To relieve the computational cost of design evaluations using expensive finite element simulations, surrogate models have been widely applied in computer-aided engineering design. Machine learning algorithms (MLAs) have been implemented as surrogate models due to their capability of learning the complex interrelations between the design variables and the response from big datasets. Typically, an MLA regression model contains model parameters and hyperparameters. The model parameters are obtained by fitting the training data. Hyperparameters, which govern the model structures and the training processes, are assigned by users before training. There is a lack of systematic studies on the effect of hyperparameters on the accuracy and robustness of the surrogate model. In this work, we proposed to establish a hyperparameter optimization (HOpt) framework to deepen our understanding of the effect. Four frequently used MLAs, namely Gaussian Process Regression (GPR), Support Vector Machine (SVM), Random Forest Regression (RFR), and Artificial Neural Network (ANN), are tested on four benchmark examples. For each MLA model, the model accuracy and robustness before and after the HOpt are compared. The results show that HOpt can generally improve the performance of the MLA models in general. HOpt leads to few improvements in the MLAs accuracy and robustness for complex problems, which are featured by high-dimensional mixed-variable design space. The HOpt is recommended for the design problems with intermediate complexity. We also investigated the additional computational costs incurred by HOpt. The training cost is closely related to the MLA architecture. After HOpt, the training cost of ANN and RFR is increased more than that of the GPR and SVM. To sum up, this study benefits the selection of HOpt method for the different types of design problems based on their complexity.
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as monotonic functions of the hyperparameters. Our proposed algorithm adapts Bayesian optimization methods to incorporate the monotonicity constraints. We illustrate the advantages of exploiting monotonicity using illustrative examples and demonstrate the improvements in optimization ef…
Indian Institute of Management Ahmedabad（印度管理学院艾哈迈达巴德分校）
Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive techniques, such as random search and grid search. However, most of these methods seldom lead to an optimal set of hyperparameters and often get very expensive. In this paper, we propose a bilevel solution method for solving the hyperparameter optimization problem that does not suffer from the drawbacks of the earlier studies. The proposed method is general a…
Twitter（推特）；Facebook（脸书）；SigOpt, an Intel company（SigOpt（英特尔公司旗下））；Valohai；Paradigm（第四范式）；ChaLearn
This paper presents the results and insights from the black-box optimization (BBO) challenge at NeurIPS 2020 which ran from July-October, 2020. The challenge emphasized the importance of evaluating derivative-free optimizers for tuning the hyperparameters of machine learning models. This was the first black-box optimization challenge with a machine learning emphasis. It was based on tuning (validation set) performance of standard machine learning models on real datasets. This competition has widespread impact as black-box optimization (e.g., Bayesian optimization) is relevant for hyperparamete…
University of Freiburg（弗莱堡大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by ex…
Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview
Fraunhofer Institut für integrierte Schaltungen（弗劳恩霍夫集成电路研究所）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Technische Universität Dortmund（多特蒙德工业大学）；Universidad Pontificia Comillas（康普卢滕塞大学）；Warwick Business School（华威商学院）
University of Milano-Bicocca（米兰比可卡大学）；OAKS srl（OAKS有限责任公司）
There is a consensus that focusing only on accuracy in searching for optimal machine learning models amplifies biases contained in the data, leading to unfair predictions and decision supports. Recently, multi-objective hyperparameter optimization has been proposed to search for machine learning models which offer equally Pareto-efficient trade-offs between accuracy and fairness. Although these approaches proved to be more versatile than fairness-aware machine learning algorithms -- which optimize accuracy constrained to some threshold on fairness -- they could drastically increase the energy …
