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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.

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Why does the square term get omitted in Gradient derivation of parameter θ-th

I get it that my question may sound a bit sophisticated or overwhelming, but it's pretty straightforward when you read the image below. As you can see, the square ^2 completely dissipates, despite ...
iHunter's user avatar
2 votes
1 answer
21 views

Is Mean Square Prediction Error acceptable to use if predicted values are continuous but actual observed values are discrete?

I would like to compare the predictive power of 2 models. The models are meant to model count data, so the actual observed values are discrete. However both models are designed such that they output ...
Astral's user avatar
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Standard error of RMSE and differences in RMSE

I have a set of models $M = \{1, ..., m, ..., K\}$, and for each I am calculating RMSE on out-of-sample data as standard: \begin{equation} \mathrm{RMSE_{m}} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (\...
user_15's user avatar
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How to improve a model with little dataset? [duplicate]

I have a dataset that has 20 features and 65 samples. I did data scaling. I also did feature selection in different ways. But this is the result. ...
Erfan Mollai's user avatar
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34 views

Is there any test I can apply to the data to tell whether the adaptive LASSO or the LASSO is likely to perform better in prediction?

Is there a. test I can perform on a sample that will tell me if coefficients estimated using the LASSO, the adaptive LASSO, or the relaxed adaptive LASSO are likely to give better (in the mean squared ...
andrewH's user avatar
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MSE of VAR impulse responses in R

I am using the vars library in R. How do I calculate the MSE of the impulse responses I generate with the irf function? The <...
Kweku Yamoah's user avatar
1 vote
0 answers
18 views

Optimal estimate under altered MSE loss function

Suppose I am interested in estimating $\theta \in \mathbb{R}$ and I observe a noisy data point $\tilde{\theta}=\theta + N(0,\sigma^2)$ where $\sigma^2$ is known. I am interested in constructing an ...
econ_enthusiast's user avatar
1 vote
0 answers
171 views

Determining an optimal level of aggregation that balances accuracy and granularity

I am looking for ideas for aggregating prediction outcomes in a way that maximizes the number of classes while minimizing classification error. As a motivating example, say I'm working on a prediction ...
mle_in_paris's user avatar
0 votes
1 answer
38 views

using MSE loss paired with F-score in a classification model

for a video summarization project i use the features of each frame as input to predict if some of these frames are included in the summary or not. one of the famous implementations i found had treated ...
moha tech's user avatar
1 vote
1 answer
37 views

results of a regression predictor

I have a neural network trained to predict values from timeseries. the target (which is hopefully to be predicted by NN) is always in range 0.0~1.0, and has these statistic features: ...
Bikay's user avatar
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Sample Size for Adaptive Lasso

Be gentle, I'm learning here. I have a fairly simple adaptive lasso regression that I'm trying to test for a minimum sample size. I used cross-validated mean squared error as the "score" of ...
JRW's user avatar
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Lasso regression test MSE lower than train MSE

Im currently using Lasso to build a predictive model for numeric variable . Before scaling the features I split the data for train test and validation . I have a feature named 'year' and i wanted the ...
liza read's user avatar
4 votes
1 answer
104 views

Mean Squared Error for point estimation

I am attempting to understand Mean Squared Error when evaluating point estimators for particular parameters of interest. The book we are reading for class states the following: The mean squared error (...
Harry Lofi's user avatar
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0 answers
30 views

Compare Root Mean Square Values

I'm trying to compare a regression neural network to a commonly used equation. I have an 80:20 split for my training:test, and I get the root mean square error on the test set from the neural network ...
Jack789's user avatar
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51 views

Why the MSE of the fitted data is not equal to the sum of the bias and the variance in R?

I use simple linear regression and I want to find the decomposition of MSE, that is as a sum of the bias, the variance and the variance of the error terms. I have the following code: ...
Vassilis Chasiotis's user avatar
3 votes
1 answer
128 views

is there hidden cost function for hidden layer in the neural network?

In the case of a neural network,are there different cost functions for different hidden layers? or is there one cost function for the final layer ? For example, in the neural network, the hidden layer ...
farhana hossain's user avatar
1 vote
1 answer
47 views

MSPE and $R^2_{OOS}$

I've been looking at a paper for a while that I find interesting. It's essentially a comparative analysis where the authors are comparing PCA/PLS to different machine learning methods. The aim is to ...
Nbs610's user avatar
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1 vote
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Model fit / Forecast accuracy / Predictors / Explanatory power predictors (panel data)

I have the following data structure: 100 individuals (forecasters) predicted the likelihood of the outcomes of 50 events (binary outcomes, 1 or 0). For each event, each forecaster made two different ...
Marc J. Muller's user avatar
8 votes
2 answers
385 views

As Brier Score = MSE, does MSE in a regression have a calibration-discrimination decomposition?

