# 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 ...
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### 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 ...
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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: \mathrm{RMSE_{m}} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (\...
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1 vote
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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. ...
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### 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 ...
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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 <...
1 vote
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### 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 ...
1 vote
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 ...
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 ...
1 vote
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: ...
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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 ...
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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 ...
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 (...
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### 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 ...
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### 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: ...
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 ...
1 vote
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 ...
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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 ...
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. ...
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### 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 ...
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 ...
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1 vote
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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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1 vote
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 ...
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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. ...
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 ...
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1 vote
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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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1 vote
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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 ...
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 ...
1 vote
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 ...
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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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### 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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