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I'm running Logistic Regression on a dataset for a classification problem.

I used the model on the dataset when it was normalized and I had no problem with it converging.

Now, I wanted to see the results without feature normalization and I am getting the warning:

ConvergenceWarning: lbfgs failed to converge. Increase the number of iterations.
  "of iterations.", ConvergenceWarning)

I've tried increasing the number of iterations and I have upped it to 8000 so far and am still getting the error.

I wanted to ask, is this error is critical? Because, I'm still getting my cross validated results even after the error. What exactly is convergence?

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An iterative algorithm is said to converge when, as the iterations proceed, the output gets closer and closer to a specific value. More precisely, no matter how small an error value you choose, if you continue long enough the function will eventually stay closer than that error value from some final value.

In some circumstances, an algorithm will not converge; it could even diverge, where its output will undergo larger and larger oscillations, never approaching a useful result. More precisely, no matter how long you continue, the function value will never settle down within a range of any "final" value.

You could use the results which did not converge, but it's not recommended.

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