When the outcome of a supervised learning problem is binary and probabilities are predicted, Brier score can be decomposed into a measure of calibration and a measure of discrimination. ...
Dave's user avatar
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4 votes
1 answer
85 views

Why isn't there a square root version of the Brier score similar to how RMSE complements MSE?

When computing the mean squared error of a regression model, we get a metric in square units. For ease of interpretation, we can therefore instead compute the root mean squared error, which are in ...
another_student's user avatar
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33 views

Why is MSE score for GAM an NA value?

I am trying to compare the MSE values for two GAMs that are modeling water temperature. The only difference between the two is that one model has an auto-regressive (lag = 1) term. When I run the ...
Phoebe's user avatar
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1 vote
1 answer
69 views

Does increasing number of observations lead to the decreasing of Mean Square Error of consistent estimators?

I know that not all weakly consistent estimators exhibit MSE-consistency : https://stats.stackexchange.com/a/610835/397467. Anyway, does increasing the sample size leads to a reduction in their mean ...
whn's user avatar
  • 11
1 vote
2 answers
542 views

Mean squared error (MSE) vs Least squares error (LSE)

From my understanding the only difference between MSE and LSE is that with MSE you divide the sum of squared errors by the total number of values to get an average rather than just using the sum. This ...
Frobot's user avatar
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4 votes
2 answers
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Can someone help me understand why the MAE, MSE and RMSE scores for my regression model are very low but the R2 is negative?

I am using a random forest regression model to make predictions and leave one out cross validation for my prediction task. I am having a difficult time understanding why my R2 score is negative when ...
Rai's user avatar
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Help needed for interpretation of mtry and MSE calculation for bagging and random forests

I have a question regarding the mtry values for the two models Bagging and Random Forests. I applied the mtry measure for the California Housing Dataset and then for another dataset about white wine. ...
Marie_wue's user avatar
15 votes
3 answers
849 views

Best estimator of the mean of a normal distribution based only on box-plot statistics

Suppose $X_1,\ldots,X_n\sim\operatorname N(\mu,\sigma^2)$ and you can observe only the sample size $n,$ the two extreme values, and the first, second, and third quantiles of the sample. Among unbiased ...
Michael Hardy's user avatar
1 vote
1 answer
27 views

How to combine a noisy (but unbiased) estimate with a precise (but possibly biased) estimate in A/B tests?

Suppose I want to estimate some set of unknown quantities $\theta_1$, …, $\theta_N$. For each $i \in \{1, …, N\}$, I have two estimators: $\hat{\theta_i}_A$ and $ \hat{\theta_i}_B$. The goal is to ...
frelk's user avatar
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1 vote
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35 views

How should I write the units for MSE in its formula and in a plot axis?

I am trying to write a paper for IEEE and would like to know if for MSE, which can have any units, it correct to write "MSE (error^2)" in its formula (i.e. MSE (error^2) = ) and in a plot ...
Baldovín Cadena Mejía's user avatar
0 votes
1 answer
405 views

How to choose between R2 and MSE scores?

I have a dataset with approximately 2500 observations and 50 variables. The response variable is numerical, so my objective is to build a regression model. I have built one penalized linear regression ...
Alberto Perez Martinez's user avatar
1 vote
0 answers
154 views

Which evaluation metric should I choose? AIC or MSE?

I am currently at a total loss, so I hope someone can point me in the right direction regarding my model selection. The situation I want to create a linear model that best forecasts my data. I am ...
eork's user avatar
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0 answers
97 views

How to compare the performance of a volatility forecast like GARCH (1,1) with exogenous variables (MSE?)

I want to investigate, weather financial news have an influence on the volatility prediction of asset returns (daily data) when including them into the variance model/mean model. I have fit a GARCH/...
Jascäcilie's user avatar
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0 answers
31 views

What is the general procedure to come up with different estimator with smaller MSE?

PDF of a random variable $X$ is, $$ \begin{equation} f\left(x|\gamma\right)= \begin{cases} \frac{1}{\gamma} \exp(-\frac{x}{\gamma}) & x > 0 \\ 0 & \text{otherwise.} \end{cases} \end{...
N00BMaster's user avatar
1 vote
0 answers
386 views

Mean Squared Error (MSE) formula for data points in higher dimensions

The form for MSE for $N$ data points with scalar values $Y=[Y_1,Y_2,...,Y_N]$ is given by the formula: $$ MSE = \frac{1}{N} \sum_{i=1}^N (Y_i - \hat{Y}_i)^2 $$ How I see it, $ d_i = Y_i - \hat{Y}_i$, ...
Aditya's user avatar
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2 votes
0 answers
839 views

Gaussian Negative log likelihood loss vs MSE

I'm training a neural network on a regression problem. I wanted to compare between (1) Gaussian negative log likelihood (GNLL) loss (the output of the network is the mean and log variance) and (2) the ...
Eman.suradi's user avatar
1 vote
1 answer
150 views

Why can LASSO MAE be worse than individual feature linear regression MAE?

