Deep Neural Decision Forests [pdf]

Sure.

Random forests are a very powerful machine learning method that has proven to give excellent performance with very little tuning. Neural networks with many layers (aka deep learning) is the new frontier of machine learning - they are very powerful but require extensive tuning (the architecture of the network) and lots of examples before they become practical.

In this paper, the authors combine the two methods - they basically stack a random forest on top of a neural network, and obtain some cutting edge results. One of the main theoretical results in the paper is that they propose a differentiable (which means you can use gradient-based optimization techniques) technique to optimize the parameters of the trees (which are the building blocks of the random forest).

I second that question!

Super high level of deep nets, skip if you already know:

Deep nets are good at taking a vector of size N and transforming it to a vector of size M, where M is perhaps a more general, abstract, or "useful" representation.

e.g.

Your N-vector might be a length 786 vector of floating point values representing black-intensity in a 28x28 grayscale image. This is the case in the MNIST dataset (lots of 28x28 images of the digits 0-9), a classic dataset in machine learning.

After a layer or two of a deep net, this N-vector might be transformed into an M-vector where each component represents some particular edge, curve, or blip within the source image.

So you've gone from the representation of "pixel 0 is gray, pixel 1 is dark gray, pixel 2 is white..." to a representation of "There is a vertical edge on the central lefthand side of the image, there is an upwards facing curve in the central top part of the image....".

It's clear that the latter representation is more compact and useful for the purpose of digit recognition.

It's also worth noting this representation is specific to the problem at hand. The edges and curves you have learned would probably be unable to accurately reproduce say, letters of the alphabet, as they are specialized to reproducing digits. The net has learned a more compact representation by using statistics to figure out that most of the information is redundant. There are only 10 possible outputs, but the input space is 256 grayscale values ^ 768 pixels.

In a traditional deep net, your output layer for this particular problem (digit recognition) might be a vector of length 10, where element of the vector is the probability of that digit being the one shown. So a result of <0.1, 0.1, 0.998, 0.0 ... 0.0> would indicate that the net thought the digit was a 2.

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Super high level of decision trees and forests, skip if you already know:

A decision tree is somewhat self-explanatory -- it's kind of like a flow chart for making judgments. Here is an example, classifying cool vs. uncool based on 3 attributes.

My dataset:

          | bow_tie | socks | sandals | cool
    ------|---------|-------|---------|------
    Alice | true    | true  | true    | true
    Bob   | false   | true  | true    | false
    Carol | false   | true  | false   | true
    Doug  | true    | false | true    | true
    Ella  | false   | false | false   | false

A possible decision tree:

    if bow_tie == true
        return true
    else
        if socks == true
            if sandals == true
                return false
            else
                return true
        else
            if sandals == true
                return true
            else
                return false

It's also worth noting that decisions trees can be equal with different representation. The following will always return the same value as the above for the elements of the dataset:

    if socks == true
        if sandals == true
            if bow_tie == true
                return true
            else
                return false
        else
            return true
    else
        if sandals == true
            return true
        else
            if bow_tie == true
                return true
            else
                return false
       

The difference is how you pick the divisions. The first one uses a more entropy-reducing strategy -- we notice that the bow_tie division is a simple, hard rule. Bowties are cool. The second is more of a random decision decision tree, so it's less "efficient" in that it must make potentially more judgments.

Why would we ever want to be less efficient? It turns out if you train several (hundreds, thousands, etc) decision trees on subsets of the data, and then average their results together, they are alarmingly good classifiers. Extremely simple to code, train, and use. This is called a decision forest. A decision tree on its own is often weak, but decision forests are a powerful tool.

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High level of why this work is interesting:

The traditional means of training a deep neural net is with gradient descent. The most common form of this is some method of "backpropagation". You run a training example through your network, calculate the error between the result and expected result, and then propagate this error gradient back through the network to tune the transformations to produce closer to what you want. This method often requires the functions you use within the deep network to be differentiable.

As mentioned above, there are several training strategies for decision trees, but the most common is some form of "mostly random".

To extend my example from the first section, one could use the deep neural net to transform the 768 grayscale pixel values into perhaps 30 higher level edge/curve features. Then one could use this length 30 vector as the input to train a decision forest.

This might end up getting better results than either strategy by itself. You use the neural net to do the abstracting and the decision forest to make the final decision. This uses both of their advantages in tandem -- deep neural nets are great at generating more abstract and general features, and decision forests are quite good at producing accurate classifications given high-quality, lower-dimensional input data.

This idea of multi-tiered systems isn't particularly new. What this paper does, though, is introduce a differentiable decision tree. This means that they can train their decision trees with gradient descent, the same way they train the neural network. This means that, rather than training the two tiers of their system individually, they can train them together, producing even better results.

To elaborate on Fede_V's comment, Deep Neural Networks seem to work well on classification problems because they can automatically build abstract features from a dataset and combine them in different ways. Like, in image data they will automatically identify common shapes and patterns of light and dark, and combine these simple patterns together to identify faces or whatever (like by saying a face is a circle with two dots for eyes and a line for a mouth). Random Forests, on the other hand, are really good at classifying things if you give them meaningful dataset features to learn on, but aren't as good at building these features in the first place. By combining them together, they get a system with the classification abilities of random forests and the automated feature discovery of deep neural nets, and it seems to work a bit better than either.

GoogLeNet "won" ImageNet 2014[1], but VGG is often found to be more flexible.

I'm not entirely sure, but I think that the multiple softmax layers in GoogLeNet might make it easier to modify for this purpose than the VGG architecture.

[1] http://image-net.org/challenges/LSVRC/2014/results (look for "Classification+localization with provided training data: Ordered by classification error")