Find the value of x by using least means square method

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Discussion Overview

The discussion revolves around applying the Least Mean Squares method to find the value of x in the function y = 4x² that results in y = 2. Participants explore the application of this method, including initial estimates and learning rates, while also discussing the potential confusion between Least Mean Squares and Least Squares methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the problem and seeks assistance in applying the Least Mean Squares method to find x.
  • Another participant questions whether the method intended is "least mean squares" or "least squares," providing links to clarify the differences between the two methods.
  • A participant confirms the use of the Least Mean Squares algorithm but struggles to apply the equations to the problem presented.
  • Another participant clarifies that the goal is to find the x value for which 4x² - 2 = 0, noting that the problem does not provide a series of values typically needed for the algorithm.
  • A participant mentions a recent explanation from a lecturer but finds it challenging to relate it to the Least Mean Squares method, indicating a desire to share their MATLAB and Excel work with others.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correct method to apply and whether the problem aligns with the typical use of the Least Mean Squares algorithm. There is no consensus on how to proceed with the calculations or the applicability of the method to the problem.

Contextual Notes

Participants note the lack of a series of values needed for the Least Mean Squares method, which may limit the applicability of the algorithm to the problem at hand.

Who May Find This Useful

Students and individuals interested in understanding the application of the Least Mean Squares method in mathematical problems, particularly in the context of finding roots of equations.

xugi
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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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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
 
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...
 
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:
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
 

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