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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11 views

model has very good MSE and R-square

I made a glm model for log(price) and got that for my model R-square = 0.98 and MSE = 0.14. These values are very good for a model, even too good. So my question is can very high values of these be a ...
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Mallows' C MSE bias and sampling error component

If a true quadratic regression function is E(Y) = 15+20X+3X^2, and the fitted linear regression function is Y_hat=13+40X, for which E(b_0) = 10 and E(b_1) = 45. What are the bias and sampling error ...
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30 views

How does GARCH compute the realized daily volatility to be compared to the output of the model, to compute in-sample MSE?

How do GARCH and GJR-GARCH models (as implemented in rugarch or in EViews) calculate the in-sample MSE if they use the time series of daily returns as the input and don't use a time series of daily ...
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28 views

Mean Squared Error random variable

I'm reading Elements of Statistical Learning (2nd edition, 12th printing) and there are two things that are bothering me. Regarding Equation 2.25, one is the training set Ξ€. I'm assuming that it is a ...
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14 views

Regression loss function to yield high correlation

I am using a neural network to predict a target. Currently, my loss is the mean squared error. I am not interested in the absolute values of my predictions, thus I evaluate the predictions using the ...
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15 views

Prediction vs. model stability in inner and outer loop of repeated nested cross validation

Imagine I want to optimize some hyperparameters and get an estimation of the generalization error to compare different prediction models. I use a nested k-fold cross validation to avoid data leakage ...
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14 views

Evaluation metric for classification + regression, as in weighted True by another objective? AUC + MSE?

I'm using purchase data to build a cross-selling T/F response model for the banking industry, to score customers based on their likelihood to acquire a loan. On the other hand, I'm also building a ...
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59 views

What is the relationship between mean squared error and classification error?

I've trained a network using a genetic algorithm and I have two possible fitness functions for my GA: MSE and CErr. If I use MSE as my fitness function, over time MSE decreases and classification ...
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9 views

Effect of increasing standard deviation of noise and independet varibales on MSE

We have $Y=f(X)+\epsilon$. We generate data, where $X\sim \mathcal{N}(0,\sigma_X)$ and $\epsilon \sim \mathcal{N}(0,\sigma_{\epsilon})$. We calculate the expected test mean squared error as follow (...
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27 views

Strategies to achieve a near-perfect Adjusted R square (0.99<=) with only the lm function in R while only using 25 variables?

The simulated data has 9 (All continuous) independent variables and 500 observations, the given response variable is a continuous variable. Currently, I am at an R squared of 0.965 with 22 variables. ...
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51 views

MSE of the Jackknife Estimator for the Uniform distribution

The Jackknife is a resampling method, a predecessor of the Bootstrap, which is useful for estimating the bias and variance of a statistic. This can also be used to apply a "bias correction" to an ...
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Ensemble error can never be lower than best base learner

A common ensemble approach is ensemble averaging, where predictions from individual base learners are averaged (individual predictions are weighted equally to form the combined prediction). If the ...
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24 views

Obtaining MSE for a smoothing spline model in R

So I've fit a smoothing spline regression model on a training set (code below) and I obtain an 8 digit number as MSE value. When I fit a regular cubic polynomial to the same dataset I obtain a 7 digit ...
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14 views

Comparing Neural Network to ARMA

I used a neural network tool in MATLAB to predict data, and it gave it's accuracy as MSE and an R-value. I used the econometricModeler tool in MATLAB to predict data using ARMA. It gave it's accuracy ...
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43 views

Reconstruction Loss in Keras with custom loss function

Using Tensorflow 2: My model has an input RGB image of shape (64, 64, 3) and outputs a RGB image of the same shape. I want to use a custom reconstruction loss, therefore I write my loss function to ...
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Correct application of RMSE and MAE

I have ~ 120 different datasets (different scales, sample size etc) and for each dataset, I predict ONE statistical parameter (doesn't matter what for my question) with different methods. To compare ...
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56 views

Confusion on Mean Squared Error for Regression

In common statistical textbooks' linear regression topic, Mean Squared Error is often defined as $$MSE = \dfrac{(y-\hat{y})^T(y-\hat{y})}{n-p} = \dfrac{RSS}{n-p}$$ where the $y$ and $\hat{y}$ is a ...
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Who first discovered the decomposition of mean squared error?