Aggregating multiple learners through an ensemble of models aim to make better predictions by capturing the underlying distribution of the data more accurately. Different ensembling methods, such as bagging, boosting, and stacking/blending, have been studied and adopted extensively in research and practice. While bagging and boosting focus more on reducing variance and bias, respectively, stacking approaches target both by finding the optimal way to combine base learners. In stacking with the weighted average, ensembles are created from weighted averages of multiple base learners. It is known …
Tuning hyperparameters for machine learning algorithms is a tedious task, one that is typically done manually. To enable automated hyperparameter tuning, recent works have started to use techniques based on Bayesian optimization. However, to practically enable automated tuning for large scale machine learning training pipelines, significant gaps remain in existing libraries, including lack of abstractions, fault tolerance, and flexibility to support scheduling on any distributed computing framework. To address these challenges, we present Mango, a Python library for parallel hyperparameter tun…
Hyperparameter optimization is the process of identifying the appropriate hyperparameter configuration of a given machine learning model with regard to a given learning task. For smaller data sets, an exhaustive search is possible; However, when the data size and model complexity increase, the number of configuration evaluations becomes the main computational bottleneck. A promising paradigm for tackling this type of problem is surrogate-based optimization. The main idea underlying this paradigm considers an incrementally updated model of the relation between the hyperparameter space and the o…
Hyperparameters play a critical role in the performances of many machine learning methods. Determining their best settings or Hyperparameter Optimization (HPO) faces difficulties presented by the large number of hyperparameters as well as the excessive training time. In this paper, we develop an effective approach to reducing the total amount of required training time for HPO. In the initialization, the nested Latin hypercube design is used to select hyperparameter configurations for two types of training, which are, respectively, heavy training and light training. We propose a truncated addit…
University of Freiburg（弗赖堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Bayesian Optimization (BO) is a common approach for hyperparameter optimization (HPO) in automated machine learning. Although it is well-accepted that HPO is crucial to obtain well-performing machine learning models, tuning BO's own hyperparameters is often neglected. In this paper, we empirically study the impact of optimizing BO's own hyperparameters and the transferability of the found settings using a wide range of benchmarks, including artificial functions, HPO and HPO combined with neural architecture search. In particular, we show (i) that tuning can improve the any-time performance of …
Automated hyperparameter tuning aspires to facilitate the application of machine learning for non-experts. In the literature, different optimization approaches are applied for that purpose. This paper investigates the performance of Differential Evolution for tuning hyperparameters of supervised learning algorithms for classification tasks. This empirical study involves a range of different machine learning algorithms and datasets with various characteristics to compare the performance of Differential Evolution with Sequential Model-based Algorithm Configuration (SMAC), a reference Bayesian Op…
Competence Center for High Performance Computing Fraunhofer ITWM Kaiserslautern（弗劳恩霍夫研究所ITWM高性能计算能力中心（凯泽斯劳滕））；Institute for Machine Learning and Analytics (IMLA) Offenburg University（奥芬堡大学机器学习与分析研究所（IMLA））
We introduce an open source python framework named PHS - Parallel Hyperparameter Search to enable hyperparameter optimization on numerous compute instances of any arbitrary python function. This is achieved with minimal modifications inside the target function. Possible applications appear in expensive to evaluate numerical computations which strongly depend on hyperparameters such as machine learning. Bayesian optimization is chosen as a sample efficient method to propose the next query set of parameters.
