Decision trees – the unreasonable power of nested decision rules(mlu-explain.github.io) |
Decision trees – the unreasonable power of nested decision rules(mlu-explain.github.io) |
Use the non-thresholded version of that linear classifier output as one additional feature-dimension over which you learn a decision tree. Then wrap this whole thing up as a system of boosted trees (that is, with more short trees added if needed).
One of the reasons why it works so well, is that it plays to their strengths:
(i) Decision trees have a hard time fitting linear functions (they have to stair-step a lot, therefore need many internal nodes) and
(ii) linear functions are terrible where equi-label regions have a recursively partitioned structure.
In the decision tree building process the first cut would usually be on the synthetic linear feature added, which would earn it the linear classifier accuracy right away, leaving the DT algorithm to work on the part where the linear classifier is struggling. This idea is not that different from boosting.
One could also consider different (random) rotations of the data to form a forest of trees build using steps above, but was usually not necessary. Or rotate the axes so that all are orthogonal to the linear classifier learned.
One place were DT struggle is when the features themselves are very (column) sparse, not many places to place the cut.
For example you start with the raw coordinates of snake in a snake game, but you now can calculate how many escape routes the snake has, and train on it.
I’ve spent most of the last 20 years doing reinforcement learning and it is exceptionally simple conceptually
The challenge is data acquisition and the right types of process frameworks
But non-structured data? Pretty pointless to hand off to a neural network imo.
Normalising the numeric features to a common range has been adequate. This too is strictly not necessary for DTs, but pretty much mandatory for linear models. (DTs are very robust to scale differences among features, linear models quite vulnerable to the same.)
One can think of each tree path from root to leaf as a data driven formulation/synthesis of a higher level feature built out of logical conjunctions ('AND' operation).
These auto-synthesized / discovered features are then ORed at the top. DTs are good at capturing multi-feature interactions that single layer linear models can't.
NNs certainly synthesize higher level features, but what does not get highlighted enough is that learning-theory motivated Adaboost algorithm and it's derivatives do that too.
Their modus operandi is "BYOWC, bring your own weak classifier, I will reweigh the data in such a way that your unmodified classifier will discover a higher level feature on its own. Later you can combine these higher features linearly, by voting, or by averaging".
I personally favor differentiable models over trees, but have to give credit where it's due, DTs work great.
What leaves me intellectually unsatisfied about decision trees is that the space of trees cannot be searched in any nice principled way.
Or to describe in terms of feature discovery, in DT, there's no notion of progressing smoothly towards better high level features that track the end goal at every step of this synthesis (in fact greedy hill climbing hurts performance in the case of decision trees). DTs use a combinatorial search over the feature space partitioning, essentially by trial and error.
Neural nets have a smooth way of devising these higher level features informed by the end goal. Roll infinitesimally in the direction of steepest progress -- that's so much more satisfying than trial and error.
As for classification performance where DT have struggled are cases where columns are sparse (low entropy to begin with).
Another weakness of DT is the difficulty of achieving high throughput runtime performance, unless the DT is compiled into machine code. Walking a runtime tree structure with not so predictable branching probabilities that doe'snt run very fast on our standard machines. Compared to DNNs though this is a laughable complaint, throughput of DTs are an order of one or two faster.
> Ironically, NN can detect such latent features
Could you explain what "equi-label regions having a partitioned structure" mean?
Consider connected regions in the domain that have the same label. Much like countries on a political map. The situation where this has a short description in terms of recursive subdivision of space, is what I am calling a partitioned structure. It's really rather tautological.
Oblique Decision trees, Model Trees. (M5 Trees for example), Logistic Model Trees (LMT) or Hierarchical Mixture of Experts (HME).
I mention restricted oblique trees in passing in my original comment. In my experience, oblique trees tend to add considerable complexity, the others more so. Of course whether the complexity is warranted or not will depend on the dataset.
The merit of what I used is in its simplicity. Any simple ML library would have a linear classifier and a tree learner.
Super easy to implement, train, maintain, debug. One to two person team can handle this fine.
Mine is a quick but effective practical hack fuelled by a little bit of insight.
In theory, this means you can 'compile' most neural networks into chains of if-else statements but it's not well understood when this sort of approach works well.
I didn't exactly understood what was meant here, so I went out and read a little. There is an interesting paper called "Neural Networks are Decision Trees" [1]. Thing is, this does not imply a nice mapping of neural networks onto decision trees. The trees that correspond to the neural networks are huge. And I get the idea that the paper is stretching the concept of decision trees a bit.
Also, I still don't know exactly what you mean, so would you care to elaborate a bit? :)
Single Bit Neural Nets Did Not Work - https://fpga.mit.edu/videos/2023/team04/report.pdf
> We originally planned to make and train a neural network with single bit activations, weights, and gradients, but unfortunately the neural network did not train very well. We were left with a peculiar looking CPU that we tried adapting to mine bitcoin and run Brainfuck.
