This code creates optimized sparse decision trees. It is a direct competitor of CART[3] and C4.5 [6], as well as DL8.5[1], BinOct[7], and OSDT[4]. Its advantage over CART and C4.5 is that the trees are globally optimized, not constructed just from the top down. This makes it slower than CART, but it provides better solutions. On the other hand, it tends to be faster than other optimal decision tree methods because it uses bounds to limit the search space, and uses a black box model (a boosted decision tree) to “guess” information about the optimal tree. It takes only seconds or a few minutes on most datasets.
To make it run faster, please use the options to limit the depth of the tree, and increase the regularization parameter above 0.02. If you run the algorithm without a depth constraint or set the regularization too small, it will run more slowly.
This work builds on a number of innovations for scalable construction of optimal tree-based classifiers: Scalable Bayesian Rule Lists[8], CORELS[2], OSDT[4], and, most closely, GOSDT[5].
You may use the following commands to install GOSDT along with its dependencies on macOS, Ubuntu and Windows.
You need Python 3.7 or later to use the module gosdt in your project.
pip3 install attrs packaging editables pandas scikit-learn sortedcontainers gmpy2 matplotlib
pip3 install gosdtYou can find a list of available wheels on PyPI.
Please feel free to open an issue if you do not see your distribution offered.
Please refer to the manual to build the C++ command line interface and the Python extension module and run the experiment with example datasets on your machine.
The configuration is a JSON object and has the following structure and default values:
{
"regularization": 0.05,
"depth_budget": 0,
"reference_LB": false,
"path_to_labels": "",
"time_limit": 0,
"uncertainty_tolerance": 0.0,
"upperbound": 0.0,
"worker_limit": 1,
"stack_limit": 0,
"precision_limit": 0,
"model_limit": 1,
"verbose": false,
"diagnostics": false,
"balance": false,
"look_ahead": true,
"similar_support": true,
"cancellation": true,
"continuous_feature_exchange": false,
"feature_exchange": false,
"feature_transform": true,
"rule_list": false,
"non_binary": false,
"costs": "",
"model": "",
"timing": "",
"trace": "",
"tree": "",
"profile": ""
}regularization
- Values: Decimal within range [0,1]
- Description: Used to penalize complexity. A complexity penalty is added to the risk in the following way.
ComplexityPenalty = # Leaves x regularization - Default: 0.05
- Note: We highly recommend setting the regularization to a value larger than 1/num_samples. A small regularization could lead to a longer training time. If a smaller regularization is preferred, you must set the parameter
allow_small_regto true, which by default is false.
allow_small_reg
- Values: true or false
- Description: Flag for allowing regularization < 1/n , where n = num_samples (if false, regularizations below 1/n are automatically set to 1/n)
- Default: false
depth_budget
- Values: Integers >= 1
- Description: Used to set the maximum tree depth for solutions, counting a tree with just the root node as depth 1. 0 means unlimited.
- Default: 0
reference_LB
- Values: true or false
- Description: Enables using a vector of misclassifications from another (reference) model to lower bound our own misclassifications
- Default: false
- Note: If
reference_LBis set to true, you must provide a validpath_to_labels.
path_to_labels
- Values: String representing a path to a file.
- Description: This file must be a single-column csv representing a class prediction for each training observation (in the same order as for the training data, using the same class labels as for the training data, and predicting each class present in the training set at least once across all training points). Typically this csv is obtained by fitting a gradient boosted decision tree model on the training data, and saving its training set predictions as a csv file.
- Example for a dataset with classes 1 and 0:
predicted_class 0 1 1 1 0 - Default: Empty string
time_limit
- Values: Decimal greater than or equal to 0
- Description: A time limit upon which the algorithm will terminate. If the time limit is reached, the algorithm will terminate with an error.
- Special Cases: When set to 0, no time limit is imposed.
- Default: 0
balance
- Values: true or false
- Description: Enables overriding the sample importance by equalizing the importance of each present class
- Default: false
cancellation
- Values: true or false
- Description: Enables propagate up the dependency graph of task cancellations
- Default: true
look_ahead
- Values: true or false
- Description: Enables the one-step look-ahead bound implemented via scopes
- Default: true
similar_support
- Values: true or false
- Description: Enables the similar support bound implemented via the distance index
- Default: true
feature_exchange
- Values: true or false
- Description: Enables pruning of pairs of features using subset comparison
- Default: false
continuous_feature_exchange
- Values: true or false
- Description: Enables pruning of pairs continuous of feature thresholds using subset comparison
- Default: false
feature_transform
- Values: true or false
- Description: Enables the equivalence discovery through simple feature transformations
- Default: true
rule_list
- Values: true or false
- Description: Enables rule-list constraints on models
- Default: false
non_binary
- Values: true or false
- Description: Enables non-binary encoding
- Default: false
diagnostics
- Values: true or false
- Description: Enables printing of diagnostic trace when an error is encountered to standard output
- Default: false
verbose
- Values: true or false
- Description: Enables printing of configuration, progress, and results to standard output
- Default: false
uncertainty_tolerance
- Values: Decimal within range [0,1]
- Description: Used to allow early termination of the algorithm. Any models produced as a result are guaranteed to score within the lowerbound and upperbound at the time of termination. However, the algorithm does not guarantee that the optimal model is within the produced model unless the uncertainty value has reached 0.
