formula:技术分享图片
  • Example:技术分享图片
  • There is no need to do feature scaling with the normal equation.
  • 技术分享图片
  • If (X^TX) is non-invertibale:
  1. Delete redundant features such as x1 = size in feet^2 and x2 = size in m^2.
  2. Delete features to make sure that m > n or use regularization.
Octave:
 
Week3:
Classfication:
  • The classification problem is just like the regression problem, except that the values we now want to predict take on only a small number of discrete values.
  • x(i):Feature
  • y(i):Label for the tranning example
Logistic Regression:
  • We change the form for our hypotheses to satisfy 0 <= h(x) =1 by pluggin θ^Tx into the Logistic Function.
  • Formula:技术分享图片
  • 技术分享图片
  • Decision Boundary:The line that separates the area where y = 0 and where y = 1.It is created by hypothesis function(θ^Tx=0).
  • Cost Function:技术分享图片
We can compress our cost function‘s two conditional cases into one case:技术分享图片
  • Gradient Descent:技术分享图片                  This algorithm is identical to the one we used in linear regression.But the h(x) is changed.
Optimization Algorithms:
  • Conjugate gradient
  • BFGS
  • L-BGFS
  • We can write codes below to use Octave‘s "fminunc()"技术分享图片技术分享图片
Multiclass Classification:
  • 技术分享图片                       
  • Train a logistic regression classifier hθ(x) for each class? to predict the probability that ? ?y = i? ?. To make a prediction on a new x, pick the class ?that maximizes hθ(x)
Overfitting:
  • 技术分享图片
  • Even though the fitted curve passes through the data perfectly, we would not expect this to be a very good predictor.
  • Options to address overfitting:
  1. Reduce the number of features.
  2. Regularzation.
  • Regularized Linear Regression:

  1. Cost Funcion:技术分享图片(lambda is the regularization parameter.)
  2. Gradient Descent:技术分享图片                                                                                           技术分享图片
  3. Normal Equation:技术分享图片
  • Regularized Logistic Regression:
  1. Cost Function:技术分享图片
  2. Gradient Descent:技术分享图片
 
Week4:
Neural Network:Representation:
  • 技术分享图片
  • If we had one hidden layer, it would look like:技术分享图片
  • The values for each of the "activation" nodes:技术分享图片
  • Each layer gets its own matrix of weights:技术分享图片(The ‘+1‘ comes from the ‘bias nodes‘,the output nodes will not include the bias nodes while the inputs will.)
  • Vectorized:技术分享图片
  • We can set different theta matrix to construct fundamental options by using a small neural network.技术分享图片
  • We can construct more complex options by using hidden layers.技术分享图片
  • Multiclass Classification:We use one-vs-all method and let hypothesis function return a vector of values.
 
Week 5:
Neural Network:Learning:
 
Cost Function:
  • L:Total number of layers in the network
  • Sl:Number of units (not counting bias unit) in layer l
  • K:number of output units/classes
  • 技术分享图片
Backpropagation Algorithm:
  • "Backpropagation" is neural-network terminology for minimizing our cost function.
  • Algorithm:For t = 1 to m: 
  1. 技术分享图片
  2. 技术分享图片
  3. 技术分享图片
  4. We get技术分享图片
  • Using code like this to unroll all the elements and put them into one long vector.技术分享图片Using code like this to get back original matrices.技术分享图片
  • Gradient Checking:We can approximate the derivative with respect to θj as follows:技术分享图片
  • Training:技术分享图片
Week 6:
Applying Machine Learning:
 
