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When we implement penalized regression models we are saying that we are going to add a penalty to the sum of the squared errors. Recall that the sum of squared errors is the following and that we are trying to minimize this value with Least Squares Regression: $$SSE = \sum_{i=1}^{n}(y_i-\hat{y_i})^2$$ When the model overfits or there is collinearity present, ...


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I am unsure there will be a formal way to show which is best in which situations as it depends on many factors like your dataset, architecture of the your ANN - simply trying out different combinations is likely best. It is worth noting that Dropout* is actually doing more than just regularization, it makes the model more robust,allowing it to try different ...


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The teacher/student model approach (at least as I understand it) could be used. It is normally used to replace all layers, but there is nothing stopping you applying it to a subset of layers. First you create training data, by running your training data through the (trained) network, and recording the inputs to layer i, as your new training data (x) and the ...


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According to wikipedia, the definition regularization is the process of adding information in order to solve an ill-posed problem or to prevent overfitting. One common approach is to add a penalty term for large parameter values to the loss function. There are many other approaches to regularization. Here are a couple of other examples: Increasing the ...


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Lasso does feature selection in the way that a penalty is added to the OLS loss function (see figure below). So you can say that features with low "impact" will be "shrunken" by the penalty term (you "regulate" the features). Because of the L1 penalty, the $\beta_i$ can become zero (which is not the case with Ridge, L2). In the ...


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Kaggle is a crowd source platform with no quality control. It is to be expected that there will be deviations from best practices.


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Have a look at svc_cv.cv_results_: there are many values of C that tied for best, with accuracy 99.6%, and the chosen C is the smallest of those. The point is that the width of the margin doesn't affect the actual hyperplane very much, and so the accuracy score doesn't change very much. A few suggestions: With larger and less-separable data sets, this ...


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@Ethan is correct about the formulation of the lasso penalty, and I think it's particularly important to understand it in that form (for one thing, because that same penalty can work with other models like neural networks, tree models, generalized linear models, ...). But, to your question: If $\lambda=0.5$ then does it mean that those coefficients whose ...


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No - non-parametric methods only means that the method does not assume a function form of the data. There are non-parametric methods such as Random Forest that do not always overfit. In fact nonparametric methods could underfit, it could lack the ability to fit the training data. An example of this would be a decision stump.


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