The Quest for Blackbox Interpretability (Take 1, Random Forests and Feature Importances)

Written on June 21, 2019
[ machine-learning  random-forest  predictive-modeling  model-interpretability  easi  ]

So you created a random forest, and it seems like its making great predictions! But now your boss wants to know why. This is where things can get tricky.

The first stab at interpreting your random forest seems simple engouh: the RF models in sklearn provide a ranked list of feature importances, right? They do, and I’ve taken them seriously once upon a time. It might be the case that you take them seriously, or that you don’t, but you print them out for your boss anyway.

In this post I tell a cautionary tale about the “feature importances” of a random forest in scikit-learn. This has been talked about ad nauseum (e.g., [here] and [here]), yet people (including myself sometimes) will take a look-see at the feature importances as if they mean something … uh, important!

Hard to say it better than said here:

“Have you ever noticed that the feature importances provided by scikit-learn’s Random Forests™ seem a bit off, perhaps not jiving with your domain knowledge? We’ve got some bad news -— you can’t always trust them. It’s time to revisit any business or marketing decisions you’ve made based upon the default feature importances (e.g., which customer attributes are most predictive of sales).”

In follow-up posts, I will talk about LIME, Shapley numbers, and more – and associated cautionary tales.

Let’s get started!

Random Forests (the Gist)

I wasn’t going to include a part describing what a Random Forest is, but then I read through this paper and liked their description so much I wanted to save it somewhere. It serves as a nice recap of these models and gives the sections below some more context.

“In random forests and the related method bagging, an ensemble of classification trees is created by means of drawing several bootstrap samples or subsamples from the original training data and fitting a single classification tree to each sample. Due to the random variation in the samples and the instability of the single classification trees, the ensemble will consist of a diverse set of trees. For prediction, a vote (or average) over the predictions of the single trees is used and has been shown to highly outperform the single trees: By combining the prediction of a diverse set of trees, bagging utilizes the fact that classification trees are instable but on average produce the right prediction. This understanding has been supported by several empirical studies and especially the theoretical results of Bühlmann and Yu, who could show that the improvement in the prediction accuracy of ensembles is achieved by means of smoothing the hard cut decision boundaries created by splitting in single classification trees, which in return reduces the variance of the prediction.”

“In random forests, another source of diversity is introduced when the set of predictor variables to select from is randomly restricted in each split, producing even more diverse trees. In addition to the smoothing of hard decision boundaries, the random selection of splitting variables in random forests allows predictor variables that were otherwise outplayed by their competitors to enter the ensemble. Even though these variables may not be optimal with respect to the current split, their selection may reveal interaction effects with other variables that otherwise would have been missed and thus work towards the global optimality of the ensemble.”

I also thought this article by SydneyF from the Alteryx community had a very nice breakdown as well – also worth saving!

“Creating and then combining the results of a bunch of decisions trees seems pretty basic, however, simply creating multiple trees out of the exact same training data wouldn’t be productive – it would result in a series of strongly correlated trees. All of these trees would sort data in the same way, so there would be no advantage to this method over a single decision tree. This is where the fancy part of random forests starts to come into play. To decorrelate the trees that make up a random forest, a process called bootstrap aggregating (also known as bagging) is conducted. Bagging generates new training data sets from an original data set by sampling the original training data with replacement (bootstrapping). This is repeated for as many decision trees that that will make up the random forest. Each individual bootstrapped data set is then used to construct a tree. This process effectively decreases the variance (error introduced by random noise in the training data, i.e., overfitting) of the model without increasing the bias (underfitting). On its own, bagging the training data to generate multiple trees creates what is known as a bagged trees model.”

“A similar process called the random subspace method (also called attribute bagging or feature bagging) is also implemented to create a random forest model. For each tree, a subset of the possible predictor variables is sampled, resulting in a smaller set of predictor variables to select from for each tree. This further decorrelates the trees by preventing dominant predictor variables from being the first or only variables selected to create splits in each of the individual decision trees. Without implementing the random subspace method, there is a risk that one or two dominant predictor variables would consistently be selected as the first splitting variable for each decision tree, and the resulting trees would be highly correlated. The combination of bagging and the random subspace method result in a random forest model.”

