Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear relations in a compact human comprehensible model, by recursively splitting the population and predicting a distinct survival distribution in each leaf node. We use dynamic programming to provide the first survival tree method with optimality guarantees, enabling the assessment of the optimality gap of heuristics. We improve the scalability of our method through a special algorithm for computing trees up to depth two. The experiments show that our method's run time even outperforms some heuristics for realistic cases while obtaining similar out-of-sample performance with the state-of-the-art.
Tree-based models are increasingly popular due to their ability to identify complex relationships that are beyond the scope of parametric models. Survival tree methods adapt these models to allow for the analysis of censored outcomes, which often appear in medical data. We present a new Optimal Survival Trees algorithm that leverages mixed-integer optimization (MIO) and local search techniques to generate globally optimized survival tree models. We demonstrate that the OST algorithm improves on the accuracy of existing survival tree methods, particularly in large datasets.
Credit scoring plays a vital role in the field of consumer finance. Survival analysis provides an advanced solution to the credit-scoring problem by quantifying the probability of survival time. In order to deal with highly heterogeneous industrial data collected in Chinese market of consumer finance, we propose a nonparametric ensemble tree model called gradient boosting survival tree (GBST) that extends the survival tree models with a gradient boosting algorithm. The survival tree ensemble is learned by minimizing the negative log-likelihood in an additive manner. The proposed model optimize…
Recently we proposed a general, ensemble-based feature engineering wrapper (FEW) that was paired with a number of machine learning methods to solve regression problems. Here, we adapt FEW for supervised classification and perform a thorough analysis of fitness and survival methods within this framework. Our tests demonstrate that two fitness metrics, one introduced as an adaptation of the silhouette score, outperform the more commonly used Fisher criterion. We analyze survival methods and demonstrate that $ε$-lexicase survival works best across our test problems, followed by random survival wh…
Enhancing Visual Interpretability and Explainability in Functional Survival Trees and Forests
Department of Mathematics and Physics, University of Campania Luigi Vanvitelli（数学与物理系，坎帕尼亚卢igi vanvitelli大学）；Department of Economics, Statistics and Business, Universitas Mercatorum（经济学、统计学与商业系，默卡托鲁姆大学）
University of California, Los Angeles（加州大学洛杉矶分校）；Nuffield College, Oxford University（牛津大学纳菲尔德学院）；Oxford Man Institute, Oxford University（牛津大学牛津曼研究所）；Alan Turing Institute（艾伦·图灵研究所）
Given the limited pool of donor organs, accurate predictions of survival on the wait list and post transplantation are crucial for cardiac transplantation decisions and policy. However, current clinical risk scores do not yield accurate predictions. We develop a new methodology (ToPs, Trees of Predictors) built on the principle that specific predictors should be used for specific clusters within the target population. ToPs discovers these specific clusters of patients and the specific predictor that perform best for each cluster. In comparison with current clinical risk scoring systems, our me…
Supervised Machine Learning for Breast Cancer Risk Factors Analysis and Survival Prediction
LYRICA Laboratory（LYRICA实验室）；School of Information Sciences（信息科学学院）；Laboratoire Pathologie Humaine, Biomedecine et Environnement（人类病理、生物医学与环境实验室）；Faculty of Medicine and Pharmacy（医学与药学院）
Delft University of Technology（代尔夫特理工大学）；LAAS CNRS（法国国家科学研究中心LAAS实验室）；RMIT University（皇家墨尔本理工大学）；University of Melbourne（墨尔本大学）；Monash University（莫纳什大学）；DATA61（DATA61研究所）
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy. A commonly criticised point, however, is that the resulting trees may not necessarily be the best representation of the data in terms of accuracy and size. In recent years, this motivated the development of optimal classification tree algorithms that globally optimise the decision tree in contrast to heuristic methods that perform a sequence of locally optim…
Heterogeneous Treatment Effect in Time-to-Event Outcomes: Harnessing Censored Data with Recursively Imputed Trees
Faculty of Data and Decisions Sciences, Technion - Israel Institute of Technology（数据与决策科学学院，技术ion-以色列理工学院）；Department of Statistics and Operations Research, Tel Aviv University（统计与运筹学系，特拉维夫大学）
Shandong Normal University（山东师范大学）；Nanjing University of Science and Technology（南京理工大学）
Source code can be parsed into the abstract syntax tree (AST) based on defined syntax rules. However, in pre-training, little work has considered the incorporation of tree structure into the learning process. In this paper, we present TreeBERT, a tree-based pre-trained model for improving programming language-oriented generation tasks. To utilize tree structure, TreeBERT represents the AST corresponding to the code as a set of composition paths and introduces node position embedding. The model is trained by tree masked language modeling (TMLM) and node order prediction (NOP) with a hybrid obje…
University of Edinburgh（爱丁堡大学）；University of Amsterdam（阿姆斯特丹大学）
We treat projective dependency trees as latent variables in our probabilistic model and induce them in such a way as to be beneficial for a downstream task, without relying on any direct tree supervision. Our approach relies on Gumbel perturbations and differentiable dynamic programming. Unlike previous approaches to latent tree learning, we stochastically sample global structures and our parser is fully differentiable. We illustrate its effectiveness on sentiment analysis and natural language inference tasks. We also study its properties on a synthetic structure induction task. Ablation studi…
Survival regression is used to estimate the relation between time-to-event and feature variables, and is important in application domains such as medicine, marketing, risk management and sales management. Nonlinear tree based machine learning algorithms as implemented in libraries such as XGBoost, scikit-learn, LightGBM, and CatBoost are often more accurate in practice than linear models. However, existing state-of-the-art implementations of tree-based models have offered limited support for survival regression. In this work, we implement loss functions for learning accelerated failure time (A…
Josef Ressel Centre for Symbolic Regression（约瑟夫·雷塞尔符号回归中心）；University of Applied Sciences Upper Austria（上奥地利应用科学大学）；Johannes Kepler University（约翰内斯·开普勒大学）
We introduce in this paper a runtime-efficient tree hashing algorithm for the identification of isomorphic subtrees, with two important applications in genetic programming for symbolic regression: fast, online calculation of population diversity and algebraic simplification of symbolic expression trees. Based on this hashing approach, we propose a simple diversity-preservation mechanism with promising results on a collection of symbolic regression benchmark problems.