Most machine learning algorithms are configured by one or several hyperparameters that must be carefully chosen and often considerably impact performance. To avoid a time consuming and unreproducible manual trial-and-error process to find well-performing hyperparameter configurations, various automatic hyperparameter optimization (HPO) methods, e.g., based on resampling error estimation for supervised machine learning, can be employed. After introducing HPO from a general perspective, this paper reviews important HPO methods such as grid or random search, evolutionary algorithms, Bayesian opti…
Ludwig-Maximilians-University Munich（路德维希-马克西米利安慕尼黑大学）；Leibniz University Hannover（莱布尼茨汉诺威大学）
Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final model performance. This lack of explainability makes it difficult to trust and understand the automated HPO process and its results. We suggest using interpretable machine learning (IML) to gain insights from the experimental data obtained during HPO with Bayesian optimization (BO). BO tends to focus on promising regions with potential high-performance configura…
To solve a machine learning problem, one typically needs to perform data preprocessing, modeling, and hyperparameter tuning, which is known as model selection and hyperparameter optimization.The goal of automated machine learning (AutoML) is to design methods that can automatically perform model selection and hyperparameter optimization without human interventions for a given dataset. In this paper, we propose a meta-learning method that can search for a high-performance machine learning pipeline from the predefined set of candidate pipelines for supervised classification datasets in an effici…
Bayesian Optimization is a popular tool for tuning algorithms in automatic machine learning (AutoML) systems. Current state-of-the-art methods leverage Random Forests or Gaussian processes to build a surrogate model that predicts algorithm performance given a certain set of hyperparameter settings. In this paper, we propose a new surrogate model based on gradient boosting, where we use quantile regression to provide optimistic estimates of the performance of an unobserved hyperparameter setting, and combine this with a distance metric between unobserved and observed hyperparameter settings to …
Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is noisy. The most popular application of bayesian optimization is the automatic hyperparameter tuning of machine learning algorithms, where we obtain the best configuration of machine learning algorithms by optimizing the estimation of the generalization error of these algorithms. Despite being applied with success, bayesian optimization methodologies also hav…
Leibniz University Hannover（莱布尼茨汉诺威大学）；University of Freiburg（弗莱堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Algorithm parameters, in particular hyperparameters of machine learning algorithms, can substantially impact their performance. To support users in determining well-performing hyperparameter configurations for their algorithms, datasets and applications at hand, SMAC3 offers a robust and flexible framework for Bayesian Optimization, which can improve performance within a few evaluations. It offers several facades and pre-sets for typical use cases, such as optimizing hyperparameters, solving low dimensional continuous (artificial) global optimization problems and configuring algorithms to perf…
Data science relies on pipelines that are organized in the form of interdependent computational steps. Each step consists of various candidate algorithms that maybe used for performing a particular function. Each algorithm consists of several hyperparameters. Algorithms and hyperparameters must be optimized as a whole to produce the best performance. Typical machine learning pipelines typically consist of complex algorithms in each of the steps. Not only is the selection process combinatorial, but it is also important to interpret and understand the pipelines. We propose a method to quantify t…
Data science relies on pipelines that are organized in the form of interdependent computational steps. Each step consists of various candidate algorithms that maybe used for performing a particular function. Each algorithm consists of several hyperparameters. Algorithms and hyperparameters must be optimized as a whole to produce the best performance. Typical machine learning pipelines consist of complex algorithms in each of the steps. Not only is the selection process combinatorial, but it is also important to interpret and understand the pipelines. We propose a method to quantify the importa…
Hyperparameter tuning is an omnipresent problem in machine learning as it is an integral aspect of obtaining the state-of-the-art performance for any model. Most often, hyperparameters are optimized just by training a model on a grid of possible hyperparameter values and taking the one that performs best on a validation sample (grid search). More recently, methods have been introduced that build a so-called surrogate model that predicts the validation loss for a specific hyperparameter setting, model and dataset and then sequentially select the next hyperparameter to test, based on a heuristic…
