## Is there any domain where Bayesian Networks outperform neural networks?

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Neural networks get top results in Computer Vision tasks (see MNIST, ILSVRC, Kaggle Galaxy Challenge). They seem to outperform every other approach in Computer Vision. But there are also other tasks:

I'm not too sure about ASR (automatic speech recognition) and machine translation, but I think I've also heard that (recurrent) neural networks (start to) outperform other approaches.

I am currently learning about Bayesian Networks and I wonder in which cases those models are usually applied. So my question is:

Is there any challenge / (Kaggle) competition, where the state of the art are Bayesian Networks or at least very similar models?

(Side note: I've also seen decision trees, 2, 3, 4, 5, 6, 7 win in several recent Kaggle challenges)

It's not a question of domain. It's a question of how much data you have, how good your priors are, and whether you want posteriors.Emre 2016-01-17T18:22:27.547

@Emre Which is a question of domain... (and, of course, of money when you have the possibility to not only use existing datasets but can also hire people to create / label new data).Martin Thoma 2016-01-17T18:26:05.697

It would be a question of domain if there were some property of the data, some structure, that one algorithm took advantage of better than the other, but that is not what I am suggesting.Emre 2016-01-17T19:16:20.560

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One of the areas where Bayesian approaches are often used, is where one needs interpretability of the prediction system. You don't want to give doctors a Neural net and say that it's 95% accurate. You rather want to explain the assumptions your method makes, as well as the decision process the method uses.

Similar area is when you have a strong prior domain knowledge and want to use it in the system.

See also: The Mythos of Model Interpretability

Martin Thoma 2017-01-05T09:14:04.683

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Bayesian networks and neural networks are not exclusive of each other. In fact, Bayesian networks are just another term for "directed graphical model". They can be very useful in designing objective functions neural networks. Yann Lecun has pointed this out here: https://plus.google.com/+YannLeCunPhD/posts/gWE7Jca3Zoq.

One example.

The variational auto encoder and derivatives are directed graphical models of the form $$p(x) = \int_z p(x|z)p(z) dz.$$ A neural networks is used to implemented $p(x|z)$ and an approximation to its inverse: $q(z|x) \approx p(z|x)$.

Can the two parts be trained jointly?nn0p 2016-07-28T14:50:02.307

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One domain which I can think of, and is working extensively in, is the customer analytics domain.

I have to understand and predict the moves and motives of the customers in order to inform and warn both the customer support, the marketing and also the growth teams.

So here, neural networks do a really good job in churn prediction, etc. But, I found and prefer the Bayesian networks style, and here are the reasons for preferring it:

1. Customers always have a pattern. They always have a reason to act. And that reason would be something which my team has done for them, or they have learnt themselves. So, everything has a prior here, and in fact that reason is very important as it fuels most of the decision taken by the customer.
2. Every move by the customer and the growth teams in the marketing/sales funnel is cause-effect. So, prior knowledge is vital when it comes to converting a prospective lead into a customer.

So, the concept of prior is very important when it comes to customer analytics, which makes the concept of Bayesian networks very important to this domain.

Suggested Learning:

Bayesian Methods for Neural Networks

Bayesian networks in business analytics

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Sometimes you care as much about changing the outcome as predicting the outcome.

A neural network given enough training data will tend to predict the outcome better, but once you can predict the outcome, you then may wish to predict the effect of making changes in the input features on the outcome.

An example from real life, knowing that someone is likely to have a heart attack is useful, but being able to tell the person that if they stopped doing XX, the risk would reduce by 30% is of much greater benefit.

Likewise for customer retention, knowing why customers stop shopping with you, is worth as much as predicting the customers that are likely to stop shopping with you.

Also a simpler Bayesian Network that predicts less well but leads to more action being taken may often be better than a more “correct” Bayesian Network.

The biggest advantage of Bayesian networks over neural networks is that they can be used for causal inference . This branch is of fundamental importance to statistics and machine learning and Judea Pearl has won the Turing award for this research.

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Bayesian networks might outperform Neural Networks in small data setting. If the prior information is properly managed via the network structure, priors and other hyperparameters, it might have an edge over Neural Networks. Neural Networks, especially the ones with more layers, are very well known to be data hungry. Almost by definition lots of data is necessary to properly train them.

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I've posted this link on Reddit and got a lot of feedback. Some have posted their answers here, others didn't. This answer should sum the reddit post up. (I made it community wiki, so that I don't get points for it)

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Bayesian networks are preferred for genome interpretation. See, for example, this dissertation discussing computational methods for genome interpretation.

2Why are they preferred?Ian Ringrose 2016-01-18T14:13:44.307

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I did a small example for this once. From that, I think Bayesian Networks are preferred if you want to capture a distribution but your input training set doesn't cover the distribution well. In such cases, even a neural network that generalised well would not be able to reconstruct the distribution.

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I strongly do not agree that neural nets do well then other learners. In fact neural nets are doing pretty bad compared to other methods. There is also no methodology despite some advices on choosing parameters this beeing done very often by chance. There are some dudes also that talk random on forums about how neural nets are so good, not because they have some evidence regarding that, but because they are atracted about the fancy and buzz word ,, neural''.They are also very unstable , did you tryied a neural net to compare with xgboost?I will not try any neural net until it will be self concious .So until then happy neural neting :)

This was true before 2006 - https://www.thestar.com/news/world/2015/04/17/how-a-toronto-professors-research-revolutionized-artificial-intelligence.html. As I understand, things are done today differently, but the performance is becoming better and better ever since.

John Donn 2016-05-10T09:37:11.643

3This is too vague and conversational to make a good answer. Some specifics, facts and editing would improve it.Sean Owen 2016-01-18T17:54:56.320

,,Specific facts'' should be specified by people that post messages like that say that neural nets are the best , you cant say neural nets are doing fine just because they sound fancy , there are also data sets in wich neural networks probably do so bad in such a manner that knn are getting from far better result.gm1 2016-01-18T19:30:29.407

1While I don't deny your views, you should also not that your answer doesn't really answer the question. So, pl consider adding it as a comment. And, please add any concrete proofs and theory supporting your answer, else it might be looked at, as a rant, by future viewers :)Dawny33 2016-01-19T03:12:36.487

1@gm1 I guess you meant me with ",,Specific facts'' should be specified by people that post messages like that say that neural nets are the best". Please note that I did not write a statement which was that general. I wrote that NN win in many competitions / CV tasks. And I've added a couple of challenges in which neural networks approaches won.Martin Thoma 2016-01-19T06:02:09.383

Hi there , there are of course some Kaggle competitions in which neural nets did well (supposing they didn't used neural nets combined with other models) , but this is a small proportion of all kaggle competitions, could you use a neural network to go TOP 3 in kaggle TFI?I think I am able to do for both public and private LB with model that is non non-linear.gm1 2016-01-19T22:00:07.107

Anyway , I think kaggle should not be treated with so much seriosity.gm1 2016-01-19T22:01:14.297