Can someone here provide the earliest known reference to the decomposition of MSE into variance and bias squared?
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31 views

Mean squared error Bayesian linear regression vs lm-function in R

so I am trying to compare out-of sample mean squared errors for both the linear regression using the lm() function, and the Bayesian linear regression using the metropolis sampling algorithm on the ...
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27 views

Are the MSEs of all estimators that have an MSE, equivalent asymptotically?

Are the MSEs of all estimators that have an MSE, equivalent asymptotically or are some estimators terribly bad even when sample size approaches infinity? I was thinking about estimators with MSEs ...
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30 views

MSEP lower than MSE (regression)

I have fitted a model with weighted least squares and I wanted to look at the mean square error (MSE) and mean square error of the prediction (MSEP) value of this model. Next, I noticed that the MSEP ...
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42 views

What is the relation between MSE of K-NN for a regression problem and LOOCV?

I trying to answer this question: Denote the MSE of K-NN for a regression problem: $𝐸_{𝑖𝑛} =\frac{1}{𝑛}\sum_{i=1}^n(𝑦_𝑖 βˆ’ \frac{1}{π‘˜}\sum_{j=1}^k𝑦_𝑗)^2$ , where for each $𝑦_𝑖$, the ...
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25 views

Calculate MSE of a model after cross validation?

I used the glm function to do a 10-fold cross validation and I found the best model based on delta of cv.glm. Can I use that same delta as MSE and compare it with the MSE of another model from ...
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72 views

How to calculate MSE for logistic regression in R

I am trying to calculate Mean squared error (MSE) for logistic regression for this model below in R. ...
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13 views

Getting different values for MSE using anova(lm(y~.)) and mean(residuals(fit)^2)

Using this dataset of gas mileage for different cars I've been asked to run a ridge regression using $\frac{p*\sigma^2}{\beta'\beta}$ as the k-value. I've been told $\sigma^2 = MSE$ $p =$ ...
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35 views

Why are the MLE and MMSE corrections for sample variances different?

I have a number of samples of sample size 2 and a number of sample of sample size 3. If my samples are all samples from populations with a shared population variances, I wish to estimate population ...
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22 views

R: Bootstrap Mean Squared Error to test predictive performance of three models

I have an investigator that wants to test predictive performance of three models. The three models predict hospital stay. Formula A is a formula: (x1/100 + x2*2)/x3 = expected length of hospital ...
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54 views

Difficulty with averaging corrected sample variances of different degrees of freedom:

I have a number of measurement samples of which some have 2 measurements and some have 3. I wish to make the most accurate estimation of population variance I can, and understand that ignoring data ...
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48 views

XOR with Neural Network [closed]

I'm trying to implement a simple neural network to fit a XOR function as shown in the book 'Deep Learning' by Ian Goodfellow, Yoshua Bengio and Aaron Courville (2016). Here is my python code using ...
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18 views

Comparing differences in RMSE

I tried to search on the web as well as here. Seems like no answer. There was a question previously asked in stack exchange, but it was discussed instead of being answered. I have RMSE from 6 groups. ...
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Estimating the bias and variance of an estimator [closed]

Suppose I have a vector of values generated by an estimator of $y$. I also have corresponding values of $y$ in another vector. Starting at the first observation, and adding the remaining observations ...
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157 views

Random forest [R]: why is my OOB RMSE so much smaller than test RMSE?

I'm doing the kaggle challenge on timetravel predictions where the task is to predict the duration (Y) of a uber trip given some information about the start and end coordinates and the time the trip ...
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786 views

Help on R squared, Mean Squared Error (MSE), and/or RMSE as individual measures in regression model perfomance evaluation?