Tuning complex machine learning systems is challenging. Machine learning typically requires to set hyperparameters, be it regularization, architecture, or optimization parameters, whose tuning is critical to achieve good predictive performance. To democratize access to machine learning systems, it is essential to automate the tuning. This paper presents Amazon SageMaker Automatic Model Tuning (AMT), a fully managed system for gradient-free optimization at scale. AMT finds the best version of a trained machine learning model by repeatedly evaluating it with different hyperparameter configuratio…
The performance of any Machine Learning (ML) algorithm is impacted by the choice of its hyperparameters. As training and evaluating a ML algorithm is usually expensive, the hyperparameter optimization (HPO) method needs to be computationally efficient to be useful in practice. Most of the existing approaches on multi-objective HPO use evolutionary strategies and metamodel-based optimization. However, few methods have been developed to account for uncertainty in the performance measurements. This paper presents results on multi-objective hyperparameter optimization with uncertainty on the evalu…
Convolutional Neural Network is known as ConvNet have been extensively used in many complex machine learning tasks. However, hyperparameters optimization is one of a crucial step in developing ConvNet architectures, since the accuracy and performance are reliant on the hyperparameters. This multilayered architecture parameterized by a set of hyperparameters such as the number of convolutional layers, number of fully connected dense layers & neurons, the probability of dropout implementation, learning rate. Hence the searching the hyperparameter over the hyperparameter space are highly difficul…
Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based configuration evaluation approaches based on random search lack guidance and do not converge to the best configurations as quickly. Here, we propose to combine the benefits of both Bayesian optimization and bandit-based methods, in order to achieve the best of both worlds: strong anytime performance and fast convergence to optimal configuratio…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）；Google Research（谷歌研究院）；Determined AI
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theo…
Indian Institute of Technology Gandhinagar（甘地纳格尔印度理工学院）；Northeastern University（东北大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL) hyperparameters, specifically, the depth, width and ensemble size, for robust function mapping with uncertainty quantification, is still emerging. This paper attempts to further our understanding by mapping Bayesian connectionist representations to polynomials of different orders with varying noise types and ratios. We examine the noise-contaminated polynomials…
A typical assumption in supervised machine learning is that the train (source) and test (target) datasets follow completely the same distribution. This assumption is, however, often violated in uncertain real-world applications, which motivates the study of learning under covariate shift. In this setting, the naive use of adaptive hyperparameter optimization methods such as Bayesian optimization does not work as desired since it does not address the distributional shift among different datasets. In this work, we consider a novel hyperparameter optimization problem under the multi-source covari…
Automatically searching for optimal hyperparameter configurations is of crucial importance for applying deep learning algorithms in practice. Recently, Bayesian optimization has been proposed for optimizing hyperparameters of various machine learning algorithms. Those methods adopt probabilistic surrogate models like Gaussian processes to approximate and minimize the validation error function of hyperparameter values. However, probabilistic surrogates require accurate estimates of sufficient statistics (e.g., covariance) of the error distribution and thus need many function evaluations with a …
Systems based on artificial neural networks (ANNs) have achieved state-of-the-art results in many natural language processing tasks. Although ANNs do not require manually engineered features, ANNs have many hyperparameters to be optimized. The choice of hyperparameters significantly impacts models' performances. However, the ANN hyperparameters are typically chosen by manual, grid, or random search, which either requires expert experiences or is computationally expensive. Recent approaches based on Bayesian optimization using Gaussian processes (GPs) is a more systematic way to automatically p…
Hyperparameters are critical in machine learning, as different hyperparameters often result in models with significantly different performance. Hyperparameters may be deemed confidential because of their commercial value and the confidentiality of the proprietary algorithms that the learner uses to learn them. In this work, we propose attacks on stealing the hyperparameters that are learned by a learner. We call our attacks hyperparameter stealing attacks. Our attacks are applicable to a variety of popular machine learning algorithms such as ridge regression, logistic regression, support vecto…
We introduce the hyperparameter search problem in the field of machine learning and discuss its main challenges from an optimization perspective. Machine learning methods attempt to build models that capture some element of interest based on given data. Most common learning algorithms feature a set of hyperparameters that must be determined before training commences. The choice of hyperparameters can significantly affect the resulting model's performance, but determining good values can be complex; hence a disciplined, theoretically sound search strategy is essential.
