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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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24 views

Penalize the MSE of half of predicted values more than the other half

I'm using MSE loss for an multi-layer perceptron that learns to approximate the target feature vector $[\hat{x_1}, \dots, \hat{x_N}, \hat{y_1}, \dots, \hat{y_N}]^\intercal$. The catch here is that I'd ...
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32 views

Estimating the bias and variance of an estimator

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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19 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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1answer
53 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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31 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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2answers
1k 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 you ...
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2answers
41 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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33 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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23 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
35 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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1answer
51 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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138 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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37 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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1answer
20 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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8 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 ...
2
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3answers
48 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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2answers
50 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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1answer
63 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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1answer
13 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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34 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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38 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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2answers
44 views

Does the MSE values of regression coefficients sum up to the MSE value of the regression model in which the regression coefficients are included?

I think either i dont understand something or i try to mix something that are different things. The mse value of a regression coefficients tells me how good i estimated the coefficent. Does it mean ...
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20 views

Conditioning and linear MSE

Let $\sigma_{X|Y}^2$ denote the linear mean squared error in estimating $X$ from $Y$. Then is it always true that additional conditioning cannot increase the LLSE? In other words, is this true? $$ \...
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1answer
100 views

When does the underfitted regression model have more precise coefficient estimates?

Say we have a full regression model \begin{align*} \mathbf{y} &= \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon}\\ &= \mathbf{X}_p \boldsymbol{\beta}_p + \mathbf{X}_r \boldsymbol{\beta}...
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1answer
28 views

BIC in practice with gaussian distribution

I am considering a gaussian distribution: \begin{equation} y \sim N(net(x,w), \sigma^2). \end{equation} $net()$ is just the output of some neural net with weights $w$ and input $x$. The log-...
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20 views

Why i get the same MSE value for two least square models that differ in one explanatory variable?

I have two ols-regression models that just differ in one variable. It means that one model have the same variables like the other plus an explanatory variable more. I estimated both models on a train ...
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17 views

Loss function for one-step-ahead volatility forcasts

I'm trying to perform the MCS test using the R-package "MCS" to compare GARCH-MIDAS Models. The loss function requires as inputs a vector with some realized volatility measure ˜ σt+1 (I chose the ...
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1answer
49 views

How to calculate Bias and Variance to get the MSE value step by step?

I want to compute my MSE value for a forecast step by step for test set. For me the Bias is: Bias = mean(predicted values - actual values) Variance = mean((predicted values- actual values)^2) ...
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18 views

What is the formula that is used to calculated the MSE with Random Forest regression in R?

I am using the package randomForest in R for panel-data on conflict intensity. The dependent variable is the conflict intensity (e.g. the number of battle deaths). Independent variables are population,...
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1answer
147 views

why is VAE reconstruction loss equal to MSE loss

At which situations does reconstruction loss of VAE equals MSE loss between input and reconstructed output? Other answers where not complete!
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28 views

Do unbiased regression coefficents yield better prediction?

I ask myself if a have a omitted variables bias in my regression modell the coefficients of the model are biased so the mse growth because this coefficents are biased right? So does it mean if i ...
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1answer
123 views

K-means calculate MSE in Weka

I am doing some clustering analysis with Weka and decided to apply the k-means algorithm (the clusterer SimpleKMeans). On my first analysis I ran the algorithm with 2 clusters. Then, after finding ...
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1answer
157 views

Correct way to calculate MSE for autoencoders with batch-training

Suppose you have a network representing an autoencoder (AE). Let's assume it has 90 inputs/outputs. I want to batch-train it with batches of size 100. I will denote my input with ...
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1answer
54 views

Precision vs. Accuracy when talking about MSE

This is more of a semantic question. I'm working on translating a work from French to English related to statistics. In French, there is only 1 word as far as I can tell to describe both bias and ...
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1answer
22 views

I ran an ANN model and got an extremely low R2 but a pretty good MSE, what does this mean? [closed]

I ran an artificial neuron network on data with about 2,000 rows and 3 features. I got a R2 of .06 which is really low, but a good MSE of .41. Why are these performance evaluators of this model ...
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8 views

Why different seeds produce different mse values for regression tree and ols?

