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Essentially you want to pick a function that will give you the "size" of a matrix. The most obvious way I can think of is by choosing a matrix norm, which is a map $\lVert \cdot \rVert \colon \mathbb{R}^{k, k} \to [0, \infty)$ (or you could generalise to a complex $k \times k$ matrix if you wished). Your suggestion seems similar to computing S = \...

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Personally I think linear (through model's coefficients/weights) and tree-based models (gain importance) are the best for explainability But this is not restricted to those models since you can use model agnostic techniques to explaine any model, even those consider as "black-box" Like: SHAP Values Partial Dependence plot LIME You can check this ...

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According to the sklearn.svm.SVR documentation, the negative $R^2$ value indicates that your model is arbitrarily worse than the trend line on trainY. By default you should check the following: Does your model have a bias/intercept? If not you may observe negative $R^2$. Is testY derived from your training data? Am I using a linear function to fit the data? ...

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A $R^2$ that is that low tells you that your model is not good. Therefore, you can both make it positive and nearer to 1 by : a) getting better/more data, or b) picking a better model for your data. Also, it'd be more helpful to plot the true/pred values against the underlying $X$ values and not just as a sequence.

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If it's "find the house" then that implies that you need to find the house with those specific attributes in the dataset. I'm not sure what programming language you're using but it should be pretty simple to do such a thing anyways. If it's "find the price of a house with..." that implies there probably isn't such a house in the dataset ...

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I will use the "date" and "time" columns to pre-process your data and to construct your neural net input. RNN does not work well for very long-term dependancies... so, for example, creating a time series with all minutes in a month, won't probably work. You must select: How many samples your input data will have What is your sampling ...

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As described in the error message, the problem is that your model needs more memory than your GPU has. Note that OOM stands for "out of memory". The specific layer that is demanding too much memory is Dense(154457, activation='relu'). Nevertheless, the last layer is even bigger. You should think if you really need an output of dimensionality 154457....

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In answer to your first question: The reason that your RMSE proceeded to increase as you increased the strength of your regularization (the value of $\lambda$) can be explained by reviewing the intuition behind what is happening when you increase the regularization of your model. Why did could my RMSE have kept increasing as I increased my regularization ...

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The main problem in your test is that your X has the same scale as your noise level (0-1), as a result, adding a noise changes your data distribution significantly. This is your data distribution before and after adding noise. It is like the noise is 50-200% more than your initial data. That's why you get a better result with CV than the "ground truth ...

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The issue of using any linear model (a polynomial regression is a particular case of a linear model, with polynomial features), is that an ensemble of linear models is still a linear model. So, the family of models to optimize from given by the boosted polynomial regression and the single polynomial regression are the same. This doesn't happen with trees, as ...

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