I am comparing the MAE of LASSO regression of multiple features vs. MAE of linear regression of each individual feature, and I am having trouble understanding why the LASSO MAE can be worse than some ...
Anna's user avatar
  • 11
-2 votes
1 answer
127 views

What does the error in artificial neural network stand for, is the same with mean square error (MSE) [closed]

How do I calculate mean square error (MSE) from the error obtained from ANN output
Chris's user avatar
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1 vote
0 answers
19 views

If the most likely value is that which minimizes squared-error, what are the possible distributions?

Gauss uniquely characterised the 1D normal distribution by asking for a distribution that: is symmetric is decreasing on either side of some center point $\mu$ has the data likelihood maximized by ...
Kevin's user avatar
  • 121
4 votes
1 answer
139 views

In the problem of best linear predictor, why is $E(XX')$ positive definite equivalent to $E(XX')$ being invertible?

I came across the following statement in a textbook when discussing the classic best linear predictor problem in statistics. It says $E[XX']$ being positive definite is equivalent to it being ...
ExcitedSnail's user avatar
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1 vote
0 answers
119 views

Numerical Stability of Transformer Training

I am trying to train a Transformer for sequence model, specifically for time series denoising. I have observed that the loss function (MSE) has been significantly improved during the evaluation which ...
chen shao's user avatar
2 votes
1 answer
68 views

How do you interpret the value of RMSE/MSE in English to stakeholders?

For example, if you have a R^2 of 0.95, you can explain this number to stakeholders in a presentation as: Our model explains 95% of the total variance within the data. However, if we have a RMSE of 11,...
Katsu's user avatar
  • 1,011
2 votes
1 answer
229 views

GLM: Sigmoid link with MSE for linear regression?

I have a relatively simple regression problem where I wanted to model y given x. X is continuous and is bounded [0,inf); y is bounded (0,1). My question is, is it appropriate for me to insert a ...
jbuddy_13's user avatar
  • 3,372
3 votes
1 answer
83 views

Ideas for a loss function to use for a cost sensitive problem setting?

I have trained a model to perform regression on a dataset with MSE as its loss function. The y_real values are between 0 and 1.5 and MSE of test set is around 0.009 which if fine. However, the ...
Maz's user avatar
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1 vote
1 answer
345 views

Equivalent of $E[(a-X)^2] = E[(a-E(X))^2] + Var(X)$ for $E[|a-X|]$ and $med(X)$?

The minimzer of the MSE $E[(a-X)^2]$ is $a=E(X)$, and the MSE can be decomposed into $E[(a-X)^2] = E[(a-E(X))^2] + Var(X)$. I am wondering whether there exists a similar expression th MAE $E[|a-X|]$ ...
FZS's user avatar
  • 405
1 vote
2 answers
69 views

Does the average of a random sample minimizes MSE when you "know nothing about the distribution"?

Consider any random variable $X$ and any random sample $(X_1,\dots, X_n)$ such that $X_i \sim X$. As is well-known, $E(X)$ is the constant that minimizes the MSE of $X$, i.e., $E(X) = \arg\min_a E[(a-...
FZS's user avatar
  • 405
1 vote
0 answers
269 views

MSE or RSE, and how to interpret each?

I'm on page 69 of ISLR 2nd Edition. I've created a linear regression modeled after the toy dataset in the book, where we predict number of unit sales given a particular TV advertising budget. Here are ...
Katsu's user avatar
  • 1,011
9 votes
1 answer
314 views

Expectation as a minimizer of the loss function

It is a well-known fact that the minimizer of the mean-squared loss (MSE) $$\min\limits_\mu \mathbb{E}_{X} \left(X - \mu \right)^2$$ equals the expectation of $X$. Are there any alternative non-...
Denis  Korzhenkov's user avatar
1 vote
1 answer
333 views

Why mean squared error surface takes bowl shape

I was trying to understand geometric interpretation of regularization and came across following statement here: $$\text{Mean Square Error}\; E(y,\hat{y})=\frac{1}{n}\lVert\hat{y}-y\rVert^2$$ $$=\frac{...
Mahesha999's user avatar
0 votes
0 answers
72 views

MSE for multivariate case

This is very basic, but I want to clarify the MSE in a vector-valued setting. Given observations $$ \begin{bmatrix} [x_1, y_1,z_1] \\ \vdots \\ [x_n, y_n,z_n] \end{bmatrix} $$ And estimations $$ \...
oliverjones's user avatar
2 votes
1 answer
168 views

The Monte Carlo of the mean square error of the maximum likelihood estimates

I try to get mean square error of the maximum likelihood estimators in R (using Monte Carlo). I can write the calculation for the MLE that is repeated once, but I need to repeat the Monte Carlo ...
Hermi's user avatar
  • 747
0 votes
1 answer
88 views

RMSE for model-selection

Can I use RMSE,r2 or other metric to compare models of different datasets and variables? And if I have the same dataset but different variables?
Valt Yo's user avatar
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