diff --git a/book/_book/Machine-Learning-in-Survival-Analysis.pdf b/book/_book/Machine-Learning-in-Survival-Analysis.pdf index f78bdad..dd22068 100644 Binary files a/book/_book/Machine-Learning-in-Survival-Analysis.pdf and b/book/_book/Machine-Learning-in-Survival-Analysis.pdf differ diff --git a/book/_quarto.yml b/book/_quarto.yml index 1b1fd67..fc457b6 100644 --- a/book/_quarto.yml +++ b/book/_quarto.yml @@ -33,7 +33,7 @@ book: file: index.qmd - P0C0_notation.qmd - P0C1_intro.qmd - - part: Survival Analysis and Machine Learning + - part: Machine Learning and Survival Analysis chapters: - P1C3_machinelearning.qmd - P1C4_survival.qmd diff --git a/book/index.qmd b/book/index.qmd index 66e5f83..d1bf2aa 100644 --- a/book/index.qmd +++ b/book/index.qmd @@ -7,17 +7,19 @@ ::: {.content-visible when-format="html"} ### by Raphael Sonabend and Andreas Bender {.unnumbered .unlisted} -

+ This book is a work in progress, the final work will be published by CRC Press. -This electronic version (including pdf download) will always be free and open access ([CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/)). +This electronic version (including PDF download) will always be free and open access ([CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/)). +We appreciate that you can enjoy this book for free online or buy the physical format and we hope you choose whichever is most convenient for you. +Buying the book will be the greatest indicator to us that a second edition may be useful in the future. -We will continue to update this version after publication to correct mistakes (big and small), as well as making minor and major additions, if you notice any mistakes please feel free to [open an issue](https://github.com/mlsa-book/MLSA/issues). +We will strive to update this version after publication to correct mistakes (big and small), if you notice any mistakes please feel free to [open an issue](https://github.com/mlsa-book/MLSA/issues). ## Licensing This book is licensed under [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/), so you can adapt and redistribute the contents however you like as long as you: i) **do** cite this book (information below); ii) do **not** use any material for commercial purposes; and iii) **do** use a [CC BY-NC-SA 4.0 compatible license](https://creativecommons.org/share-your-work/licensing-considerations/compatible-licenses) if you adapt the material. -If you have any questions about licensing just [open an issue](https://github.com/mlsa-book/MLSA/issues) and we will help you out. +If you have any questions about licensing, just [open an issue](https://github.com/mlsa-book/MLSA/issues) and we will help you out. ## Citation Information @@ -29,7 +31,7 @@ https://www.mlsabook.com. @book{MLSA2025 title = Machine Learning in Survival Analysis, - editor = {Raphael Sonabend, Andreas Bender}, + author = {Raphael Sonabend and Andreas Bender}, url = {https://www.mlsabook.com}, year = {2025} } @@ -37,14 +39,18 @@ https://www.mlsabook.com. ## Contributing to this book -We welcome contributions to the electronic copy of the book, whether they're issues picking up on typos, requests for additional content, or pull requests with contributions from any size. -All contributions will be acknowledged in the preface of the book. +We welcome contributions to our book, whether you're pointing out typos, requesting content, or even adding your own text. +Major contributions (adding or reviewing content) will be acknowledged in the preface of the book. -Before you contribute please make sure you have read our [code of conduct](https://github.com/mlsa-book/MLSA/blob/main/.github/CODE_OF_CONDUCT.md). +Before you contribute, please read our [code of conduct](https://github.com/mlsa-book/MLSA/blob/main/.github/CODE_OF_CONDUCT.md) and then [open an issue](https://github.com/mlsa-book/MLSA/issues) to discuss your proposed contribution. ## Biographies {.unnumbered} -Raphael Sonabend is the CEO and Co-Founder of OSPO Now, a company providing virtual open-source program offices as a service. They are also a Visiting Researcher at Imperial College London. Raphael holds a PhD in statistics, specializing in machine learning applications for survival analysis. They created the R packages `mlr3proba`, `survivalmodels`, and the Julia package `SurvivalAnalysis.jl`. Raphael co-edited and co-authored *Applied Machine Learning Using mlr3 in R* [@Bischl2024]. +Dr Raphael Sonabend-Friend is a Scientific Adviser at the National Institute for Health and Care Excellence (NICE) and the CEO and Co-Founder of OSPO Now. +Raphael holds a PhD focussed on the accessible and transparent use of machine learning for survival analysis. +Raphael has over a decade of experience in the healthcare sector, including with large philanthropies, small local charities, governmental bodies, and private sector consulting for UK and international organisations. +Raphael has created and maintained several software packages for survival analysis and machine learning, including `mlr3proba`, `survivalmodels`, and `SurvivalAnalysis.jl`. +Raphael co-edited and co-authored *Applied Machine Learning Using mlr3 in R* [@Bischl2024]. Andreas Bender is FIXME. @@ -54,78 +60,117 @@ Andreas Bender is FIXME. > "...but in this world nothing can be said to be certain, except death and taxes." - Benjamin Franklin -A logical consequence of Bernard Shaw's quote is that if there is time enough, then everybody will have experienced a given event at some point. -This is one of the central assumptions to survival analysis (specifically to single-event analysis, but we'll