- Default: 0.0
upperbound
- Values: Decimal within range [0,1]
- Description: Used to limit the risk of model search space. This can be used to ensure that no models are produced if even the optimal model exceeds a desired maximum risk. This also accelerates learning if the upperbound is taken from the risk of a nearly optimal model.
- Special Cases: When set to 0, the bound is not activated.
- Default: 0.0
model_limit
- Values: Decimal greater than or equal to 0
- Description: The maximum number of models that will be extracted into the output.
- Special Cases: When set to 0, no output is produced.
- Default: 1
precision_limit
- Values: Decimal greater than or equal to 0
- Description: The maximum number of significant figures considered when converting ordinal features into binary features.
- Special Cases: When set to 0, no limit is imposed.
- Default: 0
stack_limit
- Values: Decimal greater than or equal to 0
- Description: The maximum number of bytes considered for use when allocating local buffers for worker threads.
- Special Cases: When set to 0, all local buffers will be allocated from the heap.
- Default: 0
worker_limit
- Values: Decimal greater than or equal to 1
- Description: The maximum number of threads allocated to executing th algorithm.
- Special Cases: When set to 0, a single thread is created for each core detected on the machine.
- Default: 1
costs
- Values: string representing a path to a file.
- Description: This file must contain a CSV representing the cost matrix for calculating loss.
- The first row is a header listing every class that is present in the training data
- Each subsequent row contains the cost incurred of predicitng class i when the true class is j, where i is the row index and j is the column index
- Example where each false negative costs 0.1 and each false positive costs 0.2 (and correct predictions costs 0.0):
negative,positive 0.0,0.1 0.2,0.0 - Example for multi-class objectives:
class-A,class-B,class-C 0.0,0.1,0.3 0.2,0.0,0.1 0.8,0.3,0.0 - Note: costs values are not normalized, so high cost values lower the relative weight of regularization
- Special Case: When set to empty string, a default cost matrix is used which represents unweighted training misclassification.
- Default: Empty string
model
- Values: string representing a path to a file.
- Description: The output models will be written to this file.
- Special Case: When set to empty string, no model will be stored.
- Default: Empty string
profile
- Values: string representing a path to a file.
- Description: Various analytics will be logged to this file.
- Special Case: When set to empty string, no analytics will be stored.
- Default: Empty string
timing
- Values: string representing a path to a file.
- Description: The training time will be appended to this file.
- Special Case: When set to empty string, no training time will be stored.
- Default: Empty string
trace
- Values: string representing a path to a directory.
- Description: snapshots used for trace visualization will be stored in this directory
- Special Case: When set to empty string, no snapshots are stored.
- Default: Empty string
tree
- Values: string representing a path to a directory.
- Description: snapshots used for trace-tree visualization will be stored in this directory
- Special Case: When set to empty string, no snapshots are stored.
- Default: Empty string
Example code to run GOSDT with threshold guessing, lower bound guessing, and depth limit. The example python file is available in gosdt/example.py. A tutorial ipython notebook is available in gosdt/tutorial.ipynb.
import pandas as pd
import numpy as np
import time
import pathlib
from sklearn.ensemble import GradientBoostingClassifier
from model.threshold_guess import compute_thresholds
from model.gosdt import GOSDT
# read the dataset
df = pd.read_csv("experiments/datasets/fico.csv")
X, y = df.iloc[:,:-1].values, df.iloc[:,-1].values
h = df.columns[:-1]
# GBDT parameters for threshold and lower bound guesses
n_est = 40
max_depth = 1
# guess thresholds
X = pd.DataFrame(X, columns=h)
print("X:", X.shape)
print("y:",y.shape)
X_train, thresholds, header, threshold_guess_time = compute_thresholds(X, y, n_est, max_depth)
y_train = pd.DataFrame(y)
# guess lower bound
start_time = time.perf_counter()
clf = GradientBoostingClassifier(n_estimators=n_est, max_depth=max_depth, random_state=42)
clf.fit(X_train, y_train.values.flatten())
warm_labels = clf.predict(X_train)