“The aggregating part of bootstrap aggregating comes from combining the predictions of each of these decision trees to determine an overall model prediction. The output of the overall model is then the mode of classes (classification) or the mean prediction (regression) of all the predictions of the individual trees, for each individual record.”

In the original random forest, each tree grew indefinitely until each leaf had 1-2 data points. In modern implementations, this is often a default, but is something that you can tweak. For example, you can choose a max_depth, which limits how many splits can occur along a single pathway through the tree. Or you might play with min_samples_leaf, which hedges against overfitting to a noisy variable. The number of features randomly selected at a split is also something you can tune. Often, given f features, the default is split on k randomly selected features, where is k < f and usually defaulted to k = sqrt(f). This default is considered good enough for most cases (e.g., here is a great video lecture on random forests), but you might find you can squeeze a bit more optimization out of your model by playing around in the neighborhood of this default.

That said, technically, growing out a huge forest should hedge against overfitting too. Quite possibly better, or not as well. So how to choose? Fortuantely, using skearn’s RandomSearch or GridSearch, you can optimize these hyperparameters. You might also have runtime requirements that help guide appropriate design decisions.

Why Random Forests?

In upcoming articles, I will talk about things like Shapley values and LIME, which are model agnostic. However, I begin with random forests because, as far as predictive models are concerned, these almost work perfectly right out of the box! Moreover, random forests compete with neural networks for “best black box” in terms of performance, depending on data set (e.g., Kagglers are never quite raving about neural networks, while computer vision folk are rarely heard talking about “recurrent convolutional random forests”).

The out-of-the-box feature is most important though. Oftentimes, you can run a baseline random forest on a data set without no clean-up, scaling, or normalization. This out-of-the-boxness scares some people – those who have spent years concerend with inference, proper imputation, taking logarithms, using Box-Cox and so on! Even spooky to the unspookable: random forests technically do not even require a validation set! (“Say whaaat?!”) It can feel a little funny to (i) not care about any of that, and (ii) expect to have any understanding of how the many predictors affect the outcome. But this is precisely what random forests offer! If you suffer from random forest fear, then I guarantee that getting your hands dirty with this technique will quickly begin to allay your anxiety.

Often, we pit predictive power versus explanatory power, but I think there has been enough research into tree-based methods at this point to make that tradeoff less sensitive and severe. Moreover, there has been enough research to show that what we often consider to be “explanatory power” isn’t as explanatory as we would like to think (e.g., regression coefficients) and some go as far as advising that the explanatory methods for black box models be applied to models that are often not considered as such (namely, things like linear and logistics regression).

“Do you have citations to back any of this up?”

Yes!

Anyway, we will start with random forests as our black box model, and look at the out-of-the-box explanatory method in the scikit-learn method, which is known as “Gini importance.” This might not be a great place to start in terms of providing a black box model with “explanatory power,” since it has been shown to be a poor explanatory tool. However, it is a great place to start in terms of drawing a line between what parts of random forests work out of the box (e.g., training them) and what does not (e.g., the default “feature imporatance” rankings provided in the scikit-learn implementation).

In the remainder of this post, things will get a bit bleak. What I’m trying to do is decide on my own path to model building, while maintaining useful explanatory power… These are kind of a mish-mash, brainstorm of lessons learned first- and second-hand. We find that “explanatory power” is a bit hard to define, especially for categorical variables, which can often take on any number of arbitrary representations at training time. Personally, my conclusion is that there is a bit of craftsmanship and artistry that must go into this: any given representation will not necessarily induce a false picture (in terms of feature importance), but might provide a perspective that does not reflect one’s intuition at first or second glance.

You’ll see what I mean… Read on!

Gini Importance (aka Mean Decrease in Impurity)

Note that for random forests in scikit-learn, (i) the CART algorithm is used to build the trees, and (ii) the Gini criterion is used for splitting. The Classification and Regression Trees (CART) algorithm “creates a binary tree — each node has exactly two outgoing edges — finding the best numerical or categorical feature to split using an appropriate impurity criterion. For classification, Gini impurity or twoing criterion can be used. For regression, CART introduced variance reduction using least squares (mean square error).” (source)

The splitting criterion doesn’t necessarily dictate the feature importance algorithm, though it obviously affects the outcome in one way or another. Specifically, one can use the Gini criterion for splitting, but choose not to use the Gini importance for ranking feature importances. (Having said that, the Gini importance itself is strictly associated with the Gini splitting criterio. So, e.g., if you use the entropy criterion in scikit learn, a similar algorithm can be used to compute the importances, but I’m not sure you would call them Gini importances at that point.)