get to that later). -As nothing can be certain (except death and taxes), machine learning can be used to predict the probability people will experience the event and *when*. -This is exactly the problem that this book tackles. - -With immortality only being a theoretical concept, there is never 'time enough', hence survival analysis assumes that the event of interest is guaranteed to occur within an object's lifetime. -This event could be a patient entering remission after a cancer diagnosis, the lifetime of a lightbulb after manufacturing, the time taken to finish a race, or any other event that is observed over time. -Survival analysis differs from other fields of Statistics in that uncertainty is explicit encoded in the survival problem; this uncertainty is known as 'censoring'. -For example, say a model is being built to predict when a marathon runner will finish a race and to learn this information the model is fed data from every marathon over the past five years. -Across this period, there will be many runners who never finish their race and are never observed to experience the event of interest (finishing the race). -Instead, these runners are said to be 'censored', this means that the model uses all information up until the point of censoring (dropping out the race), and learns that they ran for at least as long as their censoring time (they time they dropped out). -Censoring is unique to survival analysis and without the presence of censoring, survival analysis is mathematically equivalent to regression. - -This book covers survival analysis in the most common right-censoring setting for independent censoring, as well as discussing competing risk frameworks for dependent censoring - these terms will all be covered in the introduction of the book. +These quotes aptly describe the core assumptions of survival analysis (specifically single-event analysis, but we'll get to that later). +In the simplest application, the goal of predictive survival analysis is to estimate the probability of an event occurring over time, with the assumption that the event _should_ occur at some point. +Survival analysis places significant emphasis on that word 'should'. +Given enough time, and no extraneous events, the event of interest _should_ happen. +However, time is finite and occasionally competing events can prevent the target under investigation. + +For example, a runner _should_ finish a race. +However, they may fail to do so if they take _so_ long that the race ends, if the person next to them falls over and causes pile-up, or if they collapse from exhaustion. +Therefore, there is uncertainty about _if_ they will finish the race and _when_. +Survival analysis differs from other fields of statistics in that this uncertainty is explicitly encoded in the survival problem, as 'censoring'. +Instead of being excluded from a dataset, the runner is said to have been censored at the time at which they are no longer running the race. +There are also different mechanisms for censoring; indeed, in the examples above we illustrated several different censoring mechanisms, which will be discussed in detail in this book. +Censoring is central to survival analysis, and without the presence of censoring, survival analysis is mathematically equivalent to regression on the fully observed event times. + +This book focuses entirely on predictive survival analysis (which we refer to simply as 'survival analysis'), which is focused on forward-looking predictions. +This is in contrast to inference methods, which examine model parameters to learn information about a given dataset or model. +Predictive survival analysis is a hugely important area of statistics, with numerous applications across a wide variety of industries, for example: + +* Manufacturing: Predict the time to equipment failure; +* Pharmaceutical: Predict a patient's survival trajectory after novel treatment; +* Healthcare: Predict a patient's survival time after infection with meningitis; +* Finance: Predict the time until a customer defaults on a loan; +* Marketing: Predict the risk of a customer churning; +* E-commerce: Predict the time until next purchase for personalized marketing; + +And many, many more examples. + +Despite its importance in many real-world settings, survival analysis has lagged behind other predictive fields such as classification and regression. +This gap may be in part due to the sensitive and highly regulated domains in which survival analysis is typically applied. +In these environments, 'black-box models', models that are difficult to interpret, may be less appealing than transparent linear models that can be implemented easily using graphical, non-programming tools such as Excel. +The longer this gap persists, the harder it will become for practitioners to adopt modern methods and the more resistance will build. + +The rapid rise of generative artificial intelligence (genAI) with tools such as ChatGPT, Gemini, and Claude, puts the field of survival analysis at an interesting fork. +Traditional machine learning methods, those not using genAI, are deeply embedded in industry for regression and classification, with extensive experience and evidence indicating where these methods do and do not succeed; allowing for a measured and evidence-based transition to genAI. +In contrast, the slower adoption of machine learning in survival analysis means the field could leapfrog technologies directly to genAI approaches. +We are already seeing vendors selling genAI survival analysis tools to private- and public-sector organizations. +Behind the