elapsed_time = time.perf_counter() - start_time
lb_time = elapsed_time
# save the labels from lower bound guesses as a tmp file and return the path to it.
labelsdir = pathlib.Path('/tmp/warm_lb_labels')
labelsdir.mkdir(exist_ok=True, parents=True)
labelpath = labelsdir / 'warm_label.tmp'
labelpath = str(labelpath)
pd.DataFrame(warm_labels, columns=["class_labels"]).to_csv(labelpath, header="class_labels",index=None)
# train GOSDT model
config = {
"regularization": 0.001,
"depth_budget": 5,
"warm_LB": True,
"path_to_labels": labelpath,
"time_limit": 60,
"similar_support": False
}
model = GOSDT(config)
model.fit(X_train, y_train)
print("evaluate the model, extracting tree and scores", flush=True)
# get the results
train_acc = model.score(X_train, y_train)
n_leaves = model.leaves()
n_nodes = model.nodes()
time = model.utime
print("Model training time: {}".format(time))
print("Training accuracy: {}".format(train_acc))
print("# of leaves: {}".format(n_leaves))
print(model.tree)
Output
X: (10459, 23)
y: (10459,)
gosdt reported successful execution
training completed. 1.658/0.098/1.756 (user, system, wall), mem=364 MB
bounds: [0.290914..0.290914] (0.000000) loss=0.282914, iterations=13569
evaluate the model, extracting tree and scores
Model training time: 1.6584229469299316
Training accuracy: 0.7170857634573095
# of leaves: 8
if ExternalRiskEstimate<=67.5 = 1 and MSinceMostRecentInqexcl7days<=-7.5 = 1 then:
predicted class: 1
misclassification penalty: 0.027
complexity penalty: 0.001
else if ExternalRiskEstimate<=67.5 != 1 and MSinceMostRecentInqexcl7days<=-7.5 = 1 then:
predicted class: 0
misclassification penalty: 0.006
complexity penalty: 0.001
else if ExternalRiskEstimate<=74.5 = 1 and MSinceMostRecentInqexcl7days<=-7.5 != 1 and MSinceMostRecentInqexcl7days<=0.5 = 1 and PercentTradesWBalance<=80.5 = 1 then:
predicted class: 1
misclassification penalty: 0.071
complexity penalty: 0.001
else if ExternalRiskEstimate<=74.5 != 1 and MSinceMostRecentInqexcl7days<=-7.5 != 1 and MSinceMostRecentInqexcl7days<=0.5 = 1 and PercentTradesWBalance<=80.5 = 1 then:
predicted class: 0
misclassification penalty: 0.061
complexity penalty: 0.001
else if ExternalRiskEstimate<=78.5 = 1 and MSinceMostRecentInqexcl7days<=-7.5 != 1 and MSinceMostRecentInqexcl7days<=0.5 = 1 and PercentTradesWBalance<=80.5 != 1 then:
predicted class: 1
misclassification penalty: 0.033
complexity penalty: 0.001
else if ExternalRiskEstimate<=78.5 != 1 and MSinceMostRecentInqexcl7days<=-7.5 != 1 and MSinceMostRecentInqexcl7days<=0.5 = 1 and PercentTradesWBalance<=80.5 != 1 then:
predicted class: 0
misclassification penalty: 0.005
complexity penalty: 0.001
else if ExternalRiskEstimate<=67.5 = 1 and MSinceMostRecentInqexcl7days<=-7.5 != 1 and MSinceMostRecentInqexcl7days<=0.5 != 1 then:
predicted class: 1
misclassification penalty: 0.026
complexity penalty: 0.001
else if ExternalRiskEstimate<=67.5 != 1 and MSinceMostRecentInqexcl7days<=-7.5 != 1 and MSinceMostRecentInqexcl7days<=0.5 != 1 then:
predicted class: 0
misclassification penalty: 0.054
complexity penalty: 0.001
This repository contains the following directories and files:
- .github: Configurations for GitHub action runners.
- doc: Documentation
- experiments: Datasets and their configurations to run experiments
- gosdt: Jupyter notebook, Python implementation and wrappers around C++ implementation
- gosdt.xcodeproj: Xcode project file for Mac users (Intel x86-64 and Apple Silicon)
- include: Required 3rd-party header-only libraries
- log: Log files
- src: Source files for C++ implementation and Python binding
- test: Source files for unit tests
- build.py: Python script that builds the project automatically
- CMakeLists.txt: Configuration file for the CMake build system
- pyproject.toml: Configuration file for the SciKit build system
- setup.py: Python script that builds the wheel file
If you run into any issues when running GOSDT, consult the FAQs first.
This software is licensed under a 3-clause BSD license (see the LICENSE file for details).
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[3] Breiman, L.; Friedman, J.; Stone, C. J.; and Olshen, R. A. 1984. Classification and Regression Trees. CRC press.
[4] Hu, X.; Rudin, C.; and Seltzer, M. 2019. Optimal sparse decision trees. In Advances in Neural Information Processing Systems, 7267–7275.
[5] Lin, J.; Zhong, C.; Hu, D.; Rudin, C.; and Seltzer, M. 2020. Generalized and scalable optimal sparse decision trees. In International Conference on Machine Learning (ICML), 6150–6160.
[6] Quinlan, J. R. 1993. C4.5: Programs for Machine Learning. Morgan Kaufmann
[7] Verwer, S.; and Zhang, Y. 2019. Learning optimal classification trees using a binary linear program formulation. In AAAI Conference on Artificial Intelligence, volume 33, 1625–1632.
[8] Yang, H., Rudin, C., & Seltzer, M. (2017, July). Scalable Bayesian rule lists. In International Conference on Machine Learning (ICML) (pp. 3921-3930). PMLR.