Here, we will talk about the Gini importance.

The most important thing to understand is that “feature importance” is not synonymous with “Gini importance.” That is, despite random forests in scikit-learn having a ranked list referred to as rf.feature_importance_, the way this list is created is but one way to assess the importances of the input features – and not a great way either. There exist other algorithms to determine/estimate variable importance, such as “permutation importance” (aka “mean decrease in accuracy”), which are implemented in complementary packages to scikit-learn, such as rfpimp.

The Gini importance “is based on the principle of impurity reduction that is followed in most traditional classification tree algorithms. However, it has been shown to be biased when predictor variables vary in their number of categories or scale of measurement, because the underlying Gini gain splitting criterion is a biased estimator and can be affected by multiple testing effects.” (Source: Conditional variable importance for random forests)

Scikit-learn’s defense of the Gini importance can be found in its documentation. Not so sure it is a great defense all things considered, but worth recording here:

“The relative rank (i.e. depth) of a feature used as a decision node in a tree can be used to assess the relative importance of that feature with respect to the predictability of the target variable. Features used at the top of the tree contribute to the final prediction decision of a larger fraction of the input samples. The expected fraction of the samples they contribute to can thus be used as an estimate of the relative importance of the features. In scikit-learn, the fraction of samples a feature contributes to is combined with the decrease in impurity from splitting them to create a normalized estimate of the predictive power of that feature.”

“By averaging the estimates of predictive ability over several randomized trees one can reduce the variance of such an estimate and use it for feature selection. This is known as the mean decrease in impurity, or MDI.”

This is probably a good place to note that Gini importance does not appear to be the variable importance measure originally intended for random forests. One of Breiman’s webpages goes over the original implementation, where it clearly considers permutation importance to be the preferred variable importance measure:

In every tree grown in the forest, put down the oob cases and count the number of votes cast for the correct class. Now randomly permute the values of variable m in the oob cases and put these cases down the tree. Subtract the number of votes for the correct class in the variable-m-permuted oob data from the number of votes for the correct class in the untouched oob data. The average of this number over all trees in the forest is the raw importance score for variable m.

If the values of this score from tree to tree are independent, then the standard error can be computed by a standard computation. The correlations of these scores between trees have been computed for a number of data sets and proved to be quite low, therefore we compute standard errors in the classical way, divide the raw score by its standard error to get a z-score, ands assign a significance level to the z-score assuming normality.

If the number of variables is very large, forests can be run once with all the variables, then run again using only the most important variables from the first run.

For each case, consider all the trees for which it is oob. Subtract the percentage of votes for the correct class in the variable-m-permuted oob data from the percentage of votes for the correct class in the untouched oob data. This is the local importance score for variable m for this case, and is used in the graphics program RAFT.

Breiman mentions Gini importance next, as a computationally fast way of estimating the permutation importance, claiming that the two are often consistent with each other:

Every time a split of a node is made on variable m the gini impurity criterion for the two descendent nodes is less than the parent node. Adding up the gini decreases for each individual variable over all trees in the forest gives a fast variable importance that is often very consistent with the permutation importance measure.

Dependence on Variable Representation

If you have an important categorical variable that you’ve dummied down into 100 binary variables, good luck showing that those categories are more important than some weak signal in a continuous variable, or that the original categorical variable had immense explanatory power before getting castrated.

Imagine a categorical feature with 100 levels, which explains 90% of any given prediction, and a few continuous variables that hold the remaining 10% (say 4 vars at 2.5% each). Now picture that the 100-level feature is one-hotted into 100 binary variables, each taking an equal share of the predictive power (i.e., 1% of 90% each, or 0.9%). All 4 continuous variables will now rank higher than any one-hotted portion of the categorical variable. Worse, some pure noise variables might out rank the dummies too, if any overfitting took place.