scenes, some of these tools are writing code in Python or R to build machine learning survival analysis models, with limited (or no) human scrutiny. +Therefore, we argue, now more than ever, there is an urgent need for machine learning survival analysis models to be widely understood. + +This book focuses entirely on 'traditional machine learning'. +We do not advocate for or against genAI in survival analysis. +Instead, we hope to equip practitioners with a solid grounding of traditional techniques so they can choose among methodologies rather than defaulting to genAI simply because it becomes the norm. +Further, we hope that more understanding of traditional methods will also support practitioners in evaluating external technologies. **A note from Raphael**: -I wrote my PhD thesis about machine learning applications to survival analysis as I was interested in understanding why more researchers were not using machine learning models for survival analysis. -Since then I've had the pleasure to work with, and advise, researchers across different sectors, including pharmaceutical companies, governmental agencies, funding organisations, and research institutions. +I wrote my PhD thesis about machine learning applications to survival analysis because I was interested in understanding why more researchers were not using machine learning models for survival analysis. +Since then, I feel that little has changed, even with the rapid rise of generative AI. +The field continues to lag behind but now with more challenges than ever. +Over the years, I've had the pleasure to work with, and advise, researchers across different sectors, including pharmaceutical companies, governmental agencies, funding organizations, and research institutions. I hope that this book continues to help researchers discover machine learning survival analysis and to navigate the nuances and complexities it presents. **A note from Andreas**: FIXME. -## Overview to the book +## Overview of the book -This textbook is intended to fill a gap in the literature by providing a comprehensive introduction to machine learning in the survival setting. -If you are interested in machine learning or survival analysis separately then you might consider @Hastie2013, @Hastie2001, @Bishop2006 for machine learning and @Collett2014, @KalbfleischPrentice1973 for survival analysis. -This book serves as a complement to the above examples and introduces common machine learning terminology from simpler settings such as regression and classification, but without diving into the detail found in other sources, instead focusing on extension to the survival analysis setting. +This book is intended to fill a gap in the literature by providing a comprehensive introduction to machine learning in the survival setting. +If you are interested in machine learning or survival analysis separately, then you might consider @Hastie2013; @Hastie2001; or @Bishop2006 for machine learning and @Collett2014 or @KalbfleischPrentice1973 for survival analysis. +This book serves as a complement to the above works and introduces common machine learning terminology from simpler settings such as regression and classification, but without diving into the detail found in other sources. +This book is centred on the intersection of the two areas and defining the suitability of different methods and models depending on the availability data. +For example, given right-censored survival data, when might you consider a neural network instead of a Cox Proportional Hazards model? +Or given competing risks when tackling a discrimination problem, should you prefer Antolini's or Harrell's concordance index? +Can you even use a machine learning model if you have left-censored multi-state data? +All these terms and more will be defined in this book to hopefully provide a practical guide to _machine learning survival analysis_. -This book may be useful for Masters or PhD students who are specialising in machine learning in survival analysis, machine learning practitioners looking to work in the survival setting, or statisticians who are familiar with survival analysis but less so with machine learning. -The book could be read cover-to-cover, but this is not advised. -Instead it may be preferable to dip into sections of the book as required and use the 'signposts' that direct the reader to sections of the book that are relevant to each other. +This book may be useful for Master's or PhD students who are specializing in machine learning in survival analysis, machine learning engineers looking to solve problems involving censoring, or practitioners familiar with survival analysis but with less applied machine learning experience. +The book can be read cover-to-cover, but we believe it will be more useful as a reference book for you to dip into as required. -The book is split into five parts: +Following the introduction, this book is structured in four parts: -**Part I: Survival Analysis and Machine Learning**
-The book begins by introducing the basics of survival analysis and machine learning and unifying terminology between the two to enable meaningful description of 'machine learning in survival analysis' (MLSA). -In particular, the survival analysis 'task' and survival 'prediction types' are defined. +**Part I: Machine Learning and Survival Analysis**