Hyperparameter plays an essential role in the fitting of supervised machine learning algorithms. However, it is computationally expensive to tune all the tunable hyperparameters simultaneously especially for large data sets. In this paper, we give a definition of hyperparameter importance that can be estimated by subsampling procedures. According to the importance, hyperparameters can then be tuned on the entire data set more efficiently. We show theoretically that the proposed importance on subsets of data is consistent with the one on the population data under weak conditions. Numerical expe…
University of California, Irvine（加州大学欧文分校）；University of Hawai’i at Mãnoa（夏威夷大学马诺阿分校）
Sherpa is a hyperparameter optimization library for machine learning models. It is specifically designed for problems with computationally expensive, iterative function evaluations, such as the hyperparameter tuning of deep neural networks. With Sherpa, scientists can quickly optimize hyperparameters using a variety of powerful and interchangeable algorithms. Sherpa can be run on either a single machine or in parallel on a cluster. Finally, an interactive dashboard enables users to view the progress of models as they are trained, cancel trials, and explore which hyperparameter combinations are…
Lighthouse Disruptive Innovation Group, LLC（灯塔颠覆性创新集团有限责任公司）；Vueling Airlines S.A.（伏林航空公司）；Universitat Ramon Llull（拉蒙柳尔大学）
This paper presents a quantum-based Fourier-regression approach for machine learning hyperparameter optimization applied to a benchmark of models trained on a dataset related to a forecast problem in the airline industry. Our approach utilizes the Fourier series method to represent the hyperparameter search space, which is then optimized using quantum algorithms to find the optimal set of hyperparameters for a given machine learning model. Our study evaluates the proposed method on a benchmark of models trained to predict a forecast problem in the airline industry using a standard HyperParamet…
Hyperparameters in machine learning (ML) have received a fair amount of attention, and hyperparameter tuning has come to be regarded as an important step in the ML pipeline. But just how useful is said tuning? While smaller-scale experiments have been previously conducted, herein we carry out a large-scale investigation, specifically, one involving 26 ML algorithms, 250 datasets (regression and both binary and multinomial classification), 6 score metrics, and 28,857,600 algorithm runs. Analyzing the results we conclude that for many ML algorithms we should not expect considerable gains from hy…
Eindhoven University of Technology（埃因霍温理工大学）；Columbia University（哥伦比亚大学）
The performance of many machine learning algorithms depends on their hyperparameter settings. The goal of this study is to determine whether it is important to tune a hyperparameter or whether it can be safely set to a default value. We present a methodology to determine the importance of tuning a hyperparameter based on a non-inferiority test and tuning risk: the performance loss that is incurred when a hyperparameter is not tuned, but set to a default value. Because our methods require the notion of a default parameter, we present a simple procedure that can be used to determine reasonable d…
Novel technologies in automated machine learning ease the complexity of algorithm selection and hyperparameter optimization. Hyperparameters are important for machine learning models as they significantly influence the performance of machine learning models. Many optimization techniques have achieved notable success in hyperparameter tuning and surpassed the performance of human experts. However, depending on such techniques as blackbox algorithms can leave machine learning practitioners without insight into the relative importance of different hyperparameters. In this paper, we consider build…
A Linear Programming Enhanced Genetic Algorithm for Hyperparameter Tuning in Machine Learning
Brij Disa Centre for Data Science and Artificial Intelligence（布里吉·迪萨数据科学与人工智能中心）；Indian Institute of Management Ahmedabad（印度管理学院艾哈迈达巴德分校）；Department of Statistics and Data Science（统计与数据科学系）；Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）
The goal of Quality Diversity Optimization is to generate a collection of diverse yet high-performing solutions to a given problem at hand. Typical benchmark problems are, for example, finding a repertoire of robot arm configurations or a collection of game playing strategies. In this paper, we propose a set of Quality Diversity Optimization problems that tackle hyperparameter optimization of machine learning models - a so far underexplored application of Quality Diversity Optimization. Our benchmark problems involve novel feature functions, such as interpretability or resource usage of models…
Delft University of technology（代尔夫特理工大学）；Axelera AI