Straight forward quantization, just to one bit instead of 8 or 16 or 32. Training a one bit neural network from scratch is apparently an unsolved problem though.
> The trees that correspond to the neural networks are huge.
Yes, if the task is inherently 'fuzzy'. Many neural networks are effectively large decision trees in disguise and those are the ones which have potential with this kind of approach.
Examples ?
Why "naive"? Because there is no such thing as NumPy or data frames in the Guile ecosystem to my knowledge, and the data representation is therefore probably quite inefficient.
I've been using a scoring system for website analysis that's essentially a decision tree under the hood. Does the site have a meta description? Does it load in under 3 seconds? Is it mobile responsive? Each check produces a score, the tree aggregates them. Users understand why they got their score because the logic is transparent.
Try explaining why a neural network rated their website 73/100. Decision trees make that trivial.
https://en.wikipedia.org/wiki/Esagil-kin-apli#The_Sakikk%C5%...
I've long dismissed decision trees because they seem so ham-fisted compared to regression and distance-based clustering techniques but decision trees are undoubtedly very effective.
See more in chapter seven of the Oxford Handbook of Expertise. It's fascinating!
Given that assumption, the nebulous decision making could stem from expert's decisions being more nuanced in the granularity of the surface separating 2 distinct actions. It might be a rough technique, but nonetheless it should be able to lead to some pretty good approximations.
Decision trees predate KD trees by a decade.
Both use recursive partitioning of function domain a fundamental and an old idea.
Gonna try to cook up something personal. It's amazing how people are now using regression models basically all the time and yet no-one uses these things on their own.
Today, hand writing OCR is a "hello world" sample in Tensorflow.
My previous project was far from that. https://healthverity.com/audience-manager/
I had a lot of fun, really the last fun project I've had. I hope you had fun as well.
Human societies look for actual major correlations and establish classifications. Except with scientific-minded humans, we often also want, to know the why behind the correlations. David Hume got involved w that… https://brainly.com/question/50372476
Let me ask a provocative question. What, ultimately, is the difference between knowledge and bias?
https://en.wikipedia.org/wiki/Esagil-kin-apli
In this Mesopotamian text, diagnostic rules are structured as a nest of if then else rules. So I have been told, not that I have read it myself.
having 'accessible' content is not only for people with disabilities, it also help with bad color taste.
well, at least bad taste for readable content ;)
Hence why random forests have such enduring power.
I've always thought that the idea that decision trees are "explainable" is very overstated. The moment that you go past a couple of levels in depth, it becomes an un-interpretable jungle. I've actually done the exercise of inspecting how a 15-depth decision trees makes decision, and I found it impossible to interpret anything.
In a neural network you can also follow the successive matrix multiplications and relu etc through the layers, but you end up not knowing how the decision is made.
Thoughts?
My second job after physics was AI for defense, and boy is the dream of explainable AI alive there.
Honesty anyone who “needs” AI to be understandable by dissection, suffers from control issues :)
This makes me a little concerned -- the use of parameters rich opaque models in Physics.
Ptolemaic system achieved a far better fit of planetary motion (over the Copernican system) because his was a universal approximator. Epicyclic system is a form of Fourier analysis and hence can fit any smooth periodic motion. But the epicycles were not the right thing to use to work out the causal mechanics, in spite of being a better fit empirically.
In Physics we would want to do more than accurate curve fitting.
longer answer: Random forests use the average of multiple trees that are trained in a way to reduce the correlation between trees (bagging with modified trees). Boosting trains sequentially, with each classifier working on the resulting residuals so far.
I am assuming that you meant boosted decision trees, sometimes gradient boosted decisions trees, as usually one have boosted decision trees. I think xgboost added boosted RF, and you can boost any supervised model, but it is not usual.
For better or for worse (usually for better), boosted decision trees work harder to optimize the tree structure for a given problem. Random forests rely on enough trees being good enough.
Ignoring tree split selection, one technique people sometimes do makes the two techniques more related -- in gradient boosting, once the splits are chosen it's a sparse linear algebra problem to optimize the weights/leaves (iterative if your error is not MSE). That step would unify some part of the training between the two model types.
Guile like languages are very well suited for decision trees, because manipulating and operating on trees is it's mother tongue. Only thing that would be a bit more work would be to compile the decision tree into machine code. Then one doesn't have traverse a runtime structure, the former being more efficient.
BTW take a look at Lush, you might like it.
https://news.ycombinator.com/item?id=2406325
If you are looking for vectors and tensors in Guile, there is this
Also I think I did not optimize for memory usage, and my implementation might keep copies of subsets of data points for each branch. I was mostly focused on the algorithm, not that much on data representation.
Another point, that is not really efficiency related, is that data frames come with lots of functionality to handle non-numeric data. If I recall correctly, they have functionality like doing one-hot encoding and such things. My implementation simply assumes all you have is numbers.