When is this relevant? Well, say the catvar is geographic region. Your explanation to stakeholders should start by saying, “First of all, we found that geographic region has the strongest role in determining the outcome of our prediction model.” But after one-hotting the variable, you might have all kinds of weak signals (and potentially noise signals) come up first. The story that follows from the feature importances in some sense is not wrong, but it’s not exactly right – at the least, it likely has lost a lot of its intuitive power.

What can you do?

If you care about feature importance, then encoding a categorical variable with integers is a great way to keep everything together. In my experience, some folks feel uncomfortable encoding a nominal variable as if it were an ordinal variable (“label encoding” in sklearn parlance), but it is perfectly reasonable in a tree-based method like a random forest! A tree is just looking for rules – doesn’t matter if the rule corresponds to “Is this a cat?” or “Is this the number 3?”

This article does an excellent job showing that not only is a numeric representation of categorical variable ok for a decision tree, but almost always a better choice than one-hot encoding in terms of model accuracy, computational time, and more. (In fact, they show that one-hotting is almost never an optimal representation in this scenario, but instead recommend choosing a numeric representation for catvars with less than ~1k levels, and a binary encoding for any catvar with more than ~1k levels).

You might be thinking: “Wtf? If one-hot encoding is so bad, then why do I always hear about it?” It does seem like one-hot encoding has a captive audience, and not for nothing: it works great for models like logistic regression and neural networks. Another author finds:

“In general, one hot encoding provides better resolution of the data for the model and most models end up performing better. It turns out this is not true for all models and to my surprise, random forest performed consistently worse for datasets with high cardinality categorical variables.”

To be fair, this is why things like LASSO are used in logistic regression, or embeddings for neural networks. At one point, the one-hot representation of a high-cardinal categorical variable becomes a nuisance for any model (at least when considering how much data you’re willing to collect, or how long you’re willing to wait for the model to train, etc). Just so happens that tree-based methods seem to suffer from it the worst. And it can kill interpretability in the feature importance rankings, so why use it? The author in the last article has an excellent example where he has a high cardinality categorical feature which is the ranked as the most important in the model. After one-hotting this variable, the dimensionality of the model explodes and none of the variable’s one-hot associates appears in the top 10 rankings. Worse, even the order of importance of unrelated variables has changed. The authors says:

“One-hot encoding categorical variables with high cardinality can cause inefficiency in tree-based ensembles. Continuous variables will be given more importance than the dummy variables by the algorithm which will obscure the order of feature importance resulting in poorer performance.”

Admittedly, my own intuition misguides me: thinking about how trees simply look for rules, I would guess it doesn’t matter whether that rule is encoded in one numerically-encoded variable or 1000 dummies… Clearly the latter case has a suboptimal feel to it: more variables probably means more trees and splits are required, i.e., there is more paperwork to go through, but the answer is in there somewhere! But here is another article that addresses this:

“Whatever you do, at least be aware that, despite theoretical results suggesting the expressive power of random forests with one-hot encoded features is the same as for categorical variables, the practical results are very different!”

This last article also addresses how a high-cardinality catvar in the H20 framework is assigned 70% of the importance, while its one-hot encoded components in the sklearn framework do not even accumulate 10% of importance (even has a section called “why one-hot encoding is bad bad bad for trees”). One thing that I did not understand about the article is the line from the TLDR, “Our primary comparison is between H2O (which honors categorical variables) and scikit-learn (which requires them to be one-hot encoded).” There is nothing stopping you from numerically encoding categorical variables (e.g., with integers) and using them in a scikit-learn random forest. That said, I do see many blogs where folks one-hot encode anything and everything by default, so the article serves as a great read for those inclined to one-hot their catvars.

Anyway, major take away here is that (Gini) feature importances in scikit-learn’s RF have a certain arbitrariness to them that is dependent on variable representations. If your only option was Gini importance, then to keep the “inherent” Gini importances, do not one-hot encode the categorical variable (though encode it numerically, if not already). A nice side effect here is that the model should also perform better in this representation for low-cardinality catvars (levels < 1k).

Dependence on Number of CatVar Levels

One potential setback though: for Gini importances, high-cardinality catvars can artificially outrank lower-cardinality categorical variables.

