# Squared Error Loss

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Variance[edit] Further information: Sample variance The usual estimator for the variance is the corrected sample variance: S n − 1 2 = 1 n − 1 ∑ i = 1 n share|improve this answer answered Apr 18 '15 at 21:21 kristjan 1112 A little detail: "If all deviations are equally bad for you no matter their sign ..": The MAD p.60. While being near center can be happily absorbed. this content

It is not to be confused with Mean squared displacement. MSE also correspons to maximizing the likelihood of Gaussian random variables.6.1k Views · View UpvotesPromoted by Udacity.comMaster machine learning with a course created by Google.Become a machine learning engineer in this Here is a visualisation for **comparison: Now even though OLS** is pretty much the standard, different penalty functions are most certainly in use as well. However the statistical properties of your solution might be hard to assess. https://en.wikipedia.org/wiki/Mean_squared_error

## Mean Square Error Formula

Therefore errors are not 'equally bad' but 'proportionally bad' as twice the error gets twice the penalty. –Jean-Paul Apr 19 '15 at 7:05 @Jean-Paul: You are right. small deviations are worse for you than big deviations, then you can choose a different loss function and try to solve the minimizing problem. In the scalar situation it is less obvious but you captured a bit of it with: 'If you square the difference, then won't you get "warped" values depending on the size If the target is t, then a quadratic loss function is λ ( x ) = C ( t − x ) 2 {\displaystyle \lambda (x)=C(t-x)^{2}\;} for some constant C; the

Sometimes you want **your error to** be in the same units as your data. Powered by vBulletin™ Version 4.1.3 Copyright © 2016 vBulletin Solutions, Inc. In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the Root Mean Square Error Interpretation The loss function quantifies the amount by which the prediction deviates from the actual values.

The absolute error method makes much more intuitive sense. In classification, it is the penalty for an incorrect classification of an example. For example, for L2 norm, L ( f , f ^ ) = ∥ f − f ^ ∥ 2 2 , {\displaystyle L(f,{\hat {f}})=\|f-{\hat {f}}\|_{2}^{2}\,,} the risk function becomes this page MR0804611. ^ DeGroot, Morris (2004) [1970].

Reply With Quote + Reply to Thread Tweet « Use of Tukey-Kramer | When to use Fisher's exact test » Similar Threads Mean Squared Prediction Error? How To Calculate Mean Square Error Twice as far **from the mean would therefore result** in twice the penalty. Please try the request again. up vote 26 down vote favorite 21 When we conduct linear regression $y=ax+b$ to fit a bunch of data points $(x_1,y_1),(x_2,y_2),...,(x_n,y_n)$, the classic approach minimizes the squared error.

## Root Mean Square Error Formula

outliers have more effect)? Contents 1 Definition and basic properties 1.1 Predictor 1.2 Estimator 1.2.1 Proof of variance and bias relationship 2 Regression 3 Examples 3.1 Mean 3.2 Variance 3.3 Gaussian distribution 4 Interpretation 5 Mean Square Error Formula And there's also the stuff about maximum entropy distributions –ssdecontrol Apr 18 '15 at 13:46 4 @ssdecontrol I think the epigram is due to Henri Poincaré a little over a Mean Square Error Example If you square the difference, then won't you get "warped" values depending on the size of the difference? 2) This also got me thinking about what is "expected value." Expected value

least-squares error share|improve this question edited Apr 18 '15 at 5:37 Glen_b♦ 151k19250519 asked Apr 18 '15 at 2:17 Tony 3781413 There is always some optimization problem behind and news The quadratic loss **function is also used in linear-quadratic** optimal control problems. share|improve this answer edited Apr 18 '15 at 3:56 answered Apr 18 '15 at 3:37 Asterion 50647 (+1) for the reference to Laplace! –Xi'an Apr 18 '15 at 8:42 Two or more statistical models may be compared using their MSEs as a measure of how well they explain a given set of observations: An unbiased estimator (estimated from a statistical Mean Square Error Calculator

Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. In cases where you want to emphasize the spread of your errors, basically you want to penalize the errors that are farther away from the mean (usually 0 in machine learning, Square a big number, and it becomes much larger, relative to the others. have a peek at these guys Wiley. ^ CramÃ©r, H. (1930).

Is there any unique advantage that can explain its prevalence? Mean Square Error Matlab ISBN3-11-013863-8. ^ Detailed information on mathematical principles of the loss function choice is given in Chapter 2 of the book Klebanov, B.; Rachev, Svetlozat T.; Fabozzi, Frank J. (2009). There is no really "good" reason that squared is used instead of higher powers (or, indeed, non-polynomial penalty functions).

## But for risk-averse (or risk-loving) agents, loss is measured as the negative of a utility function, which represents satisfaction and is usually interpreted in ordinal terms rather than in cardinal (absolute)

New York: Springer-Verlag. The loss function is typically chosen to be a norm in an appropriate function space. In economics, when an agent is risk neutral, the objective function is simply expressed in monetary terms, such as profit, income, or end-of-period wealth. Mean Absolute Error In financial risk management the function is precisely mapped to a monetary loss.

I have long been puzzled by a question that will minimizing the squared error yield the same result as minimizing the absolute error? MR1835885. ^ Pfanzagl, J. (1994). As also explained in the wikipedia entry, the choice of the loss functions depends on how do you value deviations from your targeted object. http://nssse.com/mean-square/squared-error-consistent.html Which towel will dry faster?

New York: Springer-Verlag. That being said, the MSE could be a function of unknown parameters, in which case any estimator of the MSE based on estimates of these parameters would be a function of I hope that helps you in getting a bit more intuition for penalty functions :) share|improve this answer edited Apr 18 '15 at 19:12 answered Apr 18 '15 at 12:00 Jean-Paul ISBN0-387-96098-8.

Job offer guaranteed, or your money back.Learn More at Udacity.com Avinash Joshi, Books... According to this wikipedia entry, A common example involves estimating "location." Under typical statistical assumptions, the mean or average is the statistic for estimating location that minimizes the expected loss experienced p.229. ^ DeGroot, Morris H. (1980). Advanced Search Forum Statistics Help Statistics Squared Error vs Absolute Error loss functions Tweet Welcome to Talk Stats!

Solutions? That sort of thing. doi:10.1016/j.ijforecast.2009.10.008. ISBN0-387-95231-4.

Mean squared error is the negative of the expected value of one specific utility function, the quadratic utility function, which may not be the appropriate utility function to use under a