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 are the "Loss Functions" being Optimized in most Statistical/Machine Learning Problems usually "Quadratic"? [duplicate]

Why are the "Loss Functions" being Optimized in most Statistical/Machine Learning Problems usually "Quadratic"? Using very basic logic, in statistics/machine learning we are trying ...
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How is the decay rate in exponential smoothing optimized?

For the sake of simplicity, I just want to focus on single/level exponential smoothing. When alpha, the decay rate, is near 1, the most recent observation has the highest weight and influence of ...
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What can cause test-set MARE to be lower when trained on MSE?

I am currently working on a CNN 1D model for regression. The ultimate goal is to minimize the mean absolute percentage (relative) error, so-called MAPE or MARE. However, the MARE on the test set is ...
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What is the difference between least squares method and mean squared method in calculating the error?

I think I am a little bit confused between the LSE (Least Squared Error) and the MSE (Mean Squared Error). So how can these two methods differ in calculating the error of the linear regression model? ...
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How to calculate RMSE for two regression lines

I'm struggling on how can I calculate the RMSE for two regressions. Consider the following scenario: I have two linear regressions, and Id like to calculate the joint RMSE for this model. Any hint on ...
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Drastically high MAPE error but MAE is normal [duplicate]

I am training an autoencoder which takes sampled time series sensor data in range [-1024,1024] (0 values is possible). I use mean_squared loss and Adam optimizer. During the training MAE decreases and ...
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Difference between minimizing RMSE or MSE in non linear least squares?

I am working with R with this code from the book "Bootstrap Methods: With Applications in R" by Gerhard Dikta and Marsel Scheer: ...
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What is the theoretical justification for alternatives to MSE minimisation?

I'm trying to wrap my head around the connection between statistical regression and its probability theoretical justification. In many books on statistics/machine learning, one is introduced to the ...
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Cross Entropy for sigmoid/tanh regression

My neural network has a tanh activation function for the output layer. It would be no problem to change this to sigmoid. The labels are values in the same range. By this I mean that the target value ...
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How to prove Mean Squarred Error (MSE)

I would like to prove this equation of Mean Squared Error (MSE): m is the number of training instances. X is a m × n matrix containing all the feature values (excluding labels) of all instances in ...
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What optimisation method is used in ordered logistic regression?

I am using the polr function in R to create an ordered logistic model and am curious to know what its optimisation method is? It seems to perform better than other models I have tested it against when ...
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Conceptual error in unbiased estimates and their programming in R

A few days ago I asked a question which had a programming error, I already corrected it and I bring it to you again. By generating $n=1,000,000$ of random data with normal distribution ($\mu=35, \...
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How to calculate Mean Squared Error when there are multiple observed y values for a single x value?

Given a data set where there exists multiple different observed y-values for a given x-value, how do I calculate Mean Squared Error? The formula implies that I subtract the predicted from a singular ...
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Will MSE-based estimator generate symmetric residuals if the error has got symmetric support (not distribution)?

This question is more specific than :my old question Take follow regression model: $y=f(x)+e$ Where $e\sim D$ with a such symmetric support $A=(-a,a)$, not symmetric distribution. Now given a data set ...
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Can Mean Square Error cause underfitting?

Mean Square Error (MSE) is used in Regression problems to compute the error in prediction. Large errors have a large influence on the MSE, and small errors have almost negligible influence on the ...
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Evaluating Supervised Model Performance Against a Baseline

My question is regarding how I can interpret the performance of a supervised ML task relative to a baseline estimator. I have run a supervised ML as a regression, and used K-fold CV to evaluate ...
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"Efficiency" of a Kernel

My understanding is that the Epanechnikov kernel is "efficient" in a mean squared error sense. Footnote 4 of Wikipedia's page defines the "efficiency" of a kernel as $$\sqrt{\int u^...
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Testing bias and consistency for a parameter given variance less than infinity

I proceeded to find the expectation of the estimator to check for bias. Since Therefore and hence biased. An estimator is consistent if MSE tends to 0 as n tends to infinity but I do not know how ...
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An Implementation of MSE decomposition to Variance and Bias Squared

Before I describe my question, it is necessary to note a common fact in estimation theory that MSE can be decomposed to Variance and Bias Squared. Depending on whether it is MSE of an estimator or MSE ...
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Estimating rate of convergence from MSE

Given that I have calculated values for the MSE for differing values of $n$ and the estimator $\hat{\theta}$. Is it possible to calculate the rate of convergence, $O_p(n^{-r})$, of this estimator by ...
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Why use MSE instead of SSE as cost function in linear regression?

I am studying linear regression and I solved some problems analytically. For that I used the normal and intuitive sum of squared error function. Looking at this function, it makes all sense why it ...
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models with very similar MSE - how to select the best model?

I am trying to model the P300 complex of event-related potentials across conditions. For that, I randomly sample parameters, fit a model with these parameters and keep record of parameters vectors ...
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Why does my Mean Squared Error suddenly become so large in cv.glmnets lasso regrssion?

I performed a Lasso Regression in order to do variable selection. All varaibles are standardized and all coefficients for lambda=0 lie between - 3.3 and +1. Still, when the lambda gets small enough, ...
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Combine several performance metrics from several datasets

We are developing and evaluating a multi knee/elbow point detection algorithm. For our evaluation, we have 200 sequences of real data. These sequences were annotated manually. For each algorithm and ...
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For MSE equation does order of $y$ and $\hat{y}$ in the residual $(y-\hat{y})$ matter?

So the equation for MSE is $\frac{1}{2N}\sum(y-\hat{y})^2$. If you switch the order as in $\frac{1}{2N}\sum(\hat{y} - y)^2$ does that affect anything? The only thing I think it potentially effects is ...
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Why do we prefer unbiased estimators instead of minimizing MSE?

