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In a panel data set consisting of exponential functions, each indexed by an integer i ranging from 0 to 100. The exponential function is defined as f(i, t) = A(i) * e^(-r(i) * t), where A(i) is the launch point that increases by 10% for each successive function, and r(i) is the decay rate that decreases by 1% with each increment of i. The features for the model are i (the index of the function) and t (time), and the target is the value of f(i,t). Using Random Forest algorithm for this task. The model is trained on the first 80 exponential functions (indices 0 to 79) and tested on the last 20 (indices 81 to 100) as hold-out data. Can the Random Forest model effectively predict the values of f(i, t) for indices 81 to 100 even without seeing any sample of it?

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2 Answers 2

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The Random Forest model exhibits potential for extrapolating f(i, t) values to indices 81-100, albeit with certain caveats. Its training on functions with indices ranging from 0 to 79 allows it to learn patterns within this specific domain. The critical factor lies in the trends exhibited by features (i and t) and target values (f(i,t)) across the dataset. Assuming predictable evolutions of A(i) (10% increase) and r(i) (1% decrease), the model can attempt to extrapolate these trends to unseen indices. However, such extrapolation inherently carries uncertainties, particularly in the presence of non-linearities or complexities not represented in the training set.

Cross-validation offers a means to augment the model's robustness. By evaluating its performance on various training data subsets, it facilitates the detection of overfitting or underfitting phenomena. This practice yields a more reliable assessment of the model's generalizability to unseen data, potentially leading to improved predictions for indices 81-100.

So a segregated set of Test set(0-60), cv set(61-80) and finally test set(81-100) is likely to provide further refined and robust predictions, hence further increasing the chance of predicting accurate possibilities for the test set.

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  • $\begingroup$ Thank you very much for your contribution and input, but I think it is not a matter of increasing robustness with cross-validation. The Algorithm itself is the issue here, it is not built to solve let's say non-stationary problems. $\endgroup$ Jan 24 at 19:39
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Upon Experimentation, no Random Forest cannot extrapolate on panel data. It could not predict f(i, t) using i and t as Features. The algorithm is not built to capture evolving trends like say Neural Networks.

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