In the last section, the vibe was generally, “Leave that categorical variable alone!” Given that the one-hot representation of a catvar can severely dampen the overall importance of a catvar, it can almost seem like the (Gini) feature importance of the high-cardinality categorical variable is true and that the one-hot representation obscures this truth. But the Gini importance algorithm used to compute feature importances in scikit-learn’s RFs generally biases towards high-cardinality categorical variables.

This can hurt in a situation where you have a binary variable that is very important and a high-cardinality variable where each level is not all too important. The storyline you might expect from your data is that the binary variable is ranked higher in importance, but instead you might find the high-cardinality catvar on top. One data scientist might trust their business intuition and investigate further. Another might think they’ve stumbled onto some new insight, and sell stakeholders on a wild story that seems almost too good to be true!

Other feature importance measures address this high-cardinality bias, but I think this brings into light something to think about in any analysis of data: choosing a representation that is right for your problem.

Sticking with the idea of a geographical variable, like zipcode, you might find that it beats out variables that should be more important from a business standpoint. Breaking zipcode up into city and state variables might align things better with expectation.

That all said: this fudging can make one uneasy if the original intent is to understand feature importance in the data “as is”. Fortunately, there do appear to be feature importance measures that do not accidentally bias towards high-cardinality categorical variables (e.g., conditional permutation importance).

Some Explanation

Turns out that the two sections above are two sides of the same coin: Gini importance biases towards continuous and/or high-cardinality categorical variables.

The author of “Be Aware of Bias in RF Variable Importance Metrics” offers a nice, succinct explanation.

Gini importance is biased because:

“Each time a break point is selected in a variable, every level of the variable is tested to find the best break point. Continuous or high cardinality variables will have many more split points, which results in the ‘multiple testing’ problem. That is, there is a higher probability that by chance that variable happens to predict the outcome well, since variables where more splits are tried will appear more often in the tree.”

The author then goes over permuation importance and conditional permutation importance, which solve some of the issues with Gini importance. At the end of the article, he provides a nice set of rules for when to use each type of importance (especially when computational time or resources are limited). If using continuous variables that are not correlated, then Gini importance is ok. Similarly, if using only categorical variables that are not correlated with each other, the Gini importance is ok, but only if those catvars have the same number of levels (or at least, nearly so).

Once you have categorical variables with vastly different cardinalities, or once you introduce a continuous variable, then all bets are off: do not use the Gini importance!

On this last note, after running a bunch of simulations myself, I would have to wholeheartedly agree. Just by introducing a random, continuous variable that had nothing to do with my target variable, the Gini importances immedidately became suspect: seemed no matter how many parameters I tweaked, the noise variable ranked in first or second place every time!

Final note: given the various articles showing that one-hot encoding also diminishes model accuracy (e.g., this), I would bias towards keeping high-cardinality categorical variables, but using a better measure of feature importance.

Design Flaws: Noise & Overfitting

At least one of the reasons that a very high-cardinality catvar can appear to have more importance attributed to it than seems reasonable is due to overfitting. That is, if you are not ensuring that the random forest has enough restrictions on it (by changing the defaults on parameters like max_depth, min_samples_leaf, etc), then it turns out that something like zipcode can proxy as a semi-unique ID in the data records. In highly populated zipcodes, this obviously is unlikely to be the case, but when you consider more rarefied regions, it becomes possible to only have several customers per zipcode. Depends on the size of your customer base, or number of patients in your trial, etc.

In the same way, a pure noise variable having no correlation with the target can serve as an ID variable: the forest can overfit to the noise and decide that the noise is more important than it is (say on a holdout set).

In “How not to use random forest, the author depicts a simulation that has an target-relevant binary variable, a target-relevant continuous variable (Poisson distributed), a random noise binary variable, and a random noise continuous variable (normally distributed). His intent is to show that using scikit-learn’s random forest with default parameters runs folks into trouble, especially when one cares about feature importance. The noisy continuous variable is ultimately ranked as most important. This should send shivers down your spine: in this case, we know what variable is just noise, so we know the feature importances are somehow bogus, but in the workplace setting, you cannot be so sure what is noise and what is signal (that is, without further investigation, etc).

