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My question is about how a logistic regression model performs so accurately. In some exploratory experimentation, I compared a logistic regression model against a long short term memory recurrent neural network for binary classification of consumer reviews (Positive or Negative)(25,000 reviews). The Logistic Regression model performed better with an accuracy of 88.0% and a recall, precision, and f-score of 0.88. The Recurrent Neural Net performed with an accuracy of 81.1%, a recall of 0.83, a precision of 0.80, and an f-score of 0.81. Perhaps my building of the network was flawed but I was still surprised to see that the Logistic Regression had such a high accuracy.

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Some people have this preconceived notion that logistic regression shouldn't perform well because it is too simple. While that might be true for certain types of complex problems, the reality is that logistic regression performs relatively well in many different scenarios.
It's difficult to give a definitive answer as to why a model performs well without actually seeing the data and the model you've constructed.
That being said, it could be that the problem you're trying to solve is not very difficult so even a simple logistic regression model yields good results. Another thing to consider is that while 88% accuracy sounds good, it might actually only be OK for this type of problem (and dataset) - it would be informative to try other non-neural-network based classifiers and see how well they perform.

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