Mean squared error (why mean?)

  • Context: Undergrad 
  • Thread starter Thread starter sunone
  • Start date Start date
  • Tags Tags
    Error Mean
Click For Summary
SUMMARY

The discussion centers around the equation for mean squared error (MSE) in machine learning, specifically the formula $E= \frac{1}{2} \sum_{n=1}^N (y-t)^2$. The user questions the inclusion of the factor $\frac{1}{2}$ in the equation, suggesting that a mean should involve division by $N$. The confusion arises from a lack of context regarding the purpose of the $\frac{1}{2}$ factor, which is often used in optimization to simplify the derivative during gradient descent calculations. The user emphasizes the need for proper references when discussing equations from literature.

PREREQUISITES
  • Understanding of mean squared error (MSE) in machine learning
  • Familiarity with gradient descent optimization techniques
  • Basic knowledge of mathematical notation and LaTeX
  • Experience with machine learning literature and terminology
NEXT STEPS
  • Research the role of the $\frac{1}{2}$ factor in optimization algorithms
  • Learn about gradient descent and its application in minimizing loss functions
  • Explore different loss functions used in machine learning, including MSE and MAE
  • Study LaTeX formatting for mathematical expressions in academic writing
USEFUL FOR

Machine learning practitioners, data scientists, and students studying optimization techniques who seek to deepen their understanding of error minimization in model training.

sunone
Messages
3
Reaction score
0
Hi
I found this equation in a machine learning book:
"we want to minimize the mean squared error:"
$E= \frac{1}{2} \sum_{n=1}^N (y-t)^2$

what I do not understand is the \frac{1}{2} , if it is a mean it should be \frac{1}{N},
why are they restricting to 2? In the text there is no reference to y or t being only 2. So it cannot be that N=2.
 
Physics news on Phys.org
If you ask a question here, please always be sure to include the necessary reference. What book did you read this in? Title, author, page number?
 
sunone said:
Hi
I found this equation in a machine learning book:
"we want to minimize the mean squared error:"
$E= \frac{1}{2} \sum_{n=1}^N (y-t)^2$

what I do not understand is the \frac{1}{2} , if it is a mean it should be \frac{1}{N},
why are they restricting to 2? In the text there is no reference to y or t being only 2. So it cannot be that N=2.

Fix Latex.
 

Similar threads

MHB How Do You Minimize Mean Square Deviation in Dice Roll Predictions?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What is this formula measuring error?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Error propagation and symmetric errors
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Confused about error propagation
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Why Does Yₙ Converge to Zero for q < 1/2 in a Random Walk?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad How Should I Calculate Error on the Mean with Identical Measurements?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding 2 equivalent formulations of both data set measures
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Understanding extinction probability in simple GWP
  • · Replies 1 ·
Replies
1
Views
3K
MHB Calculate the density - Unbiased estimator for θ
  • · Replies 1 ·
Replies
1
Views
2K
MHB Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples
  • · Replies 1 ·
Replies
1
Views
4K