Lets say I have 100 independent features - 90 are binary (e.g. 0/1) and 10 are continuous variables (e.g. age, height, weight, etc). I use the 100 features to predict a classifier problem with an adequate amount of samples.
When I set a XGBClassifier function and fit it, then the 10 most important features from the standpoint of gain are always the 10 continuous variable. For now I am not interested in cover or frequency. The 10 continuous variables take up like .8 to .9 of space in gain list ( sum(gain) = 1).
I tried tuning the gamma, reg_alpha , reg_lambda , max_depth, colsample. Still top 10 features by gain are always the 10 continuous features.
Any suggestions?
small update -- someone asked why I think this is happening. I believe it's because a continuous variable can be split on multiple times per decision tree. A binary variable can only be split on once. Hence, the higher prevalence of continuous variables in trees and thus a higher gain score
Yes, it's well-known that a tree(/forest) algorithm (xgboost/rpart/etc.) will generally 'prefer' continuous variables over binary categorical ones in its variable selection, since it can choose the continuous split-point wherever it wants to maximize the information gain (and can freely choose different split-points for that same variable at other nodes, or in other trees). If that's the optimal tree (for those particular variables), well then it's the optimal tree. See Why do Decision Trees/rpart prefer to choose continuous over categorical variables? on sister site CrossValidated.
When you say "any suggestions", depends what exactly do you want, it could be one of the following:
a) To find which of the other 90 binary categorical features give the most information gain
b) To train a suboptimal tree just to find out which features those are
c) To engineer some "compound" features by combining the binary features into n-bit categorical features which have more information gain (while being sure to remove the individual binary features from the input)
d) You could look into association rules : What is the practical difference between association rules and decision trees in data mining?
If you want to explore a)...c), suggest something vaguely like this:
exclude various subsets of the 10 continuous variables, then see which binary features show up as having the most gain. Let's say that gives you N candidate features. N will be << 90, let's assume N < 20 to make the following more computationally efficient.
then compute the pairwise measure of association or correlation (Spearman or Kendall) between each of the N features. Look at a corrplot. Pick the clusters of variables which are most associated with each other. Create compound n-bit variables which combine those individual binary features. Then retrain the tree, including the compound variables, and excluding the individual binary variables (to avoid changing the total variance in the input).
iterate for excluding various subsets of the 10 continuous variables. See which patterns emerge in your compound variables. I'm sure there's an algorithm for doing this (compound feature-engineering of n-bit categoricals) more formally and methodically, I just don't know it.
Anyway, for hacking a tree-based method for better performance, I imagine the most naive way is "at every step, pick the two most highly-correlated/associated categorical features and combine them". Then retrain the tree (include new feature, exclude its constituent features) and use the revised gain numbers.
perhaps a more robust way might be:
Pick some threshold T for correlation/association, say start at a high level T = 0.9 or 0.95
At each step, merge any features whose absolute correlation/association to each other >= T
If there were no merges at this step, reduce T by some value (like T -= 0.05) or ratio (e.g. T *= 0.9 . If still no merges, keep reducing T until there are merges, or until you hit some termination value (e.g. T = 0.03)
Retrain the tree including the compound variables, excluding their constituent subvariables.
Now go back and retrain what should be an improved tree with all 10 continuous variables, and your compound categorical features.
Or you could early-terminate the compound feature selection to see what the full retrained tree looks like.
This issue arose in the 2014 Kaggle Allstate Purchase Prediction Challenge, where the policy coverage options A,B,C,D,E,F,G were each categoricals with between 2-4 values, and very highly correlated with each other. (The current option of C, "C_previous", is one of the input features). See that competitions's forums and published solutions for more. Be aware that policy = (A,B,C,D,E,F,G) is the output. But C_previous is an input variable.
Some general fast-and-dirty rules-of-thumb on feature selection from Kaggle are:
throw out any near-constant/ very-low-variance variables (because they have near-zero information content)
throw out any very-high-cardinality categorical variables (cardinality >~ training-set-size/2), (because they will also tend to have low information content, but cause lots of spurious overfitting and blow up training time). This can include customer IDs, row IDs, transaction IDs, sequence IDs, and other variables which shouldn't be trained on in the first place but accidentally ended up in the training set.
I can suggest few things for you to try.
Test your model without this data (only 90 features) and evaluate the decrease in your score. If it's insignificant you might want to remove those features.
Turn them into groups.
For example, age can be categorized into groups, 0 : 0-7, 1 : 8-16, 2 : 17-25 and so on.
Turn them into binary. Out of the box idea on how to chose the best value to split them into binary is: Build 1 tree with 1 node (max depth = 1) and use only 1 feature. (1 out of the continuous features). then, dump the model to a .txt file and see the value it chose to split on. using this value, you can transform all that feature column into binary
I'm dealing myself with very similar problems right now, So i'll be happy to hear your results and the paths you chose to try.
I learned a lot from the answer by #smci, so I would recommend to follow his suggestions.
In the case, when your binary categorical features are in fact OHE representations of several categorical features with several classes in each, you can follow two more approaches:
Convert OHE into label encoding. Yes, this has the caveat that one introduces an order into a categorical features, which might be meaningless, for example green=3 > red=2 > blue=1. But in practice is seems that trees handle label=encoded categorical variables (even with meaningless order) reasonably well.
Convert OHE into target-/mean-/likelihood encoding. This is tricky, because you need to apply regularisation to avoid data leakage.
Both of those ideas are meant to group together several binary features into a single one based on prior knowledge about feature meaning. If you do not have that luxury, you can also try to deduce such groups by doing scalar product of columns and finding those giving zero product.
