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Fast Sparse Decision Tree Optimization via Reference Ensembles

This project is the cannonical implementation of the following papers:

• McTavish, H., Zhong, C., Achermann, R., Karimalis, I., Chen, J., Rudin, C., & Seltzer, M. (2022). Fast Sparse Decision Tree Optimization via Reference Ensembles. Proceedings of the AAAI Conference on Artificial Intelligence, 36(9), 9604-9613. https://doi.org/10.1609/aaai.v36i9.21194
• Jimmy Lin, Chudi Zhong, Diane Hu, Cynthia Rudin, and Margo Seltzer. 2020. Generalized and scalable optimal sparse decision trees. In Proceedings of the 37th International Conference on Machine Learning (ICML'20), Vol. 119. JMLR.org, Article 571, 6150–6160.

A scikit-learn compatible library for generating Optimal 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].

Table of Contents

• Installation
• Example
• Frequently Asked Questions
• How to build the project
• Project Versioning
• Project Structure
• Debugging
• Related Work

Installation

GOSDT is available on PyPI and can thus be easily installed using pip.

pip3 install gosdt

Note: Our x86_64 wheels all use modern ISA extensions such AVX to perform fast bitmap operations. If you're running on an older system where that's not possible, we recommend that you build from source following the instructions bellow.

Example

This is a classification example using GOSDT with threshold guessing, lower bound guessing and a depth limit. Additional examples and notebooks are available in the examples/ folder.

import pandas as pd
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.model_selection import train_test_split
from gosdt import ThresholdGuessBinarizer, GOSDTClassifier

# Parameters
GBDT_N_EST = 40
GBDT_MAX_DEPTH = 1
REGULARIZATION = 0.001
SIMILAR_SUPPORT = False
DEPTH_BUDGET = 6
TIME_LIMIT = 60
VERBOSE = True

# Read the dataset
df = pd.read_csv("datasets/compas.csv", sep=",")
X, y = df.iloc[:, :-1], df.iloc[:, -1]
h = df.columns[:-1]

# Train test split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=2021)
print("X train shape:{}, X test shape:{}".format(X_train.shape, X_test.shape))

# Step 1: Guess Thresholds
X_train = pd.DataFrame(X_train, columns=h)
X_test = pd.DataFrame(X_test, columns=h)
enc = ThresholdGuessBinarizer(n_estimators=GBDT_N_EST, max_depth=GBDT_MAX_DEPTH, random_state=2021)
enc.set_output(transform="pandas")
X_train_guessed = enc.fit_transform(X_train, y_train)
X_test_guessed = enc.transform(X_test)
print(f"After guessing, X train shape:{X_train_guessed.shape}, X test shape:{X_test_guessed.shape}")
print("train set column names == test set column names: {list(X_train_guessed.columns)==list(X_test_guessed.columns)}")

# Step 2: Guess Lower Bounds
enc = GradientBoostingClassifier(n_estimators=GBDT_N_EST, max_depth=GBDT_MAX_DEPTH, random_state=42)
enc.fit(X_train_guessed, y_train)
warm_labels = enc.predict(X_train_guessed)

# Step 3: Train the GOSDT classifier
clf = GOSDTClassifier(regularization=REGULARIZATION, similar_support=SIMILAR_SUPPORT, time_limit=TIME_LIMIT, depth_budget=DEPTH_BUDGET, verbose=VERBOSE) 
clf.fit(X_train_guessed, y_train, y_ref=warm_labels)

# Step 4: Evaluate the model
print("Evaluating the model, extracting tree and scores", flush=True)


print(f"Model training time: {clf.result_.time}")
print(f"Training accuracy: {clf.score(X_train_guessed, y_train)}")
print(f"Test accuracy: {clf.score(X_test_guessed, y_test)}")

FAQ

• Does GOSDT (implicitly) restrict the depth of the resulting tree?

  As of 2022, GOSDT With Guesses can now restrict the depth of the resulting tree both implicitly and explicitly. Our primary sparsity constraint is the regularization parameter (lambda) which is used to penalize the number of leaves. As lambda becomes smaller, the generated trees will have more leaves, but the number of leaves doesn't guarantee what depth a tree has since GOSDT generates trees of any shape. As of our 2022 AAAI paper, though, we've allowed users to restrict the depth of the tree. This provides more control over the tree's shape and reduces the runtime. However, the depth constraint is not a substitute for having a nonzero regularization parameter! Our algorithm achieves a better sparsity-accuracy tradeoff, and saves time, with a well-chosen lambda.

• Why does GOSDT run for a long time when the regularization parameter (lambda) is set to zero?

