Find the value of x by using least means square method

In summary, the goal of using the Least Mean Squares method is to find a x value that will result in y = 2. The Least Mean Squares method was used with an initial x value of 1 and a learning rate of η=0.01. After 10 epochs/iterations, the results showed that the x value that resulted in y = 2 was x = 1.53.
  • #1
xugi
12
0
I can't understand this problem, anyone can help me...

Given a function y = 4x2, you are required to find the value of x that will result y = 2 by using the Least Mean Squares method.
Use initial estimate x0 = 1 and learning rate η = 0.01.
Write down the results of the first 10 epochs/iterations.
Give conclusion about your result.


Note: Calculation can be done manually or using Matlab

I've googled this but no way out...
 
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  • #2
Are you sure the method is "least mean squares" or "least squares"?

Wiki article on least mean squares filter, which is an adaptive filtering algorithm:

http://en.wikipedia.org/wiki/Least_mean_squares_filter

With least squares method you're given a set of data points, and you then choose a function and then calculate the coefficients for that function that minimize the sum of the squares of the differences between the input data and the values calculated by the function:

http://en.wikipedia.org/wiki/Least_squares
 
  • #3
Thx for your reference link...

Yes it is Least Mean Square algorithm...

Yes, I learn in my university which is contained in this link http://en.wikipedia.org/wiki/Least_mean_squares_filter

But the problem I don't know how to apply the equations to the problem I showed in 1st post...
 
  • #4
I don't know about adaptive filter methods.

I assume the function you're trying to model is y = 4 x^2 or y = 4 x2. What you're trying to find out is the x value for when 4 x2 - 2 = 0.

The wiki article mentions that the algorithm needs a series of values going into and out of an unknown process in order to approximate that process by observing the difference between actual and predicted outputs. However in the problem statement, you're only given an initial value, and the goal is not to find a model for the equation, but to find a root.

Hopefully someone else here will be able to help.
 
Last edited:
  • #5
This morning the lecturer explain how he did it, it is simple thought but it is difficult to relate it to least mean square...
I am trying to write the answer in equation here but since I do not know how to put math symbol and equation, I just will attach the file in MATLAB and in excel...

I wish it will help other students.

View attachment NNFL_HW1.xls
View attachment NNFL_HW1.m


Thank you Bro...:D
 

FAQ: Find the value of x by using least means square method

1. How does the least means square method work?

The least means square method is a statistical technique used to find the best fitting line or curve for a set of data points. It works by minimizing the sum of the squared differences between the actual data points and the predicted values from the line or curve.

2. What is the purpose of using the least means square method?

The main purpose of using the least means square method is to find the most accurate line or curve that represents a relationship between two variables. It is commonly used in regression analysis to determine the relationship between independent and dependent variables.

3. What are the key assumptions of the least means square method?

The key assumptions of the least means square method include linearity, constant variance, independence of errors, and normality of errors. These assumptions must be met for the method to be valid and accurate in finding the best fitting line or curve.

4. How do you interpret the results from the least means square method?

The results from the least means square method include the slope and intercept of the best fitting line or curve. The slope represents the change in the dependent variable for every one unit change in the independent variable. The intercept represents the value of the dependent variable when the independent variable is equal to zero.

5. Are there any limitations to using the least means square method?

Yes, there are some limitations to using the least means square method. It assumes a linear relationship between the variables and may not be suitable for non-linear relationships. It also assumes that the errors are normally distributed, which may not always be the case. Additionally, outliers in the data can significantly affect the results.

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