I compare regression tree and ols in terms of out of sample prediction. I realized that the mse values changed when i change the seeds before getting train and test set. Sometimes ols is better ...
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1answer
39 views

When does OLS Regression outperform regression tree in term of out of sample prediction?

In my Master thesis i compare ols regression to regression tree to predict wages. I thought that i will get better prediction with the regression tree because it cathes more interactions. But now i ...
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75 views

Use MSE in cv.glmnet for Poisson models?

I want to compare different methods (like Poisson regression using Lasso, a convolutional NN, etc.) in terms of prediction error. As error measures I chose the MSE, the MdAPE (median absolute ...
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0answers
152 views

R-squared vs MSE, why the discrepancy?

I am carrying out a project where I am imputing missing data. I am trying to compare an imputed dataset with a baseline dataset by measuring MSE and R-squared. These metrics are measured by ...
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1answer
53 views

Mean Squared Error as quantifier of the Bias-Variance tradeoff

I have acquired the impression that many of the people doing statistical work, will prefer a biased estimator $\hat b$ to an unbiased one $\hat \beta$, if the former has lower Mean Squared Error. This ...
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1answer
51 views

Calculate the constants and the MSE from two estimators related to a uniform distribution

Consider a simple random sample $X_{1},X_{2},\ldots,X_{n}$ whose distribution is given by $X\sim U(0,\theta)$. Moreover, consider the estimators $\hat{\theta}_{1} = c_{1}\overline{X}$ and $\hat{\theta}...
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1answer
42 views

How to determine mse of estimate from correlation matrix of estimate error?

I have a model of an information transmission system Y = XH + N, where X is a diagonal matrix with the transmitted "symbols" (known), H is a column vector which distorts the transmitted symbols and N ...
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46 views

Derivation of AMISE and Bandwidth

Given: Let $K(\cdot)$ be a bona fide kernel. Let $f$ be a pdf and $\widehat{f}_n$ is kernel density estimator with bandwidth $h$ based on a sample $X_1,X_2,\cdots,X_n$ of size $n$ draw iid from $f$. ...
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0answers
177 views

calculating mse for knn regression object

I'm fairly new to knn, R implementation and am trying to figure out how to calculate the MSE for a model that uses knn based on linear regression with 3 nearest neighbors and get the error shown above....
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313 views

Calculating mean square error for a knn regression object

I'm fairly new to knn, R implementation and am trying to figure out how to calculate the MSE for a model that uses knn based on linear regression with 3 nearest neighbors and get the error shown above....
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0answers
39 views

Log or MSE loss for hyperparameter tuning of probabilistic NN

I am building a predictive model of a dynamical system using a NN whose output neurons enconde the mean and diagonal covariance of a Gaussian distribution. For training, the negative log prediction ...
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0answers
46 views

Represent Mean-Squared-Prediction error as function of covariance (or Fisher) matrix

Given a simple linear model: $$ y_i = x_i^T \beta + \epsilon_i $$ For simplicity, $\epsilon_i$ is Gaussian iid with variance $\sigma_e^2$, then the solution for $\hat{\beta}$ is given via Ordinary ...
2
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1answer
79 views

variance of nonparametric estimator of mean

I'm having some trouble with understanding how to calculate the variance of a non-parametric estimator. The example comes from Wasserman's "All of statistics book" Let $X_1, \ldots,X_n \sim \text{...
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1answer
40 views

Maximum likelyhood of distribution

$L$ is the upper limit of the sample distribution $[0, L]$ which is uniform and normal. how can I show that $L=\frac{(n+1)*max(X_i)}{n}$ is unbiased. and also has a lower MSE than MLE?
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1answer
51 views

Distribution function of a biased estimator

$f(y) = ay^{a-1}/θ^a, 0<y<θ$ $ \hat{\Theta} = max(Y_1, Y_2, . . . , Y_n).$ How do I find the $E[\hat{\Theta}]$ ? I'm trying to show that it's a biased estimator, then I'm going to find ...