arXiv subjects

Philipp Kopper

Publications and source records attributed to Philipp Kopper.

8 recordsLinked to original sources

arXiv2024

How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression

Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional regression models, such as the Cox model, have received little attention so far. We close this gap by proposing a framework for distributional regression using inverse flow transformations (DRIFT), which includes neural representations of the aforementioned models. We empirically demonstrate that the neural representations of models in DRIFT can serve as a substitute for their classical statistical counterparts in several applications involving continuous, ordered, time-series, and survival outcomes. We confirm that models in DRIFT empirically match the performance of several statistical methods in terms of estimation of partial effects, prediction, and aleatoric uncertainty quantification. DRIFT covers both interpretable statistical models and flexible neural networks opening up new avenues in both statistical modeling and deep learning.

cs.LG↗

arXiv2024

On Training Survival Models with Scoring Rules

Scoring rules are an established way of comparing predictive performances across model classes. In the context of survival analysis, they require adaptation in order to accommodate censoring. This work investigates using scoring rules for model training rather than evaluation. Doing so, we establish a general framework for training survival models that is model agnostic and can learn event time distributions parametrically or non-parametrically. In addition, our framework is not restricted to any specific scoring rule. While we focus on neural network-based implementations, we also provide proof-of-concept implementations using gradient boosting, generalized additive models, and trees. Empirical comparisons on synthetic and real-world data indicate that scoring rules can be successfully incorporated into model training and yield competitive predictive performance with established time-to-event models.

cs.LG↗

arXiv2023

Deep Learning for Survival Analysis: A Review

The influx of deep learning (DL) techniques into the field of survival analysis in recent years has led to substantial methodological progress; for instance, learning from unstructured or high-dimensional data such as images, text or omics data. In this work, we conduct a comprehensive systematic review of DL-based methods for time-to-event analysis, characterizing them according to both survival- and DL-related attributes. In summary, the reviewed methods often address only a small subset of tasks relevant to time-to-event data - e.g., single-risk right-censored data - and neglect to incorporate more complex settings. Our findings are summarized in an editable, open-source, interactive table: https://survival-org.github.io/DL4Survival. As this research area is advancing rapidly, we encourage community contribution in order to keep this database up to date.

stat.ML↗

arXiv2022

When Are Scoring Rules Proper? Bridging Theory and Practice in Survival Model Evaluation

Proper scoring rules encourage probabilistic predictions that match the true underlying distribution and are central to model evaluation, with increasing relevance in automated workflows such as AutoML. In survival analysis, however, their behavior under censoring is not fully understood. We study commonly used squared and logarithmic scoring rules for right-censored survival data under independent censoring, introducing a notion of marginal properness based on observable outcomes. Within this framework, we show that the SBS, evaluated at a fixed time point, along with its integrated version (ISBS) and the RCLL are strictly proper when all individuals eventually experience the event, but can become improper under finite follow-up or in the presence of cure fractions. For the SBS, we derive a closed-form expression that reveals the true mechanism: residual mass, corresponding to individuals who remain event-free at study end, systematically biases the score toward underestimating survival, with the effect increasing at later evaluation times and under heavier censoring. Through simulation experiments, we examine how these issues manifest in finite samples and under misspecification. The SBS exhibits pronounced improperness at late evaluation times and poor discrimination between models. The ISBS is more robust due to temporal integration but remains sensitive to tail regularity violations, exhibiting detectable improperness and reduced discriminatory power. The RCLL behaves consistently with strict properness and effectively separates misspecified models. Overall, our results demonstrate how theoretical improperness can translate into misleading model comparisons, underscoring the need for further methodological development in survival model evaluation under censoring and realistic data conditions.

math.ST↗

arXiv2022

DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis

Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale data sets and complex outcome distributions, concealed by truncation and censoring processes. The piecewise exponential additive mixed model (PAMM) is a model class addressing many of these challenges, yet PAMMs are not applicable in high-dimensional feature settings or in the case of unstructured or multimodal data. We unify existing approaches by proposing DeepPAMM, a versatile deep learning framework that is well-founded from a statistical point of view, yet with enough flexibility for modeling complex hazard structures. We illustrate that DeepPAMM is competitive with other machine learning approaches with respect to predictive performance while maintaining interpretability through benchmark experiments and an extended case study.

stat.ML↗

arXiv2021

deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression

In this paper we describe the implementation of semi-structured deep distributional regression, a flexible framework to learn conditional distributions based on the combination of additive regression models and deep networks. Our implementation encompasses (1) a modular neural network building system based on the deep learning library \pkg{TensorFlow} for the fusion of various statistical and deep learning approaches, (2) an orthogonalization cell to allow for an interpretable combination of different subnetworks, as well as (3) pre-processing steps necessary to set up such models. The software package allows to define models in a user-friendly manner via a formula interface that is inspired by classical statistical model frameworks such as \pkg{mgcv}. The packages' modular design and functionality provides a unique resource for both scalable estimation of complex statistical models and the combination of approaches from deep learning and statistics. This allows for state-of-the-art predictive performance while simultaneously retaining the indispensable interpretability of classical statistical models.

stat.ML↗

arXiv2020

Semi-Structured Deep Piecewise Exponential Models

We propose a versatile framework for survival analysis that combines advanced concepts from statistics with deep learning. The presented framework is based on piecewise exponential models and thereby supports various survival tasks, such as competing risks and multi-state modeling, and further allows for estimation of time-varying effects and time-varying features. To also include multiple data sources and higher-order interaction effects into the model, we embed the model class in a neural network and thereby enable the simultaneous estimation of both inherently interpretable structured regression inputs as well as deep neural network components which can potentially process additional unstructured data sources. A proof of concept is provided by using the framework to predict Alzheimer's disease progression based on tabular and 3D point cloud data and applying it to synthetic data.

cs.LG↗

arXiv2018

pammtools: Piece-wise exponential Additive Mixed Modeling tools

Piecewise exponential additive mixed models (PAMMs) provide a flexible framework for analyzing censored and truncated time-to-event data, bridging classical hazard-based modeling with modern regression techniques. They enable the estimation of complex covariate effects, including non-linear and time-varying (cumulative) effects, and naturally incorporate time-varying covariates. Moreover, PAMMs are applicable across a wide range of survival settings, including non-proportional hazards, recurrent events, competing risks, and multi-state analyses. This article introduces the pammtools package, which facilitates data transformation, estimation, and interpretation for PAMMs within a unified workflow. The package provides a comprehensive, user-friendly, and extensible interface covering the full modeling pipeline, from data transformation to estimation and visualization. In addition, simulation-based inference allows the calculation of confidence intervals for arbitrary quantities of interest such as covariate dependent hazards, survival probabilities, restricted mean survival times and transition probabilities.

stat.CO↗