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assumptions tend to be 0, but the actual labels are 1, both of which indicate a miscarriage of judgment. Otherwise, we define the error value as 0, at which point the value is assumed to correctly classify the sample Y.Then, we can use the error rate errors to define the test error, that is, 1/mtest times the error rate errors of H (i) (xtest) and Y (i) (sum from I=1 to Mtest).Stanford University public Class mac
is that only the input paradigm is provided for this network, and it automatically identifies its potential class rules from those examples. When the study is complete and tested, it can also be applied to new cases. A typical example of unsupervised learning is clustering. The purpose of clustering is to bring together things that are similar, and we do not care what this class is. Therefore, a clustering algorithm usually needs to know how to c
-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 enti
classification model, which gives us a better evaluation value and gives us a more direct way to evaluate the good and bad of the model. One last thing to keep in mind, in the definition of precision and recall, we define precision and recall rates, and we habitually use Y=1 to show that this class appears very little. So if we try to detect a very rare situation, like cancer. I hope it's a rare situation where precision and recall are defined as Y=1 rather than y=0, as some of the fewer classe
First, how to learn a large-scale data set?In the case of a large training sample set, we can take a small sample to learn the model, such as m=1000, and then draw the corresponding learning curve. If the model is found to be of high deviation according to the learning curve, the model should continue to be adjusted on the existing sample, and the adjustment strategy should refer to the High deviation of se
invoking the example in MATLAB above, we can define the cost function of the logistic regression as follows:In the figure, Jval represents the cost function expression, where the last item is the penalty for the parameter θ; The following is a gradient of the derivation of each θj, where θ0 is not in the penalty, so gradient is not changed, and Θ1~θn has one more (λ/m) *θj respectively;At this point, regul
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
)/∂ (θ (1) JK) is tested for gradients. After the partial derivative code does not have a problem, close the Gradient check section code.6. Use gradient descent or other advanced algorithms to perform reverse propagation to find the θ values for minimizing j (θ).This paper describes the gradient descent algorithm in neural networks: starting from the random initial point, descending step by step, until the local optimal value is obtained. Algorithms such as gradient descent can at least guarante
Mainly for the week content: large-scale machine learning, cases, summary(i) Random gradient descent methodIf there is a large-scale training set, the normal batch gradient descent method needs to calculate the sum of squares of errors across the entire training set, which is a very large computational cost if the learning
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-
hypothesis that the nonlinear dividing line can be output.Put the previously drawn units together to get the neural network. The feature is input to several sigmoid units, and the input to another sigmoid cell is output. The output value of the intermediate node is set to A1,a2,a3. These intermediate nodes are called hidden layers, and neural networks can be composed of multiple hidden layers.Each intermediate node has a series of parameters:A2,a3. G is the sigmoid function. The final output va
-Cost functionFor the training set and our assumptions, we will consider how to determine the coefficients in the assumptions.What we are going to do now is to choose the right parameters, and the selection of parameters directly affects the accuracy of the resulting straight line for the training set description. The difference between the predicted value and the actual value in the training set is the modeling error (Modeling error).the
algorithms, there are also some algorithms that are often used to minimize the cost of functions. These algorithms are more complex and superior, and generally do not require manual learning rate, which is faster than gradient descent algorithms. These include:Bounded gradient(Conjugate gradient ),Local Optimization Method(Broyden Fletcher Goldfarb shann, BFGS) andLimited Memory Local Optimization Method(L
The study of this class, I believe that generally on the statistics or logistics related courses should be known to some students. Although the knowledge involved in class is very basic, it is also very important.Based on the collection of some house price related data, the linear regression algorithm is used to forecast the house price.In order to facilitate the training deduction of the algorithm, a lot of symbols of the standard provisions, from which also learned some knowledge, later in the
unreasonable. That is, in the past two months the word has not appeared in the mail, it is considered that the probability of 0, unreasonable.Generally speaking, it is unreasonable to think that these events will not happen if they have not been seen before . Solve this problem with Laplace smoothing.4. Laplace SmoothingAccording to the maximum likelihood estimate, p (y=1) = # "1" s/(# "0" s + # "1" s), that is, the probability of Y being 1 is the ratio of the number of 1 in the sample to all s
cost function least.The algorithm is:After derivation, get:Note: Although the resulting gradient descent algorithm appears to be the same as the gradient descent algorithm for linear regression, the hypothetical function here differs from the linear regression, so it is actually different. In addition, it is still necessary to perform feature scaling before applying the gradient descent algorithm.In addition, there are some alternatives to the gradie
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
-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 f
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