Just a question on regression model evaluation statistics. Here we go. I seem to be under the impression that $R^2$, MSE, and RMSE are all very closely related and essentially all play a part in ...
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502 views

Custom RMSE loss not the same as taking the root of built-in Keras MSE loss [closed]

I have defined a custom RMSE loss function: def rmse(y_pred, y_true): return K.sqrt(K.mean(K.square(y_pred - y_true))) I was evaluating it against the mean ...
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2k views

Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate]

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 ...
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52 views

What does it means when MSE almost equal with labels' variance?

I did a training for my dataset of 6000 images. running np.var(train_data), I get 2435. After training of enough epochs, my MSE is nearly 2415+-. Is this means, that the model is unable to find any ...
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230 views

Why Massive Random Spikes of Validation Loss?

My problem is to estimate the length of a straight line in an image, in pixel. My training size is 6000 images, validation is 1000 images. Each image has 200 x 200 pixels. My data is generated using ...
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134 views

Deviance and MSE confusion (Boosting, Random Forests, Bagging)

I am following Hastie & Tibshiriani ISLR In Chapter 8 they introduce Bagging, Random Forests and Boosting. To compare each model they plot a curve of Test Error VS number of trees. Various ...
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1answer
252 views

When are biased estimators with lower MSE preferred? [duplicate]

From wikipedia https://en.wikipedia.org/wiki/Bias_of_an_estimator : because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased ...
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70 views

Screening candidate models before AIC comparison?

I am interested in identifying the best of 3 physiologically reasonable models that fits my continuous data. Data is some measure derived from neurons recorded from 3 adjacent regions of brain tissue (...
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147 views

Minimizing MISE to find consistent estimator

Consider kernel regression estimation of the mean function $m$ of the process $$y_t = m(x_t) + \epsilon_t,$$ where $\epsilon_t$' s are correlated with covariance function $R(s,t) = \exp \{-\lambda|s-...
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38 views

Correct error estimation for linear fit

This may be a simple problem, but I want to be thorough in setting up my problem as I'd like to know why I should proceed in one of two ways (or another if someone thinks it is suitable), so please ...
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38 views

How to modify RMSE loss function to adopt for integer valued predictions, using a Neural Network?

Context: Prediction of dependent variables like Age, Siblings, Children, etc (which are not categorical, but bounded, and integer-valued) from a dataset using Neural Network. I'm experimenting with a ...
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33 views

Are there some guidelines to follow while combining different types of losses to make a cost function?

I'm training an Autoencoder to reproduce the input, and the architecture is a simple fully connected neural network. The initial phase of the implementation was using float/integer dataset, and ...
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72 views

Is the difference between two MSEs significant?

I developed several Elo rankings and used MSEs to compare them on their predictive capacity of the 2018 World Cup. I've been asked to use a statistical test to find if the difference between two of my ...
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103 views

MSE Intuition and Interpretation

I've got a very small question. Say I'm making a linear regression model. When I test the model with a testing set, I get an MSE of 4.31 (arbitrary). What do I interpret from this? As in, what does ...
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314 views

How to optimize MAPE in regression algorithms

I have a regression task where the label is varying from about 0.001 to 1000. One of the feature called group, for example, group A corresponding label from 0-0.1 and group G corresponding label from ...
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17 views

Choosing an estimator function due to variance and bias

I am working on an assignment that requires me to compare two estimators $T1$ & $T2$ for an unknown parameter $\theta$ based on their MSE. They both have the same MSE of 3, T1 having a variance ...
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57 views

How to replicate the predict function from R in Excel given I have access to “summary” output from R

I have run a 3rd order polynomial regression in R and have run the "summary" function, but I need to be able to replicate the "predict" function in Excel. I have my current working code below. Thank ...
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88 views

How does MAE as objective function impact gradient boosting training compared to MSE?

I have a regression problem where I want to minimize MAE as a business metric. I'm using LightGBM. I initially used the default objective function for regression ...

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