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likelihood function are:3. Algorithms3.1 Gradient Ascent gradient riseWe can use gradient descent to find the minimum point, which in turn can be used to find the maximum point with a gradient rise: first, add the logical function used in the calculation, and the derivative
1. Find the costfunction to measure the error
2. Fit the theta parameter to minimize the costfunction. Uses gradient descent, iterates n times, iteratively updates Theta, and reduces costfunction
3. Find the appropriate parameter theta for prediction.
1. Linear Regression
Computecost:
for i=1:m h = X(i,:) * theta;
You are welcome to reprint it. Please indicate the source, huichiro.Summary
This article briefly describes the implementation of the linear regression algorithm in Spark mllib, involves the theoretical basis of the linear regression algorithm itself and linear
reduced.ThetaThe value is less than an hour.ThetaIncrease,JThe value is also reduced. Therefore, the idea of gradient descent is correct.
In contrast,AlphaThe selection is not that simple,AlphaModerate selection requirements, too large or too small are not good:
As mentioned,AlphaThe value is too small, the step size is too small, it takes many steps to reduce to the minimum value, the proce
In 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. In the parametric solution of logistic regression model, the improved gradient
objective function, that is, the maximum value of the logarithm likelihood function, that is, the optimization problem. Gradient Descent Method and quasi-Newton method can be used.
4. Experience in data preprocessing during actual logical regression is summarized, but experience is limited. If anyone has a wealth of experience in this field, I would like to tha
. There are two gradient descent algorithms, the first is the Batch Gradient Descent algorithm. This method is used to accumulate the weight vectors and then update them in batches. Generally, this method is not applicable to large-scale dataset processing; the other is the Stochastic
function of the n feature is shown. For convenience, we define the x1=1 , using the column vectors to represent the parameter θ and the input X. This assumes that the function hθ (x) can be represented as: The linear regression problem with multiple features is called multivariable linear regression problem . Two, m
In 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. In the parametric solution of logistic regression model, the improved gradient
functions of ridge regression as follows:
For linear regression, we used two learning algorithms, one based on gradient descent and the other based on regular equations.(1)
Gradient Descent
First define several symbols:
Xi
Vector[x]:input data
Yi
Vector[y]:output data
H (X)
hypothesis functionGive the predicted value for the input data
Y is continous variation? Regression problem (regression problem)Y is discrete variation? Classification problem (classification problem)Part 1: Linear
In 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. In the parametric solution of logistic regression model, the improved gradient
=530.9
Question explanationWe can give an approximate estimate of theθ0 andθ1 values observing the trend of the data in the training set. We See this Y values decrease quite regularly when the x values increase, thenθ1 must is negative. Θ0 is the value of the hypothesis takes when x was equal to zero, therefore it must being superior to Y (1) in order to Satis FY the decreasing trend of the data. Among the proposed answers, the one that's meets both the conditions is hθ (x) =−569.6−530.9x.
existing data. The quasi-sum equation (model) is generally used for the calculation of the Inner Difference or a small-range error)
Likelihood function:I understand this. For example, we know a probability distribution density function of X, but this probability distribution has unknown parameters, but I want to get this unknown parameter (theat ), then we can find many known variables and multiply these probability distribution density functions. This is the likelihood function.
Maximum Likeli
Over the past few days, I have read some peripheral materials around the paper a neural probability language model, such as Neural Networks and gradient descent algorithms. Then I have extended my understanding of linear algebra, probability theory, and derivation. In general, I learned a lot. Below are some notes.
I,Neural Network
I have heard of neural networks
"one, multivariable linear regression model"Multivariate linear regression refers to the case where the input is a multidimensional feature, for example:It can be seen that the price of a house is determined by four variables (size, number of bedrooms, number of floors, age of home), in order to be able to predict the
I. Basic Concepts
The gradient descent method uses the negative gradient direction to determine the new search direction of each iteration, so that each iteration can gradually reduce the target function to be optimized. The gradient descent method is the fastest
) - - - #3 Standardized processing of training data and test data -Ss_x =Standardscaler () -X_train =ss_x.fit_transform (X_train) inX_test =ss_x.transform (x_test) - toSs_y =Standardscaler () +Y_train = Ss_y.fit_transform (Y_train.reshape (-1, 1)) -Y_test = Ss_y.transform (Y_test.reshape (-1, 1)) the * #4 Training and forecasting using two linear regression models $ #Initialize linearregression
the linear regression in many general introductions. Below we have done a phased summary of the above: linear regression, according to the law of large numbers and the central limit law, assuming that the sample infinity, its true value and the error of the predicted value of ε plus and obey u=0, variance =δ² Gaussian
Theory and formula please see Andrew Ng's machine learning in the NetEase public class, or the machine learning of Andrew Ng in CourseraFor multivariate linear regression to fit the best straight line, in order to make the error squared and the smallest, the method on the textbook is to seek the bias, and make it 0, and then solve the linear equation group.But th
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