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I was recently working on some classification problem where decision trees performed better than neural networks. I had tried various combinations with neural networks altering the number of neurons / hidden layers with an objective to beat the decision tree classifier accuracy on the test set. But the best accuracy I could achieve with neural networks was that of 0.42 and decision tree was at 0.50.

I had asked a question here, as what could be the case and someone pointed out that neural networks do not work very well with the structured data (data in tabular format) as compared to the unstructured data (like representing each pixel in an image). In the comment linked to the same answer, it was pointed out that :

Well you can take a look at kaggle competition winners. In competitions containing structured data by far the most popular algorithm is xgboost (along with other similar algorithms lightgbm, catboost, etc.). On the other hand Neural Networks are rarely used in these competitions because they are not so strong with these types of data. This is also evident by the near 20-year disappearance of neural networks, until deep learning made them relevant again. During these years trees and SVMs on top.

That could generally be true but I do not have the intuition/reason as to why neural networks do not work well with the structured data? Could someone help me reason that? It will also be great if you could point me to some paper/post that explains this.

One feeling that I have is, it could be because of the less volume of data. Neural networks might not generalize well with fewer data points as compared to other classifiers like decision trees, svms etc. But then I am not really sure about this.

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... someone pointed out that neural networks do not work very well with the structured data (data in tabular format) as compared to the unstructured data (like representing each pixel in an image).

It's difficult to propose a universal analogy, but perhaps one moderately complex example which is easy to understand will suffice.

In the link you provided user JkBk mentions the "no free lunch theorem", let's add to that the "infinite monkey theorem". The fact is you can have one or more free lunches, just not as many as you like. Similarly you can not have infinite monkeys, but you can have a lot of them. Limits on each.

Take for example this data from the World Health Organization, let's only look at age versus height for boys aged 5 to 19. Let's look at a subset of the data in tabular form, I presume you understand the concept of "height-for-age".

Process this chart with your brain, what does it tell you. It tells you exactly everything averaged for a subset of the data. Can you draw any inferences from it, how about another several tables of data?

A neural network would have to process the data in all the tables and come up with a means to say "this age = this height" and "this height = this age" as an average.

Here is one of several tables:

WHO Data

Now let's look at the whole dataset in a chart:

WHO Chart

See how at age 13 there is the start of a growth spurt, that continues almost to the age 15 when it starts to slow down. Between 15 and 17 it starts to level off, and from 17 to 19 there's almost no growth at all. From 5 to 11 a simple algorithm can easily solve the equation in either direction, beyond 11 the algorithm is not so simply but it still can be solved with a polynomial.

For a neural network once it gets on track and thinks it is coming up with a solution a monkey wrench gets thrown in to the works. Look at the "Alice and Bob example" (from 'no free lunch'), trying to solve the problem rationally requires knowledge and intelligence to avoid getting trapped.

Alternatively an Equation Solver can intelligently brute-force a solution, providing a relatively simple equation that can be used efficiently on large volumes of data.

Once you have a simple equation you could apply it to a huge dataset, like the Census, to check for errors such as age not matching height. A neural network would be better for discovering that age versus height was different than the average in a particular area and supply the reason (distance to inexpensive high quality food, versus earnings, and a sprinkle of education) whereas a simple polynomial wouldn't have the additional knowledge buried within it to make deductions.

A neural network doesn't comprehend (literally or figuratively) why a solution that was working later fails; it needs to continue, to learn to ignore it's success, to reach a working solution.

A non neural network solution doesn't care (literally or figuratively) whether it was on track, figured something out and learned to apply it, it only knows to minimize error and eliminate variables.

That doesn't mean that each couldn't switch roles and learn, or be programmed, to do the job of the other; but then the neural network would be pedantic about precision throughout (slow) and the solver would over analyze (calculate left or right with high precision) rather than simply weigh the outcomes with adequate precision for each step.

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  • $\begingroup$ So provided the neural network gets sufficient data (where the data captures every possible case), they would work better than tree-based models? $\endgroup$ – Suhail Gupta Sep 18 '18 at 6:32
  • $\begingroup$ The problem, or solution, is that neural networks need not only the "data" but also counterexamples - additional data which would be trained to cause a failure and be rejected. Otherwise the neural network examines a portion of the data and gets "a bee in its bonnet" and reaches a faulty conclusion. Example: How is it possible that deep neural networks are so easily fooled? $\endgroup$ – Rob Sep 18 '18 at 6:44
  • $\begingroup$ Counterexamples would definitely mean the data for another class? If yes, any classification model would be trained on a class Aand class B( which abstracts all classes not A) $\endgroup$ – Suhail Gupta Sep 18 '18 at 6:57
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    $\begingroup$ Yes, take the chart above as an example. You need to create additional data not present already to represent lines 4,5,6,7, etc. and -4,-5,-6,-7, etc., then train the neural network that those values are unacceptable. Since you don't have that data you must figure out what it is. In that particular example it's simple to see what those values would be and trivial to calculate them. You would then train the network that if it ever decided those values were OK that it is wrong. --- With a different example, the felines I linked to in the comment above, a negative example is difficult to find. $\endgroup$ – Rob Sep 18 '18 at 7:57

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