Programming language processing (similar to natural language processing) is a hot research topic in the field of software engineering; it has also aroused growing interest in the artificial intelligence community. However, different from a natural language sentence, a program contains rich, explicit, and complicated structural information. Hence, traditional NLP models may be inappropriate for programs. In this paper, we propose a novel tree-based convolutional neural network (TBCNN) for programming language processing, in which a convolution kernel is designed over programs' abstract syntax t…
IBM Research（IBM研究院）；Lehigh University（理海大学）；Argonne National Laboratory（阿贡国家实验室）；Cornell University（康奈尔大学）
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 …
Federal University of Ouro Preto（欧鲁普雷图联邦大学）；KU Leuven（鲁汶大学）；Federal University of Lavras（拉夫拉斯联邦大学）
Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic configuration based on aggregate results such as the average. In this paper, we propose Integer Programming based approaches to build decision trees for the Algorithm Selection Problem. These techniques allow automate three crucial decisions: (i) discerning the most important problem features to determine problem classes; (ii) grouping the problems into classes and (iii…
Generalized Optimal Classification Trees: A Mixed-Integer Programming Approach
Department of Computing, The Hong Kong Polytechnic University（计算机系，香港理工大学）；Department of Management and Marketing, The Hong Kong Polytechnic University（管理与市场营销系，香港理工大学）；Business School, Sichuan University（四川大学商学院）
The task of translating between programming languages differs from the challenge of translating natural languages in that programming languages are designed with a far more rigid set of structural and grammatical rules. Previous work has used a tree-to-tree encoder/decoder model to take advantage of the inherent tree structure of programs during translation. Neural decoders, however, by default do not exploit known grammar rules of the target language. In this paper, we describe a tree decoder that leverages knowledge of a language's grammar rules to exclusively generate syntactically correct …
We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk minimization over the choice of trees and node decision rules. We decompose the problem, which is known to be intractable, into combinatorial (tree structures) and continuous parts (node decision rules) and propose to solve them separately. Using training data we greedily solve for the combinatorial tree structures and for the continuous part, which is a non-conv…
This article analyzes the problem of estimating the time until an event occurs, also known as survival modeling. We observe through substantial experiments on large real-world datasets and use-cases that populations are largely heterogeneous. Sub-populations have different mean and variance in their survival rates requiring flexible models that capture heterogeneity. We leverage a classical extension of the logistic function into the survival setting to characterize unobserved heterogeneity using the beta distribution. This yields insights into the geometry of the problem as well as efficient …
The modeling of time-to-event data, also known as survival analysis, requires specialized methods that can deal with censoring and truncation, time-varying features and effects, and that extend to settings with multiple competing events. However, many machine learning methods for survival analysis only consider the standard setting with right-censored data and proportional hazards assumption. The methods that do provide extensions usually address at most a subset of these challenges and often require specialized software that can not be integrated into standard machine learning workflows direc…
Program comprehension is a fundamental task in software development and maintenance processes. Software developers often need to understand a large amount of existing code before they can develop new features or fix bugs in existing programs. Being able to process programming language code automatically and provide summaries of code functionality accurately can significantly help developers to reduce time spent in code navigation and understanding, and thus increase productivity. Different from natural language articles, source code in programming languages often follows rigid syntactical stru…
Efficient Constant Optimization for Symbolic Regression with GPU-Accelerated Tree-Based Genetic Programming
The Hong Kong Polytechnic University（香港理工大学）；University of Washington（华盛顿大学）；Amazon Web Services（亚马逊网络服务）；Jiangxi University of Finance and Economics（江西财经大学）；EEO Education Technology（EEO教育科技）；Chongqing Medical University（重庆医科大学）；Eastern Institute of Technology（东方理工学院）
