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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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Understanding tensorflow calculation of MSE for output vector of N dimensions
Here is the code example with variable names guiding the process:
...
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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/...
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What is the general procedure to come up with different estimator with smaller MSE?
PDF of a random variable $X$ is,
$$
\begin{equation}
f\left(x|\gamma\right)=
\begin{cases}
\frac{1}{\gamma} \exp(-\frac{x}{\gamma}) & x > 0 \\
0 & \text{otherwise.}
\end{cases}
\end{...
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Mean Squared Error (MSE) formula for data points in higher dimensions
The form for MSE for $N$ data points with scalar values $Y=[Y_1,Y_2,...,Y_N]$ is given by the formula:
$$ 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$, ...
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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 ...
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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 ...
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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
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Pairwise comparison test for out-of-sample MSEs
In order to compare the out-of-sample forecasting accuracy of two competing models, I am trying to implement the equal accuracy test proposed in this article: http://www.timberlake-consultancy.com/...
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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 ...
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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 ...
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Variational Autoencoder - What's the best way to output and which loss function? [duplicate]
I'm hoping this is the right place to ask. I'm new to deep learning and especially variational NNs.
I'm trying to create a VAE using tensorflow/tensorflow_probability which can recreate a gaussian ...
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Optimal kernel regression with random target functions
The classic kernel regression problem fixes a target function $f^*$ that we seek to learn, and says that for a dataset/observations $D = \{x_i, y_i\}_{i=1}^n$ where $y(x) = f^*(x) + \epsilon$, for ...
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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 ...
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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,...
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How to compare Predictive Power of Models, why will some models work better than others?
for an assignment, I am doing a regression problem on this dataset: https://archive.ics.uci.edu/ml/datasets/Online+News+Popularity, where I need to run Multiple linear regression, Forward stepwise, ...
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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 ...
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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 ...
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Comparison of RMSE (root mean squared error) values
I want to see if my models work better univariate or multiple. But how can I do this? Normally I train the model, calculate the RMSE/MSE on the test data and compare these values. Now I trained the ...
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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|]$ ...
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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-...
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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 ...
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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$$ equals the expectation of $X$.
Are there any alternative non-...
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Choosing the best hyperparameter combination from a fluctuating MSE vs Epoch graph
I have chosen five hyperparameters and a total of 216 combinations to search the best one in a regression task. When I draw the MSE vs Epoch graph on the validation data, it improves with increasing ...
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Why mean squared error surface takes bowl shape
I was trying to understand geometric interpretation of regularization and came across following statement here:
$$\text{Mean Square Error}\; E(y,\hat{y})=\frac{1}{n}\lVert\hat{y}-y\rVert^2$$
$$=\frac{...
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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
$$ \...
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The Monte Carlo of the mean square error of the maximum likelihood estimates
I try to get mean square error of the maximum likelihood estimators in R (using Monte Carlo).
I can write the calculation for the MLE that is repeated once, but I need to repeat the Monte Carlo ...
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RMSE for model-selection
Can I use RMSE,r2 or other metric to compare models of different datasets and variables?
And if I have the same dataset but different variables?
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How to choose a predictive model between MSE and graphical plot (observed against predicted value)?
After regularisation with Lasso and Ridge, I currently have a model under each, taking MSE values as shown below,
MSE, Ridge = 0.1923102
MSE, Lasso = 0.1292252
Both models have the same number of ...
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Polynomial regression has good Mean Squared Error but poor prediction on unseen data [closed]
In a dataset, the unseen target value is 2500000000.
In a polynomial regression with degrees from 1 through 7, I have the following results:
...
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Maximum likelihood estimation - effect of reducing the number of data rows (by averaging)
Say I want to estimate $\overline x$ given matrix $A$ and $\overline y$ and assume $\overline \epsilon \sim N(0,\sigma^2 I)$:
$$\overline y = A \overline x + \overline\epsilon$$
I want to study the ...
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How to perform crossvalidation for regression on 100 time series and one hyperparameter?
I want to find the best hyperparameter $\lambda$ for a penalized linear regression. For the regression I use 100 time series with random starting conditions (derived from simulation). 80% of the date ...
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How error derivative becomes zero in gradient descent
Previous questions this & this does not answer my question
Code
...
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Problem in showing $\rm MSE = Var + Bias^2.$ [duplicate]
I am trying to prove the equality of $$\rm MSE(\langle I\rangle)=Var(\langle I \rangle)+Bias(\langle I \rangle)^2$$ but obviously I got something wrong as they don't equal in my calculation:
So here ...
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Can there be any situations where MLE performs better than MPS in terms of MSE or Bias?
Cheng and Amin (1983) proposed the maximum product of spacing estimation method as an alternative to maximum likelihood estimation. They stated that MPS behaves better in small sample cases than MLE ...
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Confused on the definition of Residual standard error
I am confusing with the actuarial text book. It said the residual standard error is s =RSS/(n-2), why it is not $\sqrt{\frac{RSS}{n-2}}$?
And also, what is the difference between the MSE and RSS, ...
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Foreacast Combinations: derivation of minimum MSE / variance approach
I am just despairing of the derivation of the minimum variance procedure. The method of the combination of forecasts was first established in 1969 by Bates and Granger. They also invented the minimum ...
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How to interpret MSE, RMSE and MAE
I understand in general MSE, RMSE and MAE means average distance between the actual and predicted value, and the lower the MSE, RMSE and MAE, the better the model fits the dataset.
I try to understand ...
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Backpropagation in mini-batch stochastic gradient descent with mean squared error loss
Suppose I have an ANN which has one input layer of size $128$, one hidden layer of size $64$ and one output layer of size $10$ for a classification problem. Let's assume we have a training sample of $...
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Which factor should I consider to choose the best model, stationarity or lowest MSE?
Recently, I did a project where I modelled a dataset of Gold price. I used ARIMA(1,1,1) and ARIMA(2,2,3) to model the data. The results that I get was ARIMA(1,1,1) was not stationary but the MSE value ...
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MAE vs MSE for Linear regression
Several articles says that MAE is robust to outliers but MSE is not and MSE can hamper the model if errors are too huge. My question is that MSE and MAE both are error matrices, our priority is to ...
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Is the use of approximate MSEs of seperate and combined ratio estimators apt for small sample sizes?
The problem below is from Cochran's Sampling Techniques, chapter 6, titled Ratio Estimators:
The following data are for a small artificial population with $N= 8$ and two strata of equal size.
$ \...
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