  The running time depends on the dataset itself and the regularization parameter (lambda). In general, setting lambda to 0 will make the running time longer. Setting lambda to 0 is kind of deactivating the branch-and-bound in GOSDT. In other words, we are kind of using brute force to search over the whole space without effective pruning, though dynamic programming can help for computational reuse. In GOSDT, we compare the difference between the upper and lower bound of a subproblem with lambda to determine whether this subproblem needs to be further split. If lambda=0, we can always split a subproblem. Therefore, it will take more time to run. It usually does not make sense to set lambda smaller than 1/n, where n is the number of samples.

• Is there a way to limit the size of the produced tree?

  Regularization parameter (lambda) is used to limit the size of the produced tree (specifically, in GOSDT, it limits the number of leaves of the produced tree). We usually set lambda to [0.1, 0.05, 0.01, 0.005, 0.001], but the value really depends on the dataset. One thing that might be helpful is considering how many samples should be captured by each leaf node. Suppose you want each leaf node to contain at least 10 samples. Then setting the regularization parameter to 10/n is reasonable. In general, the larger the value of lambda is, the sparser a tree you will get.

• In general, how does GOSDT set the regularization parameter?

  GOSDT aims to find an optimal tree that minimizes the training loss with a penalty on the number of leaves. The mathematical description is min loss+lambda*# of leaves. When we run GOSDT, we usually set lambda to different non-zero values and usually not smaller than 1/n. On page 31 Appendix I.6 in our ICML paper, we provide detailed information about the configuration we used to run accuracy vs. sparsity experiments.

How to build the project

Step 1: Install required development tools

GOSDT uses CMake as its default cross-platform build system and Ninja as the default generator for parallel builds. GOSDT relies on pybind11 for Python bindings and scikit-build-core as its Python meta build system for the generation of wheel files. GOSDT also uses delocate, auditwheel and delvewheel to copy all required 3rd-party dynamic libraries into the wheel archive (Each of these different tools are used for the three OS platforms we support: macOS, Linux, and Windows).

Note that delocate, auditwheel and delvewheel are only only needed if building wheels for deployment to PyPI.

macOS: We rely on the brew package manager to install 3rd-party libraries and dependencies.

brew install cmake ninja pkg-config
pip3 install --upgrade scikit-build-core pybind11 delocate

Ubuntu:

sudo apt install -y cmake ninja-build pkg-config patchelf
pip3 install --upgrade scikit-build-core pybind11 auditwheel

Windows: Please make sure that you launch Powershell as Admin.

Step 1.1.: Install Chocolatey

In addition to Windows Package Manager (a.k.a. winget), Chocolatey is used to install tools that are not yet provided by winget. Please follow this guide or use the following commands to install Chocolatey.

Set-ExecutionPolicy Bypass -Scope Process -Force
[System.Net.ServicePointManager]::SecurityProtocol = [System.Net.ServicePointManager]::SecurityProtocol -bor 3072
iex ((New-Object System.Net.WebClient).DownloadString('https://community.chocolatey.org/install.ps1'))

Step 1.2: Install vcpkg

GOSDT requires the C++ package manager vcpkg to install all necessary C and C++ libraries on Windows. Please follow this guide or use the following commands to install vcpkg to C:\vcpkg.

cd C:\
git clone https://github.com/Microsoft/vcpkg.git
.\vcpkg\bootstrap-vcpkg.bat

Once you have installed vcpkg, for example, to C:\vcpkg, you need to...

• Update your PATH variable to include C:\vcpkg.
• Add a new environment variable VCPKG_INSTALLATION_ROOT with a value of C:\vcpkg.

The following Powershell script modifies the system environment permanently. In other words, all users can see these two new variables.

$vcpkg = "C:\vcpkg"
$old = (Get-ItemProperty -Path 'Registry::HKEY_LOCAL_MACHINE\System\CurrentControlSet\Control\Session Manager\Environment' -Name PATH).path
$new = "$old;$vcpkg"
Set-ItemProperty -Path 'Registry::HKEY_LOCAL_MACHINE\System\CurrentControlSet\Control\Session Manager\Environment' -Name PATH -Value $new
Set-ItemProperty -Path 'Registry::HKEY_LOCAL_MACHINE\System\CurrentControlSet\Control\Session Manager\Environment' -Name VCPKG_INSTALLATION_ROOT -Value $vcpkg

You can verify whether the new variable VCPKG_INSTALLATION_ROOT is set properly by typing the following command in Powershell: Note that you may need to restart your terminal or reboot your computer to apply the changes.