Evaluating a Hypothesis:
  • Set 70% of date to be the training set and the remainning 30% to be the test set.
  • 技术分享图片
  • In order to choose the model of your hypothesis, we can test each degree of polynomial by using cross validation set.(20% training set,20% cross validation set,60% test set)
技术分享图片
Bias vs. Variance:
  • High bias is underfitting and high variance is overfitting.Ideally, we need to find a golden mean between these two.
  • High Bias:技术分享图片
  • High Variance:技术分享图片
  • 技术分享图片
  • In order to choose the model and the regularization term λ, we need to:技术分享图片
  • If a learning algorithm is suffering from high bias, getting more training data will not help much.
  • If a learning algorithm is suffering from high variance, getting more training data is likely to help.技术分享图片技术分享图片
  • 技术分享图片
  • A neural neural network with fewer parameters is prone to underfitting. It is also computationally cheaper.
  • A large neural network with more parameters is prone to overfitting. It is also computationally expensive. 
 
Machine Learning System Desing:
  • The recommended approach:
  1. Start with a simple algorithm, implement it quickly, and test it early on your cross validation data.
  2. Plot learning curves to decide if more data, more features, etc. are likely to help.
  3. Manually examine the errors on examples in the cross validation set and try to spot a trend where most of the errors were made.
  • It is very important to get error results as a single, numerical value.
  • Precision
Handling Skewed Data:
  • Skewed Classes:The ratio of positive to negative examples is very close to one of two extremes.
  • 技术分享图片                           (y = 1 in presence of rare class that we want to detect)
  • Precision Rate:TP / (TP + FP)
  • Recall Rate:TP / (TP + FN)
  • F1 Score:(2 * P * R) / (P + R)
 
Week 7:
Support Vector Machines:
 
Optimization Objective:
  • 技术分享图片
  • Because constant doesn‘t change value of the theta that achieves the miinmum,so we multiplying objective function in logistic regression by M.
  • We can both use (A + λB) or (CA + B) to control the relative.
  • 技术分享图片
  • A support vector machine just makes a prediction of y being equal to one or zero, directly. So the hypothesis will predict one
Large Margin Intuition:
  • The SVM decision boundary will become like this:技术分享图片
  • The black line gives SVM a robustness because it has a large margin:技术分享图片
Kernels:
  • Given (xi,yi),we choose li = xi as landmarks,then let fi = sim(x,li).
  • We compute new features depending on proximity to landmarks.So our function become theta0 + theta1*f1 + theta2*f2......
  • Gaussian Kernels:技术分享图片技术分享图片
  • C and Sigma:技术分享图片
  • Do perform feature scaling before using the Gaussian kernel.
  • Linear kernel:meanning no kernel.
  • 技术分享图片
Week8:

Unsupervised Learning:

 

Clustering:

  • We give unlabeled training set to an algorithm and we ask the algorithm find some structure in the data for us.
  • K-meas Algorithm:技术分享图片
  • Cost Function:技术分享图片
  • Random Initialization:Randomly pick k training examples and set Mu1 of MuK equal to these k examples.
  • Elbow Method:技术分享图片
  • Better way to choose the number of clusters is to ask, for what purpose are you running K-means.
Dimensionality Reduction:
  • Reason:Data compression or speed up our learning algorithm.
  • 技术分享图片技术分享图片
  • Visualization:We can use dimensionality reduction to reduce data from high dimensions down to 2 or 3 dimensions,so that we can plot it and understand our data better.
Principal Component Analysis:

 

  • PCA:Find a lower dimensional surface onto which to project the data, so as to minimize the square distance between each point and the location of where it gets projected. 
  • Reduce from 2D to 1D:Find a vector onto which to project the data to minimize the projection error.
  • Reduce from nD to kD:Find k vectors onto which to project the data to minimize the projection error.
  • Data preprocessing:Feature scaling/Mean normalization
  • Algorithm:
  1. 技术分享图片
  2. 技术分享图片
  3. If we want to reduce the data from n dimensions down to k dimensions, we need to do is take the first k vectors from U(n * n) as Ureduce(n * k).
  4. z = Ureduce‘ * x.
  • Reconstruction from Compressed Representation:Xapprox = Ureduce * z.
  • 技术分享图片技术分享图片
  • Applying:技术分享图片(Only if your algorithm doesn‘t do what you want then implement PCA)
Week 9:

