xgboost.plot_tree: binary feature interpretation

Okay, I understand the issue. You\’re observing unexpected split thresholds (e.g., `< -9.53674e-07`) on binary features when visualizing XGBoost trees, and you want to understand how to interpret these splits and which direction (True/False) corresponds to 0 or 1 for these binary features.\n\nHere\'s a breakdown of the problem, the likely cause, and how to interpret the results, along with a refined explanation and best practices:\n\n**Understanding the Problem**\n\n* **Binary Features:** Your features `f60150` (and others like it) are binary, meaning they can only take on the values 0 or 1.\n* **Unexpected Thresholds:** XGBoost is showing split conditions like `f60150 < -9.53674e-07`. This is problematic because no data point will *ever* satisfy this condition if `f60150` is truly binary (0 or 1). It seems nonsensical for a model to split on such a condition.\n* **Floating-Point Artifact:** You correctly suspect this is a floating-point issue, but understanding *why* it arises is key.\n* **Goal:** You need to reliably determine which branch (True/False) of these splits corresponds to 0 and 1 for your binary features.\n\n**Root Cause Explanation**\n\nXGBoost, like many gradient boosting libraries, uses decision trees with numerical splits. While your input data might be conceptually binary (0 or 1), XGBoost treats it as numerical data during the optimization process. It tries to find the *best* numerical split point to maximize information gain (or reduce impurity) at each node.\n\nThe split point being very close to zero is likely a combination of a few factors:\n\n1. **Regularization:** XGBoost employs regularization techniques (L1 and L2 regularization on the tree weights, and tree depth limits) to prevent overfitting. Even if a split at `f60150 < 0.5` would seem more \"natural\" for a binary feature, the regularization might penalize it slightly if a split at `< -9.53674e-07` yields a very marginally better (but likely statistically insignificant) improvement in the training objective after regularization is applied.\n\n2. **Floating-Point Precision:** Computers represent floating-point numbers with finite precision. Tiny numerical errors can accumulate during the training process, leading to split points that aren\'t exactly what you\'d expect. The `-9.53674e-07` is essentially \"zero\" within the limits of floating-point precision for XGBoost in this context.\n\n3. **Missing Value Handling:** XGBoost has built-in handling of missing values. By default, it learns which direction to go (left or right) when a value is missing. This behavior can also interact with the choice of split points. *Crucially, in the absence of explicitly defined missing values, XGBoost will not treat 0 as a missing value. Therefore, it will still try to find the \"best\" numerical split, even on a boolean feature.*\n\n**How to Interpret and Handle These Splits**\n\nThe key insight is that, for all practical purposes, you should treat splits like `f60150 < -9.53674e-07` as equivalent to `f60150 == 0`. Here\'s a robust way to determine the direction:\n\n1. **Empirical Check:** The most reliable method. Pick a tree with a split on a suspect binary feature. Manually trace a few data points with `f60150 = 0` and `f60150 = 1` through the tree. Observe which branch each value takes. This will definitively tell you which direction corresponds to 0 and 1.\n\n2. **Assumption and Validation:** You can *assume* that `feature < very_small_negative_number` implies `feature == 0`. Then, validate this assumption by checking a few trees.\n\n**Important Considerations and Best Practices**\n\n* **No Perfect Guarantee:** Even with these methods, there\'s no *guarantee* that the interpretation will be consistent across *all* trees in the ensemble. XGBoost is a complex model, and the trees are grown in a greedy fashion. However, it *should* be consistent for the vast majority of cases.\n\n* **Consider `sklearn.tree` for simpler trees:** If interpretability of individual trees is paramount, consider training a single decision tree using `sklearn.tree`. These tend to have much more straightforward split conditions, and can be easier to visualize and interpret.\n* **Feature Interaction Analysis** Don\'t focus solely on individual splits. Use feature importance scores (available in XGBoost) and SHAP values to understand the *overall* impact of your binary features on the model\'s predictions. SHAP values, in particular, can show you how each feature contributes to the prediction for a specific instance, which can be much more informative than examining individual tree splits.\n* **Data Preprocessing:** If you want to ensure clean splits, you can try explicitly setting the data type of your binary features to `bool`. While this might not completely eliminate the floating-point issue, it can sometimes help.\n\n**Revised Code with Added Explanation**\n\n```python\nimport numpy as np\nimport scipy.sparse\nfrom sklearn.datasets import fetch_20newsgroups\nfrom sklearn.feature_extraction.text import CountVectorizer\nfrom xgboost import plot_tree, XGBClassifier\nimport matplotlib.pyplot as plt\n\ndef booleanize_csr_matrix(mat):\n \'\'\' Convert sparse matrix with positive integer elements to 1s \'\'\'\n nnz_inds = mat.nonzero()\n keep = np.where(mat.data > 0)[0]\n n_keep = len(keep)\n result = scipy.sparse.csr_matrix(\n (np.ones(n_keep), (nnz_inds[0][keep], nnz_inds[1][keep])),\n shape=mat.shape\n )\n return result\n\n### Setup dataset\nres = fetch_20newsgroups()\n\ntext = res.data\noutcome = res.target\n\n### Use default params from CountVectorizer to create initial count matrix\nvec = CountVectorizer()\nX = vec.fit_transform(text)\n\n# Whether to \”booleanize\” the input matrix\nbooleanize = True\n\n# Whether to, after \”booleanizing\”, convert the data type to match what\’s returned by `vec.fit_transform(text)`\nto_int = True\n\nif booleanize and to_int:\n X = booleanize_csr_matrix(X)\n X = X.astype(np.int64) # or np.bool_ Try setting to bool, although may not eliminate the issue\n\n# Make it a binary classification problem\ny = np.where(outcome == 1, 1, 0)\n\n# Random state ensures we will be able to compare trees and their features consistently\nmodel = XGBClassifier(random_state=100)\nmodel.fit(X, y)\n\nplot_tree(model, rankdir=\’LR\’); plt.show()\n\n\n# Interpretation advice:\n# 1. Treat splits like \”feature < -9.53674e-07\" as \"feature == 0\"\n# 2. To be absolutely sure, trace a few data points with feature=0 and feature=1\n# through the tree to confirm which branch each value takes.\n# 3. Focus on feature importance and SHAP values for a more holistic understanding\n# of feature contributions.\n\n```\n\n**In summary,** don\'t be too concerned about the seemingly strange floating-point split thresholds. Treat them as essentially checking for equality with zero for your binary features, and validate this interpretation by tracing a few samples through the tree. For the most reliable understanding of your model, focus on feature importance and SHAP values.\n