arXiv subjects

Christoph Schultheiss

Publications and source records attributed to Christoph Schultheiss.

7 recordsLinked to original sources

arXiv2024

Ancestor regression in structural vector autoregressive models

We present a new method for causal discovery in linear structural vector autoregressive models. We adapt an idea designed for independent observations to the case of time series while retaining its favorable properties, i.e., explicit error control for false causal discovery, at least asymptotically. We apply our method to several real-world bivariate time series datasets and discuss its findings which mostly agree with common understanding. The arrow of time in a model can be interpreted as background knowledge on possible causal mechanisms. Hence, our ideas could be extended to incorporating different background knowledge, even for independent observations.

stat.ME↗

arXiv2024

Assessing the overall and partial causal well-specification of nonlinear additive noise models

We propose a method to detect model misspecifications in nonlinear causal additive and potentially heteroscedastic noise models. We aim to identify predictor variables for which we can infer the causal effect even in cases of such misspecification. We develop a general framework based on knowledge of the multivariate observational data distribution. We then propose an algorithm for finite sample data, discuss its asymptotic properties, and illustrate its performance on simulated and real data.

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arXiv2023

On the Identifiability and Estimation of Causal Location-Scale Noise Models

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect $Y$ can be written as a function of the cause $X$ and a noise source $N$ independent of $X$, which may be scaled by a positive function $g$ over the cause, i.e., $Y = f(X) + g(X)N$. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of $Y$ given $X$ as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

stat.ML↗

arXiv2023

On the pitfalls of Gaussian likelihood scoring for causal discovery

We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We present a surprising negative result for Gaussian likelihood scoring in combination with nonparametric regression methods.

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arXiv2023

Ancestor regression in linear structural equation models

We present a new method for causal discovery in linear structural equation models. We propose a simple ``trick'' based on statistical testing in linear models that can distinguish between ancestors and non-ancestors of any given variable. Naturally, this can then be extended to estimating the causal order among all variables. We provide explicit error control for false causal discovery, at least asymptotically. This holds true even under Gaussianity, where other methods fail due to non-identifiable structures. These type I error guarantees come at the cost of reduced empirical power. Additionally, we provide an asymptotically valid goodness of fit p-value to assess whether multivariate data stems from a linear structural equation model.

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arXiv2022

Higher-order least squares: assessing partial goodness of fit of linear causal models

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings.

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arXiv2021

Multicarving for high-dimensional post-selection inference

We consider post-selection inference for high-dimensional (generalized) linear models. Data carving (Fithian et al., 2014) is a promising technique to perform this task. However, it suffers from the instability of the model selector and hence, may lead to poor replicability, especially in high-dimensional settings. We propose the multicarve method inspired by multisplitting to improve upon stability and replicability. Furthermore, we extend existing concepts to group inference and illustrate the applicability of the methodology also for generalized linear models.

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