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Optimal decision trees for categorical data via integer programming
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. Here we show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.
Properly Learning Decision Trees in almost Polynomial Time
We give an n O (log log n ) -time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over { ± 1} n . Even in the realizable setting, the previous fastest runtime was n O (log n ) , a consequence of a classic algorithm of Ehrenfeucht and Haussler. Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of O’Donnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be “pruned” so that every variable in the resulting tree is influential.
Linear model decision trees as surrogates in optimization of engineering applications
Machine learning models are promising as surrogates in optimization when replacing difficult to solve equations or black-box type models. This work demonstrates the viability of linear model decision trees as piecewise-linear surrogates in decision-making problems. Linear model decision trees can be represented exactly in mixed-integer linear programming (MILP) and mixed-integer quadratic constrained programming (MIQCP) formulations. Furthermore, they can represent discontinuous functions, bringing advantages over neural networks in some cases. We present several formulations using transformations from Generalized Disjunctive Programming (GDP) formulations and modifications of MILP formulations for gradient boosted decision trees (GBDT). We then compare the computational performance of these different MILP and MIQCP representations in an optimization problem and illustrate their use on engineering applications. Importantly, we observe faster solution times for optimization problems with linear model decision tree surrogates when compared with GBDT surrogates using the Optimization and Machine Learning Toolkit (OMLT).
Enhanced Oblique Decision Tree Enabled Policy Extraction for Deep Reinforcement Learning in Power System Emergency Control
Deep reinforcement learning (DRL) algorithms have successfully solved many challenging problems in various power system control scenarios. However, their decision-making process is usually regarded as black-boxes. Furthermore, how DRL models interact with human intelligence remains an open problem. Thus, this paper proposes a policy extraction framework to extract a complex DRL model into an explainable policy. This framework includes three parts: 1) DRL training and data generation. We train an agent for a specific control task and generate data, which contains the control policy of the agent. 2) Policy extraction. We propose an information gain rate based weighted oblique decision tree (IGR-WODT) for DRL policy extraction. 3) Policy evaluation. We define three metrics to evaluate the performance of the proposed approach. A case study for the under-voltage load shedding problem shows that the IGR-WODT presents a performance enhancement compared with DRL, weighted oblique decision tree, and univariate decision tree. The proposed policy extraction method could provide an intuitive explanation of the neural network decision-making process to the dispatchers when making final decisions on power grid operation. Also, the resulted rule-based controller could replace the deep neural network-based controller in many field edge devices with limited computing resources, providing comparable performance.
PySIDT: Subgraph Isomorphic Decision Trees for Molecular Property Prediction
Accurate molecular property prediction is important across all fields of chemistry. Deep neural networks (DNNs) have become increasingly popular due to their ability to train automatically, avoiding the incredibly tedious process of constructing and extending traditional property estimation schemes. However, DNNs require large amounts of training data, are challenging to interpret, require large amounts of memory to load even during inference, and have severe difficulties incorporating qualitative chemical knowledge, which are often desired for molecular property prediction tasks. Here, in this study, we present PySIDT (https://github.com/zadorlab/PySIDT), a software for training and running inference on Subgraph Isomorphic Decision Trees (SIDTs). SIDTs are graph-based decision trees made of nodes associated with molecular substructures. Inference is done by descending target molecular structures down the decision tree to nodes with matching subgraph isomorphic substructures and making predictions based on the final (most specific) nodes matched. SIDTs scale down well to dataset sizes much smaller than is feasible for DNNs. As trees of molecular substructures, SIDTs are inherently readable and easy to visualize, making them easy to analyze. They are also straightforward to extend and retrain, facilitate uncertainty estimation, and enable easy integration of expert knowledge. We demonstrate the SIDT approach discussing its application to a diverse range of molecular prediction tasks: rate coefficient estimation, diffusion coefficient estimation, thermochemistry estimation, transition state bond stretch prediction, p K a prediction, stability of molecular structures, stability of surface structures, and prediction of surface lateral interaction energetics. Additionally, we demonstrate the power of the SIDT algorithms in two direct learning curve vanilla comparisons with the popular DNN-based software Chemprop and the popular gradient boosted trees-based software XGBoost on enthalpy of formation and rate coefficient prediction tasks. In particular, in the enthalpy of formation case, vanilla PySIDT is able to outperform vanilla Chemprop and XGBoost across the full range of training/validation set sizes out to 11,560 data points.