I’ve run my own simulations, similar to this article, and have come up with the same: the noisy continuous variables always rise to the top! Very disheartening. The author in the aforementioned article attributes this behavior to both using scikit-learn’s default feature importance (Gini importance), default hyperparameters (e.g., max_depth=None, max_leaf_nodes=None, min_samples_leaf=1, min_samples_split=2), and the ambiguities that can arise (especially when using the Gini importance) when mixing continuous and categorical variables. This is what allows a continuous noise variable, where each element is likely to be unique in the column, to serve as an ID for each record in the data set. That said, I experimented with tweaking the hyperparameters quite a bit and was still amazed/horrified to see that the noise variable floated to the top of feature importances.

Solutions:

  • At minimum, look at the out-of-bag (OOB) error. If it sucks, then there is no reason to trust your feature importances. If you also have an out-of-hand validation set not used in training, then you can use that in the same manner.
  • Tweak the hyperparameter defaults to help prevent overfitting to noise and accidentally considering it an important variable.
    • The RandomForestClassifier defaults do not necessarily include enough constraints (e.g., trees are defaulted to growing up to single-item leaves, which is true to the original definition of a random forest, but not always the optimal solution, as you might find in a GridSearch or RandomSearch).
    • Try manually tweaking the following parameters (or performing an automated search)
      • n_estimators
        • number of trees in the forest
      • max_features
        • this is the number of features to consider at each split
        • defaults to sqrt(num_features)
        • at each split in each tree of the forest, a random subset of full feature set is chosen (in contrast to classical DT, where all features are considered at each split)
      • min_samples_split
        • a node must have this many samples to be considered for further splitting
        • hedges against fine-tuning to noise or outliers
      • min_samples_leaf
        • a leaf must have this many samples to exist
        • that is, if a split is calculated, it only becomes a part of tree if both child nodes have this many
        • even when using min_samples_split, a resulting leaf might have only a handful of samples, so this hedges against that
        • so, if you care mainly about your leaves, you can just use this parameter since it implies min_samples_split – that is, the smallest a node split can be is 2 * min_samples_leaf, where it is a 50/50 split
          • max_depth
        • yet another way to hedge against trees in the forest fitting to random noise variables
        • limits how many splits can occur along one pathway from root to leaf
        • defaults to None, which means trees will grow until each leaf has 1-2 data points
        • interesting tip: first train your RF w/ no constraint, then use the rfpimp package to see how deep each of your trees grows (rfpimp.rfmaxdepths(rf))
    • Beware: these hyperparameters can help prevent overfitting, but also push you quickly into the realm of underfitting; read more about here
  • Use other feature importance measures in place of or in additiona to the Gini importance
    • Compute permutation importance using the rfpimp package, like rfpimp.oob_importances(rf, x_trn, y_trn)
    • You can also use the rfpimp package to look at the Spearman’s correlation matrix (rfpimp.plot_corr_heatmapt(x_trn)) or the feature dependence matrix (fdm = rfpimp.feature_dependence_matrix(x_trn); rfpimp.lot_dependence_heatmap(fdm)) of your training data to identify any correlated variables , which would suggest that permutation importance by itself will have biased estimates of feature importances. Few things you can do:
      • The rfpimp package then allows you to group these variables together (e.g., ftrs = ['ftr1', ['ftr2','ftr5'], ['ftr4','ftr6','ftr7'], 'ftr8']), so that it can better compute unbiased estimates (rfpimp.importances(x_val, y_val, features=ftrs)); note that you use the training set for rfpimp.oob_importances, but a validation set if using rfpimp.importances.
      • Alternatively, as the package authors put it: “Dependence numbers close to one indicate that the feature is completely predictable using the other features, which means it could be dropped without affecting accuracy. (Dropping features is a good idea because it makes it easier to explain models to consumers and also increases training and testing efficiency/speed.)”
    • The rfpimp package also includes an option to compute cross-validated importances and drop-column importances
      • rfpimp.cv_importances(rf, x_trn, y_trn, k=5)
      • rfpimp.dropcol_importances(rf, x_trn, y_trn)

Take Away: Feature importances are only worthwhile if the associated model serves as a worthwhile prediction model. This is an issue of generalizability: do not overfit the model.

Ambiguity from Correlated Features

Another problem with feature importances is that there is some sort of arbitrariness when highly correlated variables are in the feature set.