Binary Neural Networks (BNNs) are compact and efficient by using binary weights instead of real-valued weights. Current BNNs use latent real-valued weights during training, where several training hyper-parameters are inherited from real-valued networks. The interpretation of several of these hyperparameters is based on the magnitude of the real-valued weights. For BNNs, however, the magnitude of binary weights is not meaningful, and thus it is unclear what these hyperparameters actually do. One example is weight-decay, which aims to keep the magnitude of real-valued weights small. Other exampl…
Machine learning algorithms such as random forests or xgboost are gaining more importance and are increasingly incorporated into production processes in order to enable comprehensive digitization and, if possible, automation of processes. Hyperparameters of these algorithms used have to be set appropriately, which can be referred to as hyperparameter tuning or optimization. Based on the concept of tunability, this article presents an overview of theoretical and practical results for popular machine learning algorithms. This overview is accompanied by an experimental analysis of 30 hyperparamet…
It is typical for a machine learning system to have numerous hyperparameters that affect its learning rate and prediction quality. Finding a good combination of the hyperparameters is, however, a challenging job. This is mainly because evaluation of each combination is extremely expensive computationally; indeed, training a machine learning system on real data with just a single combination of hyperparameters usually takes hours or even days. In this paper, we address this challenge by trying to predict the performance of the machine learning system with a given combination of hyperparameters …
Warsaw University of Technology（华沙理工大学）；University of Warsaw（华沙大学）
Finding optimal hyperparameters for the machine learning algorithm can often significantly improve its performance. But how to choose them in a time-efficient way? In this paper we present the protocol of generating benchmark data describing the performance of different ML algorithms with different hyperparameter configurations. Data collected in this way is used to study the factors influencing the algorithm's performance. This collection was prepared for the purposes of the study presented in the EPP study. We tested algorithms performance on dense grid of hyperparameters. Tested datasets an…
Hyperparameter optimisation is a crucial process in searching the optimal machine learning model. The efficiency of finding the optimal hyperparameter settings has been a big concern in recent researches since the optimisation process could be time-consuming, especially when the objective functions are highly expensive to evaluate. In this paper, we introduce an intelligent evolutionary optimisation algorithm which applies machine learning technique to the traditional evolutionary algorithm to accelerate the overall optimisation process of tuning machine learning models in classification probl…
Tackling new machine learning problems with neural networks always means optimizing numerous hyperparameters that define their structure and strongly impact their performances. In this work, we study the use of goal-oriented sensitivity analysis, based on the Hilbert-Schmidt Independence Criterion (HSIC), for hyperparameter analysis and optimization. Hyperparameters live in spaces that are often complex and awkward. They can be of different natures (categorical, discrete, boolean, continuous), interact, and have inter-dependencies. All this makes it non-trivial to perform classical sensitivity…
Hyperparameter optimization (HPO) is a necessary step to ensure the best possible performance of Machine Learning (ML) algorithms. Several methods have been developed to perform HPO; most of these are focused on optimizing one performance measure (usually an error-based measure), and the literature on such single-objective HPO problems is vast. Recently, though, algorithms have appeared that focus on optimizing multiple conflicting objectives simultaneously. This article presents a systematic survey of the literature published between 2014 and 2020 on multi-objective HPO algorithms, distinguis…
Understanding the influence of hyperparameters on the performance of a machine learning algorithm is an important scientific topic in itself and can help to improve automatic hyperparameter tuning procedures. Unfortunately, experimental meta data for this purpose is still rare. This paper presents a large, free and open dataset addressing this problem, containing results on 38 OpenML data sets, six different machine learning algorithms and many different hyperparameter configurations. Results where generated by an automated random sampling strategy, termed the OpenML Random Bot. Each algorithm…
Beyond algorithm hyperparameters: on preprocessing hyperparameters and associated pitfalls in machine learning applications
Institute for Medical Information Processing, Biometry and Epidemiology, Faculty of Medicine, LMU Munich（医学信息处理、生物统计与流行病学研究所，医学学院，慕尼黑大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Department of Palliative Medicine, University Hospital, LMU Munich（姑息医学部，大学医院，慕尼黑大学）；Institute of Clinical Biometrics, Center for Medical Data Science, Medical University of Vienna（临床生物统计研究所，医学数据科学中心，维也纳医学大学）