Disentangling error structures of precipitation datasets using decision trees
Characterizing error structures in precipitation products not only facilitates their proper applications for scientific and practical purposes but also helps improve their retrieval algorithms and processing methods. Despite the fact that multiple precipitation products have been assessed in the literature, factors that affect their error structures remain inadequately addressed. By interpreting 60 binary decision trees, this study disentangles the error characteristics of precipitation products in terms of their spatiotemporal patterns and geographical factors. Three independent precipitation products - two satellite-based and one reanalysis datasets: the Integrated Multi-satellitE Retrievals for GPM (Global Precipitation Measurement) late run (IMERG-L), Soil Moisture to Rain-Advanced SCATterometer (SM2RAIN-ASCAT), and the Modern-Era Retrospective analysis for Research and Applications, Version 2 uncorrected precipitation output (MERRA2-UC), are evaluated across the contiguous United States from 2010 to 2019. Here, the ground-based Stage IV precipitation dataset is used as the ground truth. Results indicate that the MERRA2-UC outperforms the IMERG-L and SM2RAIN-ASCAT with higher accuracy and more stable interannual patterns for the analysis period. Decision trees cross-assess three spatiotemporal factors and find that the underestimation of MERRA2-UC occurs in the east of the Rocky Mountains, and SM2RAIN-ASCAT underestimates precipitation over high latitudes, especially in winter. Additionally, the decision tree method ascribes system errors to nine different geographical characteristics, of which the distance to the coast, soil type, and DEM are the three dominant features. On the other hand, the land cover type, topography position index, and aspect are three relatively weak factors.
Biomass for Carbon Removal and Storage (BiCRS) Counterfactual Decision Tree
Counterfactual is the term used to describe a "business-as-usual" scenario which used as a baseline to compare against a new project, allowing the calculation of net impacts for a life cycle analysis (LCA). The choice of counterfactual is critical for determining the results from LCA and must be carefully justified to ensure a fair and accurate comparison. Using forest residues as an example, this decision tree illustrates decision points to be considered for sustainable biomass sourcing and provides a framework for estimating the carbon emissions or storage under the "business-as-usual” scenarios for biomass otherwise destined for use in Biomass for Carbon Removal and Storage (BiCRS) projects.
Nanosecond machine learning regression with deep boosted decision trees in FPGA for high energy physics
We present a novel application of the machine learning / artificial intelligence method called boosted decision trees to estimate physical quantities on field programmable gate arrays (FPGA). The software package fwXmachina features a new architecture called parallel decision paths that allows for deep decision trees with arbitrary number of input variables. It also features a new optimization scheme to use different numbers of bits for each input variable, which produces optimal physics results and ultraefficient FPGA resource utilization. Problems in high energy physics of proton collisions at the Large Hadron Collider (LHC) are considered. Estimation of missing transverse momentum (E T miss ) at the first level trigger system at the High Luminosity LHC (HL-LHC) experiments, with a simplified detector modeled by Delphes, is used to benchmark and characterize the firmware performance. The firmware implementation with a maximum depth of up to 10 using eight input variables of 16-bit precision gives a latency value of $\mathcal{O}$(10) ns, independent of the clock speed, and $\mathcal{O}$(0.1)% of the available FPGA resources without using digital signal processors.
Using Boosted Decision Trees to Select High Quality Measurements in the Mu2e Experiment at Fermilab
This thesis presents the implementation and evaluation of a Boosted Decision Tree (BDT) model to improve the selection of high-quality track measurements in the Mu2e experiment at Fermilab. The Mu2e experiment is a high-energy physics experiments seeking to observe a rare theoretical physics process known as Charged Lepton Flavor Violation. A significant challenge faced by the Mu2e experiment are so-called background events, which are events whose data mimics that of the rare physics process the experiment seeks to observe. Without a mechanism to reduce background, it would be impossible to know whether Charged Lepton Flavor Violation occurred or not. To this end, high-quality track measurements must be distinguished from low-quality track measurements. A track can be conceived of as the reconstructed path of a particle that traveled through the Mu2e detector. In addition to other data, data about such tracks is stored using a C++-based framework, specific to the domain of high-energy physics, known as ROOT. A boosted decision tree model was trained using ROOT’s Toolkit For Multivariate Analysis by leveraging variables ancillary to track quality. In evaluation, the BDT achieves a ROC-AUC of 0.927 in discriminating good-quality tracks from poor-quality tracks. Such a score is indicative of both strong discrimination and strong generalization. Subsequently, it is shown that applying a BDT-based quality cut to the distribution of particle momenta significantly enhances the signal-to-background distinction for signal electrons, paving the way for improved sensitivity to Charged Lepton Flavor Violation.
Decision Tree for Variable Selection vs. Impact on Durability for Biomass and Biochar Burial Pathways [Slides]
Quantifying durability for lower-TRL BiCRS pathways has been challenging as limited data are available from real-world projects and long-term experiments, resulting in an overall lack of scientific consensus. We develop a decision tree that aims to summarize the current scientific understanding and state-of-the-art project experience. The decision tree can be used to (1) guide the selection of key variables and evaluate their relative impact on durability, (2) identify data and knowledge gaps for future research.