Random forest “variable importance measures have recently been suggested as screening tools for, e.g., gene expression studies. However, these variable importance measures show a bias towards correlated predictor variables.”

“[C]orrelations between predictor variables … severely affect the original random forest variable importance measures, because they can be considered as measures of marginal importance, even though what is of interest in most applications is the conditional effect of each variable.”

Often, I’ve seen “permutation importance” as the answer to the problems that arise in “Gini importance,” but these authors show that even permutation importance biases towards correlated predictors

The article, “Selecting good features – Part III: random forests,” very nicely shows how correlated features impact the interpretaction of the Gini importance rankings. For example, simulating a model where 3 correlated features contribute about the same level of importance to the response, the author shows their estimated importance to be all over the place (e.g., one var is shown to be 10x more important than another, despite them having equal importance in reality).

That said, permutation importance is also known to not deal well with correlated predictors either, but for a different reason (will talk more about this in an upcoming article). The article, “Feature Correlation and Feature Importance Bias with Random Forests,” also shows very clear examples of how adding correlated predictors reduces the relative importance of each of the correlated predictors. These simulations were an attempt to recreate the results published in “Permutation importance: a corrected feature importance measure”, which claims that both Gini importance and permutation importance are affected by this. There is a drop-column method as well, which I won’t get into in this post, but suffice it say (without any actual evidence in hand), it seems to me that it would have the same type of bias away from correlated predictors as permutation importance does. (Update: Oh, nice – upon further reading of “Beware Default Random Forest Importances”, I find that this intuition about drop-column importance is backed by evidence.)

Generally speaking, permutation importance does work better in a larger variety of situations than Gini importance, so if you have to choose GImp or PImp, choose PImp. The only downside is that it is more computationally expensive – that translates into a longer wait, which can cut into experimentation and creativity. There also exists a measure called “conditional permutation importance,” which is even more robust, but also even more time consuming. Unfortunately, this really starts to take a toll on a quadcore laptop.

Dependence on Random Seed / Number of Trees

Another thing to worry about is how tightly your results are coupled to the chosen random seed parameter… That is, if you change the random seed, how drastically do your feature importances change? Solution: Add more trees until there is little-to-no change.

I leave you with these quotes…

From “Conditional variable importance for random forests”

“[I]t should also be noted that any interpretation of random forest variable importance scores can only be sensible when the number of trees is chosen sufficiently large such that the results produced with different random seeds do not vary systematically. Only then it is assured that the differences between, e.g., unconditional and conditional importance are not only due to random variation.”

From “Be Aware of Bias in RF Variable Importance Metrics”:

“Note: Always check whether you get the same results with a different random seed before interpreting any importance rankings. If the results change, increase the number of trees with ntree.”

Last Words

If all of this has made you uncomfortable with feature importances from scikit-learns’s random forests, then good. If not? Well, you have been warned!

Ultimately, we want to provide explanatory power when using random forests. The major two points of this article are: (i) this is possible, but (ii) not out-of-the-box in the scikit-learn version of random forests.

Though to my mind, it seems like one should never use the Gini importance, there apparently circumstances when it is ok. This author reasons that the Gini importance is just fine (and desirable in terms of computation time) under either of two conditions:

  • all predictors are continuous and not correlated with each other
  • all predictors are categorical, have the same number of levels, and are not correlated with each other

Don’t know about you, but I’m thinking those make for some pretty stringent, potentially artificial scenarios. But good to know nonetheless.

In the next installment, I’ll be talking about more robust feature importance measures, namely permutation importance and conditional permutation importance.

Some References and Further Reading

Next Up

These notes were mostly focused on the shortcomings of Gini importance, which is the default feature ranking algorithm for random forests in scikit-learn. In upcoming write-ups, I want to focus a bit more on:

  • permutation importance
    • this article has a good description
  • conditional permutation importance
  • the treeinterpreter package in Python
  • LIME
  • Shapley Values
  • Extremely Randomized Trees
    • Apparently these solve a lot of the bias and computational time issues of random forests (yay!)
    • Original paper: Geurts et al (2006): Extremely Randomized Trees
    • Read about ExtRa Trees in Epilogue of “Beware Default Random Forest Importances”