+An introduction to the basics of survival analysis, with some more advanced concepts in the more general 'event history analysis' setting, which encompasses competing risks and multi-state models. +In addition, there is a brief overview to machine learning, including key concepts that are utilized throughout the survival domain. +This Part concludes by unifying terminology between machine learning and survival analysis to define what it means to have different survival prediction problems and a 'machine learning survival analysis' task. **Part II: Evaluation**
-The second part of the book discusses one of the most important parts of the machine learning workflow, model evaluation. -In the simplest case, without evaluation there is no way to know if predictions from a trained machine learning model are any good. -Whether one uses a Kaplan-Meier estimator, a complex neural network, or anything in between, there is no guarantee any of these methods will actually make useful predictions for a given dataset. -This could be because the dataset is inherently difficult for any model to be trained on, perhaps because it is very 'noisy', or because a model is simply ill-suited to the task, for example using a Cox Proportional Hazards model when its key assumptions are violated. -Evaluation is therefore crucial to trusting any predictions made from a model. - -The measures in Part II are presented in different classes that reflect the prediction types identified in Part I. -In-sample measures, which evaluate the quality of a model's 'fit' to data, are not included as this book primarily focuses on external validation of predictive machine learning models. -Readers who are interested in this are are directed to @Collett2014 and @dataapplied for discussion on residuals; @Choodari2012a and @Royston2004 for $R^2$ type measures; and @VolinskyRaftery2000, @HURVICH1989, and @Liang2008 for information criterion measures. - -In each chapter, the measure class is introduced, particular metrics are listed, and commentary is provided on how and when to use the measures. -Recommendations for choosing measures are discussed in @sec-conclusions. +The second part of the book discusses model evaluation. +Evaluation is crucial for choosing between models and eventually trusting the predictions from a trained machine learning model. +Part II introduces measures for evaluating the different types of predictive task introduced in Part I. +In each chapter, the measure class is introduced, specific metrics are listed, and commentary is provided on how and when to use the measures. +Recommendations for choosing measures are discussed in the final chapter of the book. +As this book focuses on the predictive setting, the evaluation measures introduced in Part II are all 'out-of-sample' measures, to be used for evaluating models on new, unseen data. +This is in contrast to 'in-sample' measures, which evaluate how well a model is fit to data, and are usually preferred for inference tasks. +Readers who are interested in in-sample measures are directed to @Collett2014 and @dataapplied for discussion on residuals; @Choodari2012a and @Royston2004 for $R^2$ type measures; and @VolinskyRaftery2000; @HURVICH1989, and @Liang2008 for information criterion measures. **Part III: Models**
-Part III is a deep dive into machine learning models for solving survival analysis problems. -This begins with 'classical' models that may not be considered 'machine learning' and then continues by exploring different classes of machine learning models including random forests, support vector machines, gradient boosting machines, neural networks, and other less common classes. -Each model class is introduced in the simpler regression setting and then extensions to survival analysis are discussed. -Differences between model implementations are not discussed, instead the focus is on understanding how these models are built for survival analysis - in this way readers are well-equipped to independently follow individual papers introducing specific implementations. +Part III is a deep dive into models for solving survival analysis problems. +This begins with 'traditional survival' models that may not be considered 'machine learning' by some; although, as will be shown, with a small level of tweaking, these models can be exceptionally powerful. +This Part of the book continues by exploring different classes of machine learning models including random forests, support vector machines, gradient boosting machines, and neural networks. +Whilst this book does not go into extensive detail about deep learning, the final chapter of this Part provides a foundation that can be complemented by works such as @Goodfellow2016. + +Each model class is introduced in classification or regression settings with extensions to survival analysis then discussed. +Differences between model implementations are not discussed, that is, there is not extensive detail on whether one specific algorithm is superior to another. +Instead, the focus is on understanding how these models are built for survival analysis +In this way, readers are well-equipped to independently follow papers that introduce specific implementations. **Part IV: Reduction Techniques**
-The next part of the book introduces reduction techniques in survival analysis, which is the process of solving the survival analysis task by using methods from other fields. -In particular, chapters focus on demonstrating how any survival model can be used in the competing risks setting, discrete time modelling, Poisson methods, pseudovalues (reduction to regression), and other advanced modelling methods. +The final Part introduces reduction techniques, which are methods to solve survival analysis problems by using methods from other fields. +In particular, chapters focus on demonstrating the close connections between competing risks, discrete time, Poisson, classification, and regression settings. +Practitioners who are comfortable with other machine learning fields may find this Part of the book most useful for quickly implementing familiar models within the survival analysis domain. -**Part V: Extensions and Outlook**