In machine learning, how to deal with a feature like salary. For example, if I'm applying k-nearest neighbors by measuring the distance between data points based on features. Let's say we have two points with salaries 2000 and 6000. The difference between them is 4000. Let's view another two points with salaries 102000 and 106000. The difference here is still 4000$ but we humans consider the last two points closer or more similar than the first two points.
How do I incorporate such an intuition in machine learning?
You can do one of the following things (and many more):
transform the feature using log function (thus 2000 and 6000 would be much further than 102000 and 106000)
binarize feature into multiple buckets (you would create a feature for each range of salary and you are the one creating the buckets)
change similarity function in k-nn to look at relative instead of absolute difference
I found several examples of two types.
Single feature
Given a data with only two items classes. For example only blue and yellow balls. I.e. we have only one feature in this case is color. This is clear example to show "divide and conquer" rule applicable to entropy. But this is senselessly for any prediction or classification problems because if we have an object with only one feature and the value is known we don't need a tree to decide that "this ball is yellow".
Multiple features
Given a data with multiple features and a feature to predict (known for training data). We can calculate a predicate based on minimum average entropy for each feature. Closer to life, isn't it? It was clear to me until I haven't tried to implement the algorithm.
And now I have a collision in my mind.
If we calculate entropy relatively to a known features (one per node) we will have meaningful results at classification with a tree only if unknown feature is strictly dependent from every known feature. Otherwise a single unbound known feature could break all prediction driving a decision in a wrong way. But if we calculate entropy relatively to a values of the feature which we want to predict at classification we are returned to the first senseless example. In this way there is no difference which of a known feature to use for a node...
And a question about a tree building process.
Should I calculate entropy only for known features and just believe that all the known features are bound to an unknown? Or maybe I should calculate entropy for unknown feature (known for training data) TOO to determine which feature more affects result?
I had the same problem (in maybe a similar programing task) some years ago: Do I calculate the entropy against the complete set of features, the relevant features for a branch or the relevant features for a level?
Turned out like this: In a decision tree it comes down to comparing entropies between different branches to determine the optimal branch. Comparison requires equal base sets, i.e. whenever you want to compare two entropie values, they must be based on the same feature set.
For your problem you can go with the features relevant to the set of branches you want to compare, as long as you are aware that with this solution you cannot compare entropies between different branch sets.
Otherwise go with the whole feature set.
(Disclaimer: Above solution is a mind protocol from a problem that lead to about an hour of thinking some years ago. Hopefully I got everything right.)
PS: Beware of the car dataset! ;)
I have matrices of feature vectors - 200 features long, in which the feature vectors within a matrix are temporally related, but I wish to reduce each matrix to a single, meaningful vector. I have applied PCA to the matrix in order to reduce its dimensionality to one with high variance, and am considering concatenating its rows together into one feature vector to summarize the data.
Is this a sensible approach, or are there better ways of achieving this?
So you have an n x 200 feature matrix, where n is your number of samples, and 200 features per sample, and each feature is temporally related to all others? Or you have individual feature matrices, one for each time point, and you want to run PCA on each of these individual feature matrices to find a single eigenvector for that time point, and then concatenate those together?
PCA seems more useful in the second case.
While this is doable, this is maybe not the best way to go about it because you lose temporal sensitivity by collapsing together features from different times. Even if each feature in your final feature matrix represents a different time, most classifiers cannot learn about the fact that feature 2 follows feature 1 etc. So you lose the natural temporal ordering by doing this.
If you care about the the temporal relationship between these features you may want to take a look at recurrent neural networks, which allow you feed information from t-1 into a node, at the same time as feeding in your current t features. So in a sense they learn about the relationship between t-1 and t features which will help you preserve temporal ordering. See this for an explanation: http://karpathy.github.io/2015/05/21/rnn-effectiveness/
If you don't care about time and just want to group everything together, then yes PCA will help reduce your feature count. Ultimately it depends what type of information you think is more relevant to your problem.
How to convert or visualize decision table to decision tree graph,
is there an algorithm to solve it, or a software to visualize it?
For example, I want to visualize my decision table below:
http://i.stack.imgur.com/Qe2Pw.jpg
Gotta say that is an interesting question.
I don't know the definitive answer, but I'd propose such a method:
use Karnaugh map to turn your decision table to minimized boolean function
turn your function into a tree
Lets simplyify an example, and assume that using Karnaugh got you function (a and b) or c or d. You can turn that into a tree as:
Source: my own
It certainly is easier to generate a decision table from a decision tree, not the other way around.
But the way I see it you could convert your decision table to a data set. Let the 'Disease' be the class attribute and treat the evidence as simple binary instance attributes. From that you can easily generate a decision tree using one of available decision tree induction algorithms, for example C4.5. Just remember to disable pruning and lower the minimum number of objects parameter.
During that process you would lose a bit of information, but the accuracy would remain the same. Take a look at both rows describing disease D04 - the second row is in fact more general than the first. Decision tree generated from this data would recognize the mentioned disease only from E11, 12 and 13 attributes, since it's enough to correctly label the instance.
I've spent few hours looking for a good algorithm. But I'm happy with my results.
My code is too dirty now to paste here (I can share privately on request, on your discretion) but the general idea is as the following.
Assume you have a data set with some decision criteria and outcome.
Define a tree structure (e.g. data.tree in R) and create "Start" root node.
Calculate outcome entropy of your data set. If entropy is zero you are done.
Using each criterion, one by one, as tree node calculate entropy for all branches created with this criterion. Take the minimum one entropy of all branches.
Branches created with the criterion with the smallest (minimum) entropy are your next tree node. Add them as child nodes.
Split your data according to decision point/tree node found in step 4 and remove the criterion used.
Repeat step 2-4 for each branch until your all branches have entropy = 0.
Enjoy your ideal decision tree :)