# Tag Info

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In your trained RBM model, the hidden units can indeed be seen as extracted features automatically learned from the data at the visible units. However, I think most of the time you would have a hard time trying to interpret what the learned features are, but you can try by visualizing the weights for example. In general, RBM are used to perform feature ...

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It looks like the extra numbers are an enumeration of columns that have the same name.

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You are doing lasso the wrong way. A categorical variable with four levels is represented by three dummy variables. Those three dummys together represents one variable, and should be treated as such. To do that with the lasso, use the group lasso, as discussed in Why use group lasso instead of lasso?. There are many posts about the group lasso in here.

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Correlation measures only linear relationships. Mutual information can measure non-linear relationships. For example, suppose $X \sim \text{Uniform}(-1, 1)$ and $Y = X^2 + \epsilon$. The correlation between $X$ and $Y$ is zero, yet the mutual information can be high. SelectKBest ranks all features according to its score_func parameter - mutual information in ...

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A change in dimensionality (or features) does affect the distribution of distances, and hence the values will not be comparable. This is fairly easy to see for synthetic data, and hence you cannot rely on the values enough. If you want more reliable results, evaluate all results using the same features. But that is biased the opposite way: when the ...

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There are many ways to obtain the eigenvalues and eigenvectors of a real, square, symmetric correlation (covariance) matrix $\mathbf{R}$, and SVD is one way. After you obtain eigenvalues and eigenvectors (from what ever method you want), you then use PCA for obtaining the orthogonal projection. [Factor analysis (FA) is similar to PCA, but has an infinitely ...

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No as they are in general not uncorrelated since the simple arima structure was premised that the X's didn't explicitely have an effect on Y . One needs to in one way or another to determine the best combination GIVEN of course that pulses, level/step shifts, seasonal pulses, local time trends (the I's in this image https://autobox.com/pdfs/SARMAX.pdf ) ...

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You can reduce the features by performing filter feature selection methods on the training set(s). If you reduce the features prior to splitting you will have data leakage even if you cross validate afterwards.

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Since you can assume that values are missing at random, the best solution would probably be to compare both models (using F-tests, likelihood ratio tests, mean absolute error, median absolute error, or other such approaches) using the data subset that has all predictors present in both models. Here are two other solutions to consider: Create a holdout ...

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According to the paper "Modern statistical estimation via oracle inequalities": ‘Oracle inequalities’ are a powerful decision-theoretic tool which has served to understand the optimality of thresholding rules, but which has many other potential applications, some of which we will discuss. and in page 22 An oracle inequality relates the ...

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Omitted-variable bias is an important issue in logistic regression, as noted on this page with an analytic result presented for the related probit regression. Omitting any predictor associated with outcome will bias estimates of coefficients for other predictors, even if the omitted predictors are uncorrelated with the included predictors. So best practice ...

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Look into methods such as Relief or any information theory methods such as information gain and minimum description length. CORElearn is a good package for this.

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The idea of ($x^2$)/2 might also work to obtain the quadratic features. So if n = 2500, then we know that x(i) = 2500 and substituting x in the formula will give 50 million

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Convolutional Neural Networks (CNN) are the best performing models by far on image data. Use a pretrained model that you train the last layer of, and you might get OK results. You may need to change the image size to fit one of the pretrained models. 128x128 and 96x96 are common small sizes. You can start with a small model such as MobileNet to see if the ...

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You're right that there may be an issue with trying to model so few observations with such a high number of variables. Read the Power and Sample Size section here. Essentially the problem you're running into is that there are so many variables that it's difficult to determine per instance of good or bad picture what is responsible for the good or bad rating, ...

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