Development of heavy-duty vehicle representative driving cycles via decision tree regression
Previously, researchers who developed representative driving cycles mainly focused on light-duty vehicles and only considered vehicle speed and related derivations. In this paper, we propose a novel approach to develop representative cycles for heavy-duty vehicles. By implementing decision tree regression (DTR) to the Fleet DNA on-road vehicle data, a broader set of metrics, such as engine power and fuel consumption, can be used for more robust cycle development. Additionally, the influence of each metric on the regression target is also accounted for by a weighted number derived through the DTR to enhance the representativenss of the developed cycle. As case studies, we applied the proposed method to five heavy-duty vocations (drayage, long haul, regional haul, local delivery, and transit bus) and derived the most representative cycle, as well as four extreme cycles (maximal energy consumption, maximal power-weighted work, maximal fraction of high speed, and minimal fuel economy) to advance the related alternative powertrain design.
Hyperplane decision trees as piecewise linear surrogate models for chemical process design
Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.
Decision Tree Regression to Identify Representative Road Sections for Evaluating Performance of Connected and Automated Class 8 Tractors
Currently, connected and autonomous vehicle (CAV) technology is being developed for Class 8 tractor trucks aimed at improved safety and fuel economy and reduced CO2 emissions. Despite extensive efforts conducted across the world, the reported efficiency gains were varied from different research groups, raising concerns about the fidelity of models, the performance of control, and the effectiveness of the experimental validation. One root cause for this variation stems from the fact that the efficiency gain obtained from the CAV is sensitive to real-world conditions, including surrounding traffic and road grade. This study presents an approach aimed at identifying representative public road sections and facilitating CAV research from this perspective. By employing the decision tree regression (DTR) method to the Fleet DNA database, the most representative road sections can be identified. High-level metrics and detailed information of the derived road sections are also illustrated and discussed, which demonstrate their representativeness and the effectiveness of the approach. Meanwhile, the capability of this approach can be easily extended by integrating specific constraints into the DTR algorithm. As an example, a specific representative road section with an aggressive road grade profile was also provided via this approach.
Nanosecond anomaly detection with decision trees and real-time application to exotic Higgs decays
Abstract We present an interpretable implementation of the autoencoding algorithm, used as an anomaly detector, built with a forest of deep decision trees on FPGA, field programmable gate arrays. Scenarios at the Large Hadron Collider at CERN are considered, for which the autoencoder is trained using known physical processes of the Standard Model. The design is then deployed in real-time trigger systems for anomaly detection of unknown physical processes, such as the detection of rare exotic decays of the Higgs boson. The inference is made with a latency value of 30 ns at percent-level resource usage using the Xilinx Virtex UltraScale+ VU9P FPGA. Our method offers anomaly detection at low latency values for edge AI users with resource constraints.
Boosted decision tree reweighting of simulated neutrino interactions for O ( 1 ) GeV neutrino cross-section measurements
This paper illustrates a generic method for multidimensional reweighting of O ( 1 ) GeV neutrino interaction Monte Carlo samples. The reweighting is based on a boosted decision tree algorithm trained on high-dimensional space in detector final-state observables. This enables one generator’s events to be reweighted so that its reconstructed particle content and kinematics distributions, as well as detector efficiency, match those of a target model. The approach establishes an efficient way to reuse legacy Monte Carlo data, avoiding regeneration. As an example, we test its use in a measurement of transverse kinematic imbalance of the μ - and proton in charged-current quasielastic like ν μ events from the MINERvA experiment.
FEMP Facility Evaluation (Audit) Decision Tree
This document is a resource to be used in concert with FEMP Audit Definitions, FEMP Consolidated Facility Management Guidance, and agency best practices and expert judgment—for agencies to use to determine the best approaches to evaluate their facilities. It features a decision tree that provides a framework for agencies to interpret gathered facility data to understand the existing conditions; benchmark the facility against others in the portfolio to determine whether an on-site or remote audit is appropriate for a facility; determine the best remote or on-site audit level of detail to meet agency facility auditing goals, such as meeting Energy Independence and Security Act of 2007 requirements and developing projects; and improve their energy and water management programs.
Decision-tree structures utilizing a phase-transition material
The rich internal physics due to competing electronic phases present in phase-transition materials such as VO2 offer the potential for compact building block design for emerging non-von Neumann computing technologies. Here, based on the relaxation dynamics of an insulator-metal phase transition, we demonstrate experimentally a decision-tree classifier embedded within a single volatile resistive switching device. The tree is constructed by the combination of the voltage pulse and relaxation time and can adapt to different tasks. We use machine learning to analyze the relaxation process, enabling a predictive voltage-relaxation time phase diagram for the electrical resistance state. Classification of the etiology of the chronic cough is presented as a proof-of-principle use case. Further, our approach can be generalized to broader classes of solid-state and solid-liquid interfacial systems that demonstrate a variety of phase relaxations.