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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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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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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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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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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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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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14 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 ...
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64 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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35 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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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 ...
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50 views

What is the best point forecast for gamma distributed data?

I believe that the values I am forecasting are gamma distributed with shape $k>0$ and scale $\theta>0$. I need a point forecast (i.e., a one-number summary) that minimizes the expected error. ...
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What is the best point forecast for lognormally distributed data?

I believe that the values I am forecasting are lognormally distributed with log-mean $\mu$ and log-variance $\sigma^2$. I need a point forecast (i.e., a one-number summary) that minimizes the expected ...
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How can RMSE be compared between a regression model and a neural network model?

In the calculation of RMSE, linear regression uses degrees of freedom(n-p) as divisor and neural network(feed-forward in my case) uses the total data number(does it have degrees of freedom as well?). ...
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Steps of Matrix Multiplication

It may seem kind of silly, but can anyone please show me the intermediate steps implied by the second equality in this derivation? $$e^\prime e = \left(y - Xb\right)^\prime\left(y - Xb\right) = y^\...
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Bayesian Inference and MSE. Need help to understand solution

I have problems with understanding solution of Problem 4.c (MSE) here. I couldn't get exact number. My solution is following (numbers for $X_M$ in table above): I start with calculating $E(X-X_M)^2 ...
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On dichotomizing a continuous variable and how it affects MSE of OLS

Recently I have learned about the practice of dichotomizing a continuous independent variable (or maybe even discretize it into more than 2 categories), and then run a predictive model (e.g. multiple ...
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How to evaluate neural network regression model

I have some data with 2963 observations and 7 variables. I want to use regression and train this data using neural network then evaluate the regression model. I've tried splitting the data into ...
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When MSE for CV is greater than test MSE?

In an introduction to statistical learning book, on page 311 there is a figure which compares MSE vs the number of leaves. I like to know the reason that Cross-Validation's Mean Square Error curve is ...
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26 views

Is there an advantage to normalizing labels when using MSE loss?

I am designing a NN that uses MSE as a loss regressor. Its a big network and when I train, the loss/gradients are HUGE. I have to clip my gradients our else the loss just goes to NaNs. The differences ...
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37 views

How is Test MSE being calculated here?

I'm reading Andrew Ng's CS229 course notes on machine learning, and I'm at the part about Bias-Variance Tradeoff. Here, we're modeling our data as $y_i = f(x_i) + \epsilon_i$ where $\epsilon_i$ are i....
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32 views

Reporting mean-squared error using test set

I'm reading an article in which the mean-squared error of the model $$y=X\beta + \varepsilon,~~E(\varepsilon)=0\text{ and }Var(\varepsilon) = \sigma^2$$ is defined as $$ME = E[X\hat{\beta} - X\beta]^...
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multiple linear regression error minimization

regression analysis in different statistical packages fits the best line by minimizing the error of the fit, the error term used by default is mostly MSE (mean square error), in other words, ...
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105 views

Bias-variance decomposition of MSE

I'm trying to decompose the MSE into the bias and variance terms and have done the following: $$MSE = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y_i})^2$$ $$E(MSE) = E\left[\frac{1}{n}\sum_{i=1}^{n} (y_i - ...
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Defining “variance” of a partially defined random variable

Elsewhere within CrossValidated the following survey sampling problem was mention. To each member $i$ of a population $\{1,\ldots,N\}$ there is assigned some value $c_i$ whose average $\mu=(c_1+\cdots+...
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How to interpret log-likelihood score as compared to mse

Say one has a linear dynamic system as follows: $x_k = Fx_{k-1} + v_k$ $y_k = Hx_{k-1} + w_k$ with $v \sim (0, Q)$ and $w \sim (0, R)$. I am estimating $(x)_k$ using a normal Kalman Filter and ...
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question about MSE mean square error

The following is taken literally from Wikipedia's mean squared error in the mean subheading: "Suppose we have a random sample of size $n$ from a population, $X_1$, ... ,$X_n$. Suppose the sample ...
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84 views

Feed-forward neural network (MSE and Cross-entropy) questions

Question 1 Why do we divide by the number of data points (N)? I think it's done to minimize the error being back-propagated, but can't we just don't do that and instead decrease the learning rate to ...
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Finding MSE when parameter space is restricted.

