Considering that random forests have many layers and beat deep learning in most applications, maybe we just need to rebrand them as deep forests and they'll be the next big thing.
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Let's put this way: for unstructured data (image, video, text, audio, speech), deep learning is unconstestablely better. For tabular data, we have currently a fight in which I concede traditional machine learning may *still* be slightly better, mainly considering its simplicity.
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With a sufficiently large datasets and complex features deep learning outperforms on tabular data by miles. Most people don’t have access do that much right tabular data so it might not be as well known.
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