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How much can the addition of new features improve the performance of the model during the optimization process?

Let's say I have a total of 10 features. Suppose I start the optimisation process using only 3 features. Can the addition of the 7 remaining ones improve the performance of the model (which, you can assume, might already be quite high).

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Grouping the features of the concept class being learned can be used used to reduce the time required to learn the concept because it lowers the computation time of each sample and epoch. That's done almost always when recognizing complex movements or with other concept classes where the number of dimensions in the model is high. It is not a universal solution and care must be taken to configure the approach correctly.

If there is a local minimum that is directly along a particular axis in the loss surface which is not the global minimum and that axis happens to be the axis corresponding to the first feature the practitioner unwittingly chooses to optimize. The result will be that the other nine are learned immediately, yet the result is not the optimal. That's an unlikely scenario but only one of many scenarios where the technique can trouble the learning objective.

Also, the interrelation between features of the concept class can be complex such that learning some of the features may cause the unlearning of others. Since a larger loop must be placed around the entire process so that the accuracy of the features learned earlier are further tested until all the factors affecting loss are adjusted to minimize it, the process can take longer in some cases.

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The optimization of 10 features, as opposed to optimization of 3 features, will converge more slowly.

Let's say I have a total of 10 features. Suppose I start the optimisation process using only 3 features. Can the addition of the 7 remaining ones improve the performance of the model (which, you can assume, might already be quite high).

The answer might be no.

  • The accuracy and reliability of the convergence toward ground truth (a formalized objective used to guide the optimization process) when split into groups of three and seven features may be better or worse than when left as a group of ten.
  • Except in rare cases, the results will not be the same. The likelihood of identical results is so low it may never happen in the world in the next century except when conditions are arranged solely to cause it to occur.

Why then do may approaches group the dimensions of the result and converge on groups of axes, then another, then another, and back again to the first, iterating until the convergence goal is reached? This approach is used to reduce the time and computing resources used to reach the optimal. As the problem complexity increases, the use of groupings in this way is more common.

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  • $\begingroup$ I edited your answer to reflect the edit I made to the question (in order to clarify it). $\endgroup$ – nbro May 6 at 16:50

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