-The final part of the book provides some miscellaneous chapters that may be of use to readers. -The first chapter lists common practical problems that occur when running survival analysis experiments and solutions that we have found useful. -The next lists open-source software at the time of writing for running machine learning survival analysis experiments. -The final chapter is our outlook on survival analysis and where the field may be heading. +The book's final chapter lists common practical problems that occur when running survival analysis experiments, as well as solutions that we have found useful. +We additionally provide our outlook on survival analysis and where we think the field may be heading. ## Acknowledgments -We would like to gratefully acknowledge our colleagues that reviewed the content of this book, including: Lukas Burk, Cesaire Fouodo. +We would like to gratefully acknowledge our colleagues who reviewed the content of this book, including: Lukas Burk, Dr Cesaire Fouodo, Prof. Dr.Helmut Küchenhoff, Prof. Dr. Matthias Schmid. + +Parts of this book were reviewed and revised using generative AI tools. +The authors fact-checked all responses and re-wrote any suggested text to ensure our own voice can be found throughout the book. +We acknowledge the decades of literature that was scraped (legally or otherwise) by these tools. ::: @@ -152,94 +197,15 @@ We would like to gratefully acknowledge our colleagues that reviewed the content \chapter*{Preface} -> "Everything happens to everybody sooner or later if there is time enough" - George Bernard Shaw - -> "...but in this world nothing can be said to be certain, except death and taxes." - Benjamin Franklin - -A logical consequence of Bernard Shaw's quote is that if there is time enough, then everybody will have experienced a given event at some point. -This is one of the central assumptions to survival analysis (specifically to single-event analysis, but we'll get to that later). -As nothing can be certain (except death and taxes), machine learning can be used to predict the probability people will experience the event and *when*. -This is exactly the problem that this book tackles. - -With immortality only being a theoretical concept, there is never 'time enough', hence survival analysis assumes that the event of interest is guaranteed to occur within an object's lifetime. -This event could be a patient entering remission after a cancer diagnosis, the lifetime of a lightbulb after manufacturing, the time taken to finish a race, or any other event that is observed over time. -Survival analysis differs from other fields of Statistics in that uncertainty is explicit encoded in the survival problem; this uncertainty is known as 'censoring'. -For example, say a model is being built to predict when a marathon runner will finish a race and to learn this information the model is fed data from every marathon over the past five years. -Across this period, there will be many runners who never finish their race. -Instead, these runners are said to be 'censored' and the model uses all information up until the point of censoring (dropping out the race), and learns that they ran for at least as long as their censoring time (the time they dropped out). -Censoring is unique to survival analysis and without the presence of censoring, survival analysis is mathematically equivalent to regression. - -This book covers survival analysis in the most common right-censoring setting for independent censoring, as well as discussing competing risk frameworks for dependent censoring - these terms will all be covered in the introduction of the book. - -**A note from Raphael**: -I wrote my PhD thesis about machine learning applications to survival analysis as I was interested in understanding why more researchers were not using machine learning models for survival analysis. -Since then I've had the pleasure to work with, and advise, researchers across different sectors, including pharmaceutical companies, governmental agencies, funding organisations, and research institutions. -I hope that this book continues to help researchers discover machine learning survival analysis and to navigate the nuances and complexities it presents. - -**A note from Andreas**: -FIXME. +FIXME \subsection*{Overview} -This textbook is intended to fill a gap in the literature by providing a comprehensive introduction to machine learning in the survival setting. -If you are interested in machine learning or survival analysis separately then you might consider @Hastie2013, @Hastie2001, @Bishop2006 for machine learning and @Collett2014, @KalbfleischPrentice1973 for survival analysis. -This book serves as a complement to the above examples and introduces common machine learning terminology from simpler settings such as regression and classification, but without diving into the detail found in other sources, instead focusing on extension to the survival analysis setting. - -This book may be useful for Masters or PhD students who are specialising in machine learning in survival analysis, machine learning practitioners looking to work in the survival setting, or statisticians who are familiar with survival analysis but less so with machine learning. -The book could be read cover-to-cover, but this is not advised. -Instead it may be preferable to dip into sections of the book as required and use the 'signposts' that direct the reader to sections of the book that are relevant to each other. - -The book is split into five parts: - -**Part I: Survival Analysis and Machine Learning**