Let $X_1,.. X_n$~ Exp ($\lambda$) , where $\lambda \ge 2$ . I need to find the Mean squared error (MSE) of the maximum likelihood estimator (MLE) of $\lambda$. The MLE of this is $ \hat{\lambda_{...
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33 views

A different MSE criterion

I need to use the criterion $$\text{MSE}=(\hat\beta-\beta)^T\,V\,(\hat\beta-\beta)$$ for a linear regression model to estimate the test MSE. Here $\beta$'s are ...
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138 views

How to find the root mean square error in `auto.arima` in R? [closed]

How do I find the root mean square error (RMSE) by auto.arima? What settings do I need to put into auto.arima to get the RMSE?
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regression model can't achieve low bias and low variance at the same time

I am running a RandomForestRegressor model on a dataset and it seems it can NOT achieve low bias and low variance at the same time. So I suspected that the input (independent) variables are not ...
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weighted mean square error

Here is something from my text: "A model's fit to new data can be summarized numerically by mean square error , $\frac{1}{n}\sum^n_{i=1}[y_i-E(y_i|\theta)]^2$, or weighted version such as $\frac{1}{n}...
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Model Selection using MSE

In these lecture notes, we talk about choosing among two models: $Y = \beta_0 + \beta_1X1 + \beta_2X_2 + \epsilon$ or $Y = \beta_0 + \beta_1X1 + \beta_2X_2 + \beta_3X_1X_2 + \beta_4X_1^2 + \...
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439 views

MSE and different types of activation functions in NN

Lets say I have 3 neurons in the last layer of my neural network and I am using mean squared error as a loss function. The desired output of my neural network is a vector: ...
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112 views

cv.glmnet, minimal MSEis higher than OLS MSE

I have a data with multicollinearity. I can't exclude the correlated variable as they are my variable of interest. I therefore Used Ridge regression, and tried to find optimal lambda with CV. I face ...
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83 views

Train MSE becomes smaller then test mse when model becomes morgen complex

Iam doing a ridge and lasso regression and choose my lambdas via cross validation with K = 5 and K = 10. I do this with 3 data sets because i want to analize if more variables yield to a better ...
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How to estimate the standard error of the leave-one-out cross-validation estimate of the prediction error?

How does one estimate the standard error of the leave-one-out cross-validation estimate of the prediction error? For each fold (leave out the $i^{th}$ observation), the LOOCV estimate of the ...
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How to calculate the variance of the leave-one-out cross validation estimator and why is it high?

I read from Elements of Statistical Learning that the leave-one-out cross validation estimator has high variance, and I read the related stackexchange posts as to why this is the case 1. But I'm ...
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114 views

Why do the ensemble learners do well on regression/classification tasks?

I was watching this short video on ensemble learners, and I am confused about why they tend to do better, and how is goodness measured. If the goodness means a low mean-squared error (MSE) as usual ...
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56 views

Bigger K for Cross validation ridge regression is better?

I do a ridge Regression and choose my Lambda via cross validation. When i set k = 10 in cross validation allways get smaller mse on test and training data set comparing to set k = 5. What is the ...
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1answer
162 views

MSE or MAE absolute and relative performance

I'm comparing different ARMA-GARCH specification out-of-sample in order to understand whether the more "parsimonious" models prescribed by BIC do not perform more poorly than the more "expensive" ones ...
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291 views

why is the MSE error higher than MASE and MAPE?

I have a product price time series when I apply two models on them, I calculate all of MSE (Mean Squared Error), MASE (Mean Absolute Scaled Error), and MAPE (Mean Absolute Percentage Error). I noticed ...
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99 views

Meaning of variance term in confidence interval for Multiple Linear Regression

I am currently struggling on the meaning of the variance term $\sigma$ in the equation for computing the variance and the confidence interval of the mean reponse for a MLR: $$ Var[\hat{y}(x_0)]=\sigma^...
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Confidence Interval for Regression with Input-dependant Variance

I am currently building an optimal designed Experiment. The design will have 20 runs, which will be replicated 10 times, so the total number of runs will be 200. In order to compute the confidence ...
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254 views

Is there any point in using MSE loss in modern deep neural networks?

Is there any point in using MSE loss -- (a-b)^2 instead of L1 loss -- abs(a-b) in modern DNN/CNN architectures which use ReLU/ReLU-like activations? If so, why?
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210 views

feature engineering for auto encoder anomaly detection

I am working on an unsupervised problem: to take a set of transactional data, and identify anomalous transactions. I am using h2o's auto encoder to train a model which then scores transactions based ...
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180 views

Obtaining SSE, SSR, SST on a simple example

I have a confusion in getting SSE, SSR, SST. I wrote this simple code to see how this works, but it seems that I have a mistake: ...
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1answer
77 views

Bias-Variance Decomposition Analysis

I understand how the bias-variance decomposition was done, but I'm not sure what the author means when he says "Unless the nearest neighbor is at 0, $\hat{y}_{o}$ will be smaller than f(0) in this ...
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1answer
56 views

Is there an error that considers both the absolute error and the standard deviation in a prediction?

Say I'm building some kind of regression and I want to measure how good it is. Of course I want to measure the absolute error between the prediction and the real outcome, and if that was all I cared ...
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Evaluating Error of Logistic Regression/Other Probabilistic Outputs When True Probability Hovers Around 50%

I'm using a few different machine learning techniques to output a probability of an outcome/classification (Logistic Regression is working best, but Random Forest is working pretty well too). Without ...