$ENV:VCPKG_INSTALLATION_ROOT

Step 1.3: Install required development tools

winget install Kitware.CMake
choco install -y ninja
choco install -y pkgconfiglite
pip3 install --upgrade scikit-build
pip3 install --upgrade delvewheel

If choco install -y pkgconfiglite reports SSL/TLS-related errors, please use the following commands to install it manually.

Invoke-WebRequest -UserAgent "Wget" -Uri "http://downloads.sourceforge.net/project/pkgconfiglite/0.28-1/pkg-config-lite-0.28-1_bin-win32.zip" -OutFile "C:\pkgconfig.zip"
Expand-Archive "C:\pkgconfig.zip" -DestinationPath "C:\"
Copy-Item "C:\pkg-config-lite-0.28-1\bin\pkg-config.exe" "C:\Windows"
Remove-Item "C:\pkg-config-lite-0.28-1" -Force -Recurse
Remove-Item "C:\pkgconfig.zip"

Step 2: Install required 3rd-party libraries

GOSDT relies on IntelTBB for concurrent data structures, and GMP for fast bitwise operations.

macOS:

brew install tbb gmp

Ubuntu:

sudo apt install -y libtbb-dev libgmp-dev

Windows:

vcpkg install tbb:x64-windows
vcpkg install gmp:x64-windows

Step 3: Build the project

There are two main methods for building the project:

• for local use (and development).
• wheel generation for distribution and deployment to PYPI.

The following assumes that your working directory is the project root.

Method 1: Local use/development and debugging

Note that the following command also produces the gosdt_cli target that can be used to hook gdb or other debuggers/sanitizers into the GOSDT C++ implementation. The project build artifacts can be found in the pyproject-build directory.

pip3 install .

Method 2: Wheel generation

macOS:

pip3 wheel --no-deps . -w dist/
delocate-wheel -w dist -v dist/gosdt-*.whl

Windows:

pip3 wheel --no-deps . -w dist/
python3 -m delvewheel repair --no-mangle-all --add-path "$ENV:VCPKG_INSTALLATION_ROOT\installed\x64-windows\bin" dist/gosdt-1.0.5-cp310-cp310-win_amd64.whl -w dist

Ubuntu:

We are using Ubuntu as the host, but manylinux wheel building relies on Docker. For this specific target we recommend using the cibuildwheel tool which hides some of the painful details related to wheel building for manylinux.

pipx run cibuildwheel

Project Versioning

This project uses the setuptools_scm tool to perform project versioning for the built Python library. This tool uses git commit tags to pick a reasonable version number. In the odd case where one wishes to build this project while removing all references to the git repo, there is a patch for pyproject.toml included at scripts/non_git.patch

Project Structure

This repository contains the following directories:

• datasets: Datasets that are used to generate plots and figures from the papers and run examples.
• examples: Contains sample code and notebooks demonstrating how to use the gosdt library.
• scripts/build: Scripts used while building the python library.
• scripts/gosdt: Scripts to replicate the plots and figures from the ICML 2020 paper[5].
• scripts/gosdt-guesses: Scripts to replicate the plots and figures from the AAAI 2022 paper[9]
• src: Implementation of the gosdt Python and C++ library.
• tests: pytest tests for the Python library.

Debugging

Unfortunately, there is no super clear way to run gdb on the final python version of the project, for this we've added the debug configuration option to the GOSDTClassifier class. Enabling this flag will create a debug_(current time) directory that is populated with a serialized copy of the Dataset and Configuration classes as well as some other useful debugging information.

We additionaly provide the gosdt_cli target which is a C++ terminal application that takes as an argument the path to a debug_* directory and runs the GOSDT algorithm on it. This enables the developper to use standard C++ tools to debug the algorithm, such as debuggers or sanitizers.

An example that uses the debug flag can be found at examples/debug.py

Related Work

[1] Aglin, G.; Nijssen, S.; and Schaus, P. 2020. Learning optimal decision trees using caching branch-and-bound search. In AAAI Conference on Artificial Intelligence, volume 34, 3146–3153.

[2] Angelino, E.; Larus-Stone, N.; Alabi, D.; Seltzer, M.; and Rudin, C. 2018. Learning Certifiably Optimal Rule Lists for Categorical Data. Journal of Machine Learning Research, 18(234): 1–78.

[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.

[9] McTavish, H., Zhong, C., Achermann, R., Karimalis, I., Chen, J., Rudin, C., & Seltzer, M. (2022). Fast Sparse Decision Tree Optimization via Reference Ensembles. Proceedings of the AAAI Conference on Artificial Intelligence, 36(9), 9604-9613.