-The book begins by introducing the basics of survival analysis and machine learning and unifying terminology between the two to enable meaningful description of 'machine learning in survival analysis' (MLSA). -In particular, the survival analysis 'task' and survival 'prediction types' are defined. - -**Part II: Evaluation**
-The second part of the book discusses one of the most important parts of the machine learning workflow, model evaluation. -In the simplest case, without evaluation there is no way to know if predictions from a trained machine learning model are any good. -Whether one uses a Kaplan-Meier estimator, a complex neural network, or anything in between, there is no guarantee any of these methods will actually make useful predictions for a given dataset. -This could be because the dataset is inherently difficult for any model to be trained on, perhaps because it is very 'noisy', or because a model is simply ill-suited to the task, for example using a Cox Proportional Hazards model when its key assumptions are violated. -Evaluation is therefore crucial to trusting any predictions made from a model. - -The measures in Part II are presented in different classes that reflect the prediction types identified in Part I. -In-sample measures, which evaluate the quality of a model's 'fit' to data, are not included as this book primarily focuses on external validation of predictive machine learning models. -Readers who are interested in this are are directed to @Collett2014 and @dataapplied for discussion on residuals; @Choodari2012a and @Royston2004 for $R^2$ type measures; and @VolinskyRaftery2000, @HURVICH1989, and @Liang2008 for information criterion measures. - -In each chapter, the measure class is introduced, particular metrics are listed, and commentary is provided on how and when to use the measures. -Recommendations for choosing measures are discussed in @sec-conclusions. - -**Part III: Models**
-Part III is a deep dive into machine learning models for solving survival analysis problems. -This begins with 'classical' models that may not be considered 'machine learning' and then continues by exploring different classes of machine learning models including random forests, support vector machines, gradient boosting machines, neural networks, and other less common classes. -Each model class is introduced in the simpler regression setting and then extensions to survival analysis are discussed. -Differences between model implementations are not discussed, instead the focus is on understanding how these models are built for survival analysis - in this way readers are well-equipped to independently follow individual papers introducing specific implementations. - -**Part IV: Reduction Techniques**
-The next part of the book introduces reduction techniques in survival analysis, which is the process of solving the survival analysis task by using methods from other fields. -In particular, chapters focus on demonstrating how any survival model can be used in the competing risks setting, discrete time modelling, Poisson methods, pseudovalues (reduction to regression), and other advanced modelling methods. - -**Part V: Extensions and Outlook**
-The final part of the book provides some miscellaneous chapters that may be of use to readers. -The first chapter lists common practical problems that occur when running survival analysis experiments and solutions that we have found useful. -The next lists open-source software at the time of writing for running machine learning survival analysis experiments. -The final chapter is our outlook on survival analysis and where the field may be heading. +FIXME \subsection*{Citing this book} -Whilst this book remains a work in progress you can cite it as - -``` -Sonabend. R, Bender. A. (2025). Machine Learning in Survival Analysis. -https://www.mlsabook.com. - -@book{MLSA2025 - title = {Machine Learning in Survival Analysis}, - editor = {Raphael Sonabend, Andreas Bender}, - url = {https://www.mlsabook.com}, - year = {2025} -} -``` +FIXME Please see the front page of the book website ([https://www.mlsabook.com](https://www.mlsabook.com)) for full licensing details. @@ -253,14 +219,11 @@ Raphael and Andreas \chapter*{Authors} -Raphael Sonabend is the CEO and Co-Founder of OSPO Now, a company providing virtual open-source program offices as a service. They are also a Visiting Researcher at Imperial College London. Raphael holds a PhD in statistics, specializing in machine learning applications for survival analysis. They created the R packages `mlr3proba`, `survivalmodels`, and the Julia package `SurvivalAnalysis.jl`. Raphael co-edited and co-authored *Applied Machine Learning Using mlr3 in R* [@Bischl2024]. - -Andreas Bender is... - +FIXME \chapter*{Acknowledgments} -We would like to gratefully acknowledge our colleagues that reviewed the content of this book, including: Lukas Burk, Cesaire Fouodo. +FIXME ::: diff --git a/book/library.bib b/book/library.bib index 8d49325..cc0fa11 100644 --- a/book/library.bib +++ b/book/library.bib @@ -7861,3 +7861,10 @@ @article{Muller1994 volume = {50}, } +@book{Goodfellow2016, + title={Deep Learning}, + author={Ian Goodfellow and Yoshua Bengio and Aaron Courville}, + publisher={MIT Press}, + note={\url{http://www.deeplearningbook.org}}, + year={2016} +}