There might also be efficiency left on the table in my implementation, because I use the native number types of Guile, which allow for arbitrarily large integers (which one might not need in many cases) and I might even have used fractions, instead of inexact floats.
I guess though, with good, suitable data structures and a bit of reworking the implementation, one could get a production ready thing out of my naive implementation, that is even trivially parallelized and still would have the linear speedup (within some bounds only, probably, because decision trees usually shouldn't be too deep, to avoid overfitting) that my purely functional implementation enables.
Thanks for the links!
I don't think it would survive afterwards due to quick change in technology. Even the desktop OCR applications at the time didn't use Decision Tree because the CPU was much more powerful. The DT OCR engine was competitive only under special use case.
Yes a DT on raw pixel values, or a DT on raw time values will in general be quite terrible.
That said the convolutional structure is hard coded in those neural nets, only the weights are learned. It is not that the network discovered on its own that convolutions are a good idea. So NNs too really (damn autocorrect, it's rely, rely) on human insight and structuring upon which they can then build over.
> So NNs too really (damn autocorrect, it's rely, rely) on human insight and structuring upon which they can then build over.
It is possible to train deep decision trees forests [1]. Then I believe that it is possible to train deep convolutional decision trees forests.
It turns out many dataset have such a fractal like nature but where the partitioning needs to be cut off at a certain depth and not continued till infinity.
https://www.youtube.com/watch?v=PctlBxRh0p4
(Original title was "Physicists are surrendering to AI" but it was changed since to something less clickbaity, which I appreciate. I posted it here on the original title: https://news.ycombinator.com/item?id=46859804)
What worries me is the noticeable uptick of presentations of the sort -- look ma better fit ... deep neural nets. These are mostly by more junior folks, but not necessarily. I have been in the audience in many.
These and the uptick in research proposals funded by providers of infra for such DNNs. I have been in the audience of many.
A charitable read could be that they just want the money and would do the principled thing.
To support your point of view, I haven't encountered this in particle physics. It's from other branches. I am not a Physicist myself, happened to be in a position to observe funding requests, request for collaborations.
Not so convinced about decision trees though (that process one row at a time).
Yeah, unless you had to deal with arbitrarily large integer features, Guile integers would come with a big efficiency hit.
I think one could parallelize processing rows, at the very least when classifying from learned model. Probably also during learning the model.
What I had not articulated well is that linear classifiers have the opportunity to use matvecs that have a different level of L1 L2 cacheable goodness and non-branchy code. There using proper memory layout gives an outstanding win. The win for decision trees are less impressive in comparison, so you needn't be feeling bad about your code.
It was until recently, but there is a new method which trains them directly without any floating point math, using "Boolean variation" instead of Newton/Leibniz differentiation:
https://proceedings.neurips.cc/paper_files/paper/2024/hash/7...
I don't see how that is true. Decision trees look at one parameter at a time and potentially split to multiple branches (aka more than 2 branches are possible). Single input -> discrete multi valued output.
Neural networks do the exact opposite. A neural network neuron takes multiple inputs and calculates a weighted sum, which is then fed into an activation function. That activation function produces a scalar value where low values mean inactive and high values mean active. Multiple inputs -> continuous binary output.
Quantization doesn't change anything about this. If you have a 1 bit parameter, that parameter doesn't perform any splitting, it merely decides whether a given parameter is used in the weighted sum or not. The weighted sum would still be performed with 16 bit or 8 bit activations.
I'm honestly tired of these terrible analogies that don't explain anything.
Well, step one should be trying to understand something instead of complaining :)
> Single input -> discrete multi valued output.
A single node in a decision tree is single input. The decision tree as a whole is not. Suppose you have a 28x28 image, each 'pixel' being eight bits wide. Your decision tree can query 28x28x8 possible inputs as a whole.
> A neural network neuron takes multiple inputs and calculates a weighted sum, which is then fed into an activation function.
Do not confuse the 'how' with 'what'.
You can train a neural network that, for example, tells you if the 28x28 image is darker at the top or darker at the bottom or has a dark band in the middle.
Can you think of a way to do this with a decision tree with reasonable accuracy?
I don't think it's correct to call it unsolved. The established methods are much less efficient than those for "regular" neural nets but they do exist.
Also note that the usual approach when going binary is to make the units stochastic. https://en.wikipedia.org/wiki/Boltzmann_machine#Deep_Boltzma...
By unsolved I guess I meant: this looks like it should be easy and efficient but we don't know how to do it yet.
Usually this means we are missing some important science in the classification/complexity of problems. I don't know what it could be.
Whereas if you're already using evolution strategies or a genetic algorithm or similar then I don't expect changing the bit width (or pretty much anything else) to make any difference to the overall training efficiency (which is presumably already abysmal outside of a few specific domains such as RL applied to a sufficiently ambiguous continuous control problem).