Anomaly Detection:

Density Estimation:

  • We build a model of the probability of x,if p of x-test is less than some epsilon then we flag this as an anomaly.
  • Gaussian Distribution(Normal Distribution):技术分享图片,技术分享图片
  • Parameter Estimation:技术分享图片
  • Algorithm:技术分享图片
  • Evaluation:Assume we have some labled data of anomalous and nonanomalous examples.Using training set(unlabled,assume normal examples),cross validation set and test set.技术分享图片
  • Anomaly Detection vs. Supervised Learning:技术分享图片
  • Non-gaussian Features:Let xNew = log(x)(logarithmic normal distribution),or xNew = x^(0.1)技术分享图片
  • Choose Features:Choose features that migth take on unusually large or small values in the event of an anomaly

Multivariate Gaussian Distribution:

技术分享图片技术分享图片

技术分享图片技术分享图片技术分享图片

 

Recommender Systems:

 

  • n.u = number of users
  • n.m = number of moives
  • r(i,j) = 1 if user j have rated movie i
  • y(i,j) = rating given by user j to movie i(only if r(i,j) = 1)
  • theta(j) = parameter vector for user j
  • x(i) = feature vector for movie i

Content Based Recommendations:

  • We assume we have features for different movies.
  • For each user j,learn a parameter.Predict user j as rating movie i with 技术分享图片 stars.
  • Optimization Objective:技术分享图片
  • Gradient Descent:技术分享图片

Collaborative Filtering:

 

  • We assume that each of our users has told us how much they like the romantic movies and how much they like action packed movies.
  • Optimization Algorithm:技术分享图片
  • Given x and movie ratings can estimate theta.
  • Given theta and movie ratings can estimate x.
  • Optimization Objective:技术分享图片
  • 技术分享图片
  • Mean Normalization:Compute the average rating that each movie obtained and subtract off the meaning rating.So the rating of movie become 技术分享图片 + average rating.

Week 10:

 

Large Scale Machine Learning:

Stochastic Gradient Descent:

 

  • Algorithm:

 

  1. Randomly shuffle the data set.
  2. For i = 1...m:技术分享图片 
  • SGD will only try to fit one training example at a time. This way we can make progress in gradient descent without having to scan all m training examples first.
  • We will usually take 1-10 passes through data set to get near the global minimum.
  • Convergence:Plot the average cost of the hypothesis applied to every 1000 or so training examples. We can compute and save these costs during the gradient descent iterations.技术分享图片
  • One strategy for trying to actually converge at the global minimum is to slowly decrease α over time.

Mini-Batch Gradient Descent:

 

  • Use b examples in each iteration.(b = mini-batch size)
  • Algorithm:技术分享图片
  • The advantage is that we can use vectorized implementations over the b examples.

Online Learning:

 

  • With a continuous stream of users to a website, we can run an endless loop that gets (x,y), where we collect some user actions for the features in x to predict some behavior y.
  • You can update θ for each individual (x,y) pair as you collect them. This way, you can adapt to new pools of users, since you are continuously updating theta.

Map Reduce and Data Parallelism:

 

  • Many learning algorithms can be expressed as computing sums of functions over the training set.
  • We can divide up batch gradient descent and dispatch the cost function for a subset of the data to many different machines so that we can train our algorithm in parallel.
  • 技术分享图片

Week 11:

Photo OCR:

 

  • Pipeline:
  1. Text detection
  2. Character segmentation
  3. Character classification
  • Using sliding windows and expansion to text detection and character segmentation
  • Ceiling Analysis

Artificial Data Synthesis:

 

  • Creating new data from scratch(using the ramming funds as an example)
  • Taking existing label examples and introducing distortions to it, to sort of create extra label examples.

 

技术分享图片技术分享图片







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