Questions tagged [mse]

MSE stands for Mean Squared Error. It is a measure of the performance of an estimate or prediction, equal to the mean squared difference between the observed values and the estimated / predicted values.

MSE stands for Mean Squared Error. It is a measure of the performance of an estimate or prediction, equal to the mean squared difference between the observed values and the estimated / predicted values. For predictions $\hat{y}_1, \dots, \hat{y}_N$ and corresponding actuals $y_1, \dots, y_N$, the MSE is defined as

$$\text{MSE} := \frac{1}{N}\sum_{i=1}^N(\hat{y}_i-y_i)^2.$$

Alternatives to the MSE as a point forecast accuracy measure include the , the and the .

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Examples where method of moments can beat maximum likelihood in small samples?

Maximum likelihood estimators (MLE) are asymptotically efficient; we see the practical upshot in that they often do better than method of moments (MoM) estimates (when they differ), even at small sample sizes Here 'better than' means in the sense…
Glen_b
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How to interpret error measures?

I am running the classify in Weka for a certain dataset and I've noticed that if I'm trying to predict a nominal value the output specifically shows the correctly and incorrectly predicted values. However, now I'm running it for a numerical…
FloIancu
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What is the relationship between the mean squared error and the residual sum of squares function?

Looking at the Wikipedia definitions of: Mean Squared Error (MSE) Residual Sum of Squares (RSS) It looks to me that $$\text{MSE} = \frac{1}{N} \text{RSS} = \frac{1}{N} \sum (f_i -y_i)^2$$ where $N$ is he number of samples and $f_i$ is our…
Josh
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MSE decomposition to Variance and Bias Squared

In showing that MSE can be decomposed into variance plus the square of Bias, the proof in Wikipedia has a step, highlighted in the picture. How does this work? How is the expectation pushed in to the product from the 3rd step to the 4th step? If the…
statBeginner
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Understanding bias-variance tradeoff derivation

I am reading the chapter on the bias-variance tradeoff in The elements of statistical learning and I don't understand the formula on page 29. Let the data arise from a model such that $$ Y = f(x)+\varepsilon$$ where $\varepsilon$ is random number…
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Loss function for autoencoders

I am experimenting a bit autoencoders, and with tensorflow I created a model that tries to reconstruct the MNIST dataset. My network is very simple: X, e1, e2, d1, Y, where e1 and e2 are encoding layers, d2 and Y are decoding layers (and Y is the…
AkiRoss
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Can someone give the intuition behind Mean Absolute Error and the Median?

I do not understand the intuition behind why the median is the best estimate if we are going to judge prediction accuracy using the Mean Absolute Error. Let's say you have a random variable $X$ and you want to predict what the next $X$ is. Let's…
confused
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Can the mean squared error be used for classification?

I know the mean squared error formula and how to compute it. When we talk about a regression we can compute the mean squared error. However can we talk about a MSE for a classification problem and how to compute it?
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Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)?

MAD = Mean Absolute Deviation MSE = Mean Squared Error I've seen suggestions from various places that MSE is used despite some undesirable qualities (e.g. http://www.stat.nus.edu.sg/~staxyc/T12.pdf, which states on p8 "It is commonly believed that…
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Is the mean squared error used to assess relative superiority of one estimator over another?

Suppose we have two estimators $\alpha_1$ and $\alpha_2$ for some parameter $x$. To determine which estimator is "better" do we look at the MSE (mean squared error)? In other words we look at $$MSE = \beta^2+ \sigma^2$$ where $\beta$ is the bias of…
Damien
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Is $\frac1{n+1}\sum_{i=1}^n(X_i-\overline X)^2$ an admissible estimator for $\sigma^2$?

Consider a sample $X_1,X_2,\ldots,X_n$ from a univariate $N(\mu,\sigma^2)$ distribution where $\mu,\sigma^2$ are both unknown. Then it is known that under squared error loss, the sample variance $s^2=\frac1{n-1}\sum\limits_{i=1}^n (X_i-\overline…
StubbornAtom
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MSE as a proxy to Pearson's Correlation in Regression Problems

TL;DR (too long, didn't read): I'm working on a time-series prediction problem, which I formulate as a Regression problem using Deep Learning (keras). I want to optimize for the Pearson correlation between my prediction and the true labels. I'm…
galoosh33
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What makes mean square error so good?

Our statistical inference course material states the following: The principle of mean square error can be derived from the principle of maximum likelihood (after we set a linear model where errors are normally distributed) After that the…
Atte Juvonen
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Normalized RMSE

I have several time-series in a VAR(1) and, due to some of them haven't the same unit of measure, I'd like to estimate the RMSE in percentage. I know that it could be done in several ways (see below) but I don't know precisely which is the one that…
user40899
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The difference between MSE and MAPE

i was wondering what is the differences between Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) in determining the accuracy of a forecast? Which one is better? Thanks
rendra
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