stanford machine learning coursera

m>=10n and uses multiple Gaussian distributions.In practical applications, the original model is more commonly used, the average person will manually add additional variables.If the σ matrix is found to be irreversible in practical applications, there are 2 possible reasons for this:1. The condition of M greater than N is not satisfied.2. There are redundant variables (at least 2 variables are exactly the same, XI=XJ,XK=XI+XJ). is actually caused by the linear correlation of the characteristic

Overview Cost Function and BackPropagation Cost Function BackPropagation algorithm BackPropagation Intuition Back propagation in practice Implementation Note:unrolling Parameters Gradient Check Random initialization Put It together Application of Neural Networks Autonomous Driving Review Log 2/10/2017:all the videos; Puzzled about Backprogation 2/11/2017:reviewed backpropaga

, i.e., all of our training examples lie perfectly on some straigh T line. If J (θ0,θ1) =0, that means the line defined by the equation "y=θ0+θ1x" perfectly fits all of our data. For the To is true, we must has Y (i) =0 for every value of i=1,2,..., m. So long as any of our training examples lie on a straight line, we'll be able to findθ0 andθ1 so, J (θ0,θ1) =0. It is not a necessary that Y (i) =0 for all of our examples. We can perfectly predict the value o

-Learning RateIn the gradient descent algorithm, the number of iterations required for the algorithm convergence varies according to the model. Since we cannot predict in advance, we can plot the corresponding graphs of iteration times and cost functions to observe when the algorithm tends to converge.Of course, there are some ways to automatically detect convergence, for example, we compare the change value of a cost function with a predetermined thr

-Gradient descentThe gradient descent algorithm is an algorithm for calculating the minimum value of a function, and here we will use the gradient descent algorithm to find the minimum value of the cost function.The idea of a gradient descent is that we randomly select a combination of parameters and calculate the cost function at the beginning, and then we look for the next combination of parameters that will reduce the value of the cost function.We continue this process until a local minimum (

, the weight of the high-weighted data is increased by 1000 times times the probability, which is equivalent to replication. However, if you are traversing the entire test set (not sampling) to calculate the error, there is no need to modify the call probability, just add the weights of the corresponding errors and divide by N. So far, we have expanded the VC Bound, which is also set up on the issue of multiple classifications!SummaryFor more discussion and exchange on

use of MATLAB. *.4.gradientdescent.mfunction [Theta, j_history] =gradientdescent (X, y, theta, Alpha, num_iters)%gradientdescent performs gradient descent to learn theta% theta = gradientdescent (X, y, theta, Alpha, num_iters) up Dates theta by% taking num_iters gradient steps with learning rate alpha% Initialize Some useful valuesm= Length (y);%Number of training examplesj_history= Zeros (Num_iters,1); forITER =1: Num_iters% ======================

-Gradient descent for linear regressionHere we apply the gradient descent algorithm to the linear regression model, we first review the gradient descent algorithm and the linear regression model:We then expand the slope of the gradient descent algorithm to the partial derivative:In most cases, the linear regression model cost function is shaped like a convex body, so the local minimum value is equivalent to the global minimum:The following is the entire convergence and parameter determination pr

Overview photo OCR problem Description and Pipeline sliding Windows getting Lots of data and Artificial data ceiling analysis:what part of the Pipeline to work on Next Review Lecture Slides Quiz:Application:Photo OCR Conclusion Summary and Thank You Log 4/20/2017:1.1, 1.2; Note Ocr? ... Coursera-

mathematical expression was unfolded using Taylor's formula, and looked a bit ugly, so we compared the Taylor expansion in the case of a one-dimensional argument.You know what's going on with the Taylor expansion in multidimensional situations.in the [1] type, the higher order infinitesimal can be ignored, so the [1] type is taken to the minimum value,should maketake the minimum-this is the dot product (quantity product) of two vectors, and in what case is the value minimal? look at the two vec

On Github, Afshinea contributed a memo to the classic Stanford CS229 Course, which included supervised learning, unsupervised learning, and knowledge of probability and statistics, linear algebra, and calculus for further studies. Project Address: https://github.com/afshinea/stanford-cs-229-

. Optimal interval classifierThe optimal interval classifier can be regarded as the predecessor of the support vector machine, and is a learning algorithm, which chooses the specific W and b to maximize the geometrical interval. The optimal classification interval is an optimization problem such as the following:That is, select Γ,w,b to maximize gamma, while satisfying the condition: the maximum geometry in

two classification problem, so the model is modeled as Bernoulli distributionIn the case of a given Y, naive Bayes assumes that each word appears to be independent of each other, and that each word appears to be a two classification problem, that is, it is also modeled as a Bernoulli distribution.In the GDA model, it is assumed that we are still dealing with a two classification problem, and that the models are still modeled as Bernoulli distributions.In the case of a given y, the value of x is

be trained and predicted immediately, which is called Online learning. each of the previously learned models can do online learning, but given the real-time nature, not every model can be updated in a short time and the next prediction, and the perceptron algorithm is well suited to do online learning:The parameter Update method is: if hθ (x) = y is accurate, the parameter is not updated otherwise, θ:=θ+ y

distribution with the mean value of μ 0 and the covariance matrix of Σ, X | y = 1 follows the multivariate Gaussian distribution where the mean value is μ1 and the covariance matrix is Σ (This will be discussed later ). The log function for maximum likelihood estimation is recorded as L (ø, μ 0, μ 1, Σ) = Log 1_mi = 1 p (x (I) | Y (I); μ 0, μ 1, Σ) P (Y (I); ø), our goal is to obtain the parameter ø, μ 0, μ 1, Σ to make L (ø, μ 0, 1, Σ) to obtain the maximum value. The values of the four para

hyper-plane (w,b) and the entire training set is defined as:Similar to the function interval, take the smallest geometric interval in the sample.The maximum interval classifier can be regarded as the predecessor of the support vector machine, and is a learning algorithm, which chooses the specific W and b to maximize the geometrical interval. The maximum classification interval is an optimization problem s

be able to find the global optimal solution.When the training sample is very large, each update parameter needs to traverse all the sample calculation total error, so that the learning speed is too slow; this time the random gradient descent algorithm that calculates the error update parameters of a sample is usually more thanThe batch gradient descent method is faster. (Theoretically, there is no guarantee that the random gradient descent can conver

would the Vectorize this code to run without all for loops? Check all the Apply. A: v = A * x; B: v = Ax; C: V =x ' * A; D: v = SUM (A * x); Answer: A. v = a * x; v = ax:undefined function or variable ' Ax '. 4.Say you has a vectors v and Wwith 7 elements (i.e., they has dimensions 7x1). Consider the following code: z = 0; For i = 1:7 Z = z + V (i) * W (i) End Which of the following vectorizations correctly compute Z? Check all the Apply.

default is to use a hidden layer is a reasonable choice, but if you want to choose the most appropriate layer of hidden layer, you can also try to split the data into training sets, validation sets and test sets, and then try to use a hidden layer of neural network to train the model. Then try two, three hidden layers, and so on. Then see which neural network behaves best on the cross-validation set. That means you get three neural network models, one, two, and three hidden layers, respectively

-Normal equationSo far, the gradient descent algorithm has been used in linear regression problems, but for some linear regression problems, the normal equation method is a better solution.The normal equation is solved by solving the following equations to find the parameters that make the cost function least:Assuming our training set feature matrix is x, our training set results are vector y, then the normal equation is used to solve the vector:The following table shows the data as an example:T