I was thinking about why, usually, $\hat{\sigma}^2=\hat{p}(1-\hat{p})$ is used to estimate the variance in a Bernoulli population instead of $s^2=\hat{p}(1-\hat{p})\frac{n}{n-1}$. $s^2$ is unbiased, ...
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How does minimizing MSE maximize variance?

I was reading about PCA and they had this interesting line that "A line or plane that is the least squares approximation of a set of data points makes the variance of the coordinates on the line ...
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Eta squared for biased estimates

It is possibile to use eta squared index with MSE instead of variance? More specifically I've to deal with biased estimates so I can't use Variance but I've use to use the MSE. Given that Eta squared ...
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How to compute the "true test mean square error"?

In page 182 of An Introduction To Statistical Learning, author wrote this: When we examine real data, we do not know the true test MSE, and so it is difficult to determine the accuracy of the cross-...
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MSE Proof for an estimator

I am trying to figure out the following proof. The third line is not clear. We all know that (a+b)^2=a^2+2ab+b^2. The term 2ab should be 0, but I can't figure out why. I have found other proofs here ...
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What's the difference between Average Square Error and Mean Square Error ? Are they the same thing?

I have a bit of confusion regarding ASE and MSE as in SAS Enterprise Miner it shows these two measurement scales. What is the difference or similarity between the two and why are they both so similar? ...
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RMSE vs MSE loss function - the optimization solutions are equivalent?

If we optimize a function $f$ with respect to loss $L$, which is defined as RMSE; Are we going to get the same solution as optimizing MSE ? Even, if the function $f$ is non-linear (e.g. a neural ...
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What conditioning assumptions are hidden in the bias-variance tradeoff proof?

I've read through this question and its answers quite a few times. I'm curious to know what conditioning assumptions are used that are hidden from the derivation. Here's what I mean: let's say I have ...
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Confusion (possibly due to terminology)

Disclaimer.. This is a post regarding help with homework but I have done some work. I am stuck between C and D since they both seem right. First of all, I think since the variance explained by the ...
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Why is REML default if it inflates MSE?

Within the mixed effects model world, REML has become the method of choice in order to correct for the downward bias in variance components. For years, I accepted this rationale without thinking about ...
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Deriving the risk of the Hodges-Le Cam estimator under squared-error loss

In order to better understand the behaviour of the Hodges-Le Cam estimator, $\tilde{\theta}_n$, I am trying to derive an expression for the risk $R_n(\tilde{\theta}_n, \theta)$ under squared error ...
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When would linear regression out-perform Lasso regression RMSE?

In what situation would linear regression out-perform Lasso regression with respect to RMSE?
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How to calculate mean squared error when a process is modeled with simple brownian motion?

I want to model a time series process with simple Brownian motion and want to know to what extent does the estimated model fit the original time series. While I am aware of the method two-sample ...
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Out-of-sample MSE and MAE for volatility forecasting [duplicate]

I have been searching through the whole CrossValidated but couldn't find the answer. I want to test out-of-sample the volatility forecasts (if it means something ARCH-like ones, MSGARCH, Multifractal ...
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Why do my cross validation delta values and MSE calculation conclude very different model fits?

My data: My model: mod <- glm(Y2/Y1 ~ Var_1, data = df, family = binomial, weights = Y1) summary(mod) shows that my ...
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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=\...
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How to prove that the expected value minimizes mean square error [duplicate]

In this wiki subpage about conditional probability we read that if $(\Omega, \mathcal{F}, \mathcal{P})$ is a probability space and $X:\Omega\to\mathbb{R}$ is a random variable with mean and variance, ...
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Intuition behind training and test MSE when using regression trees

Imagine that we have a supervised learning setting. Training data is given by the input-output pairs $(\mathbf{x}_n, y_n)$ for $n=1,\dotsc,N$ and similarly, the test data $(\mathbf{x'}_n, y'_n)$ for $...
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How do the training and cross validation mean squared error curves behave as a function of $\lambda$?

I am currently looking into methods of choosing optimal tuning parameter $\lambda$ for ridge regression. I think that for the cross-validation the MSE should be relatively high for $\lambda=0$. Then I ...
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Bagged Decision trees / Random Forests: why ISLR uses validation set instead of OOB to compute out-of-sample MSE?

I am reading the book "An Introduction to Statistical Learning" available here. Chapter 8.3.3 at page 328 of the book computes a bagged decision tree (which is a random forest where we use ...
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MSPE predictor of MA model

Assume $e_i=(\epsilon_i+\epsilon_{i+1})/2, i=1,...,n$ where $\epsilon_1,...,\epsilon_{n+1}$ are iid with mean zero and variance $\sigma^2$. Then $e_i$ are the moving average errors. Now, consider the ...
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bias–variance decomposition related to median?

In evaluating or designing an estimator $\hat\theta$ of a population parameter $\theta$, the most common approach is to look at its bias, $\operatorname{E} \hat\theta - \theta$, its variance, $\...
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Meaning of θj in equation for partial derivative of MSE

The equation to find the partial derivative of a cost function with respect to a parameter θj is given in the book Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: $$ \frac{\partial}...
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Comparison of Bayesian and Classical estimates

Is it correct to compare Bayesian and Classical estimates using Mean Squared Error (MSE)? MSE is a criterion that is used in the classical paradigm. For example: I am comparing the performance of ...
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Why is loss after training with normalized data higher than the loss of the same, but non-normalized, data?

I am toying around with training a simple LSTM model using time series data generated from the f(x) = sin(x) function to make predictions about the next value. I know this is non-sensical but I use it ...

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