logistic regression book

1. OverviewIn the optimization problem of machine learning, the gradient descent method and Newton method are two common methods to find the extremum of convex function, they are all in order to obtain the approximate solution of the objective function. The aim of the gradient descent is to solve the minimum value of the objective function directly, and the Newton's law solves the objective function by solving the parameter value of the first order zero of the objective function in a disguised w

Recently looking at Wunda's machine learning course, which talks about the One-vs-all classification of the logistic regression classifiers, here are some personal summaries:1. For the multi-classification problem, in fact, it is to draw a number of decision boundary, in the training, in fact, each time just choose a class for training.2. In the specific implementation, the current training class is 1, the

Test questions:Code Description:1. In main I used an input file to represent the input, which should be removed when testing2. The following functions are the calculation of the predicted values, the calculation of costfunction, the implementation of the Luo series regression3. Specifically similar to linear regression, can refer to the gradient descent of linear regressionThe code is as follows:#include Operation Result solution diagramC + + implemen

In the original: "Bi thing" Microsoft logistic regression algorithm--Forecast stock rise and fallData preparation:A set of stock history sold data (stock code: 601106 China One heavy), starting Date: 2011-01-04 to date, where variables are "open", "highest", "minimum", "close", "Total hand", "Amount", "ups and downs" and so onUPDATEFactstockSET [Ups and Downs] =N'Rise'WHERE [gains] > 0UPDATEFactstockS

Mark some of the problems in logistic regression. In LR, what happens to the Feature dimension > Sample quantity? Reference: https://www.zhihu.com/question/31554489 In LR, linear can be divided and linearly non-divided, and how to influence the convergence. Reference: HTTPS://WWW.ZHIHU.COM/QUESTION/29163846/ANSWER/43849528?UTM_SOURCE=WEIBOUTM_MEDIUM=WEIBO_SHAREUTM _content=share_answerutm_campaign=s

-0.576525 11.778922 0-0.346811-1.678730 1-2.124484 2.672471 11.217916 9.597015 0-0.733928 9.098687 0-3.642001-1.618087 10.315985 3.523953 11.416614 9.619232 0-0.386323 3.989286 10.556921 8.294984 11.224863 11.587360 0-1.347803-2.406051 11.196604 4.951851 10.275221 9.543647 00.470575 9.332488 0-1.889567 9.542662 0-1.527893 12.150579 0-1.185247 11.309318 0-0.445678 3.297303 11.042222 6.105155 1-0.618787 10.320986 01.152083 0.548467 10.828534 2.676045 1-1.237728 10.549033 0-0.683565-2.166125 10.229

The neural network can be seen in two ways, one is the set of layers, the array of layers, and the other is the set of neurons, which is the graph composed of neuron.In a neuron-based implementation, you need to define two classes of Neuron, WeightAn instance of the neuron class is equivalent to a vertex,weight consisting of a linked list equivalent to an adjacency table and a inverse adjacency table.In the layer-based implementation, each layer corresponds to a layer class, namely Logisticregre

#-*-Coding:utf-8-*-Import NumPyDef loaddataset ():Return Datamat,labelmatdef sigmoid (InX):Return 1.0/(1+numpy.exp (-inx))def gradascent (datamatin,classlabels):Datamatrix=numpy.mat (Damamatin)Labelmat=numpy.mat (Classlabels). Transpose ()#上升梯度alpha=0.01#迭代次数maxcycles=500#初始回归向量M,n=numpy.shape (Datamatrix)Weights=numpy.ones ((n,1))for k in range (Maxcycles):H=sigmoid (datamatrix*weights)Error= (labelmat-h)Weights=weights+alpha*datamatrix.transpose () *errorPassReturn weightsdef test ():Dataarr,l

1.sensitivity, also known as recall,true positive rate, means that the predicted positive case is proportional to (true positive) and all facts are positive.2.specificity, also called, true negative rate, meaning is the proportion of case that is predicted to be negative (true negative) and all facts are negative.3.roc (receiver operating characteristic)ROC can be used to evaluate the classification algorithms of two classifications.The longitudinal axis of the ROC curve is the ratio of sensitiv

Data preparation:A set of stock history sold data (stock code: 601106 China One heavy), starting Date: 2011-01-04 to date, where variables are "open", "highest", "minimum", "close", "Total hand", "Amount", "ups and downs" and so onUPDATEFactstockSET [Ups and Downs] =N'Rise'WHERE [gains] > 0UPDATEFactstockSET [Ups and Downs] =N'Fall'WHERE [gains] 0UPDATEFactstockSET [Ups and Downs] =N'Flat'WHERE [gains] = 0SELECT [Ups and Downs] , COUNT(*) asCnt fromFactstockGROUP by [

] = Data.flatmap (_ (1). Split (";")). Map (_.split (":") (0)). Distinct (). zipwiThindex (). Collectasmap ()//Build the training dataset, where sample represents a sample containing tags and feature val traindata:rdd[labeledpoint] = Data.map (sample=> {//Because Mllib only receives 1.0 and 0.0 to classify, here we pattern match, turn into 1.0 and 0.0 val label = sample (0) Match {case "1" => 1.0 case _ => 0.0}//Find a non-0 element subscript, look up subscript in dictionary map with the charact

monotonically increasing function , so when the logarithm function takes the maximum value, the original function also obtains the maximum value. (Logarithmic function Y=logax y=\log_a{x}, monotonically incrementing when A>1 a>1, and monotonically decreasing when 0 (3) the derivative is 0 to obtain the likelihood equation; (4) to solve the likelihood equation, get The parameters are the desired, and the The below uses the maximum likelihood method to estimate the parameters in

, sig (x)-> 0. Order In fact, the output of this function can be viewed as P (y = 1 | X, ω ). If y =-1 and y = 1 are output: That is: The image of the former is that the image of the latter is symmetric. We have a new hypothesis. The output is between (0, 1). When h '(x)> 0.5, we think the tumor is malignant (1 ), when h '(x) 4. Decoding Algorithm For logistic regression without regularization, we c

R Language Generalized linear Model GLM () functionGLM (formula, family=family.generator, Data,control = List (...))Formula data relationships, such as y~x1+x2+x3Family: Each response distribution (exponential distribution family) allows various correlation functions to correlate the mean with the linear predictor.Common family: Binomal (link= ' logit ')--the response variable is subject to two distributions, and the connection function is logit, i.e. logis