arXiv subjects

Lasse Petersen

Publications and source records attributed to Lasse Petersen.

4 recordsLinked to original sources

arXiv2023

Nonparametric Conditional Local Independence Testing

Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional processes, and it is important for the description and learning of causal relations among processes. We develop a model-free framework for testing the hypothesis that a counting process is conditionally locally independent of another process. To this end, we introduce a new functional parameter called the Local Covariance Measure (LCM), which quantifies deviations from the hypothesis. Following the principles of double machine learning, we propose an estimator of the LCM and a test of the hypothesis using nonparametric estimators and sample splitting or cross-fitting. We call this test the (cross-fitted) Local Covariance Test ((X)-LCT), and we show that its level and power can be controlled uniformly, provided that the nonparametric estimators are consistent with modest rates. We illustrate the theory by an example based on a marginalized Cox model with time-dependent covariates, and we show in simulations that when double machine learning is used in combination with cross-fitting, then the test works well without restrictive parametric assumptions.

math.ST↗

arXiv2021

Robustly Removing Deep Sea Lighting Effects for Visual Mapping of Abyssal Plains

The majority of Earth's surface lies deep in the oceans, where no surface light reaches. Robots diving down to great depths must bring light sources that create moving illumination patterns in the darkness, such that the same 3D point appears with different color in each image. On top, scattering and attenuation of light in the water makes images appear foggy and typically blueish, the degradation depending on each pixel's distance to its observed seafloor patch, on the local composition of the water and the relative poses and cones of the light sources. Consequently, visual mapping, including image matching and surface albedo estimation, severely suffers from the effects that co-moving light sources produce, and larger mosaic maps from photos are often dominated by lighting effects that obscure the actual seafloor structure. In this contribution a practical approach to estimating and compensating these lighting effects on predominantly homogeneous, flat seafloor regions, as can be found in the Abyssal plains of our oceans, is presented. The method is essentially parameter-free and intended as a preprocessing step to facilitate visual mapping, but already produces convincing lighting artefact compensation up to a global white balance factor. It does not require to be trained beforehand on huge sets of annotated images, which are not available for the deep sea. Rather, we motivate our work by physical models of light propagation, perform robust statistics-based estimates of additive and multiplicative nuisances that avoid explicit parameters for light, camera, water or scene, discuss the breakdown point of the algorithms and show results on imagery captured by robots in several kilometer water depth.

cs.CV↗

arXiv2021

Testing Conditional Independence via Quantile Regression Based Partial Copulas

The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. We consider a test statistic based on generalized correlation between $U_1$ and $U_2$ and derive its large sample properties under consistency assumptions on the quantile regression procedure. We demonstrate through a simulation study that the resulting test is sound under complicated data generating distributions. Moreover, in the examples considered the test is competitive to other state-of-the-art conditional independence tests in terms of level and power, and it has superior power in cases with conditional variance heterogeneity of $X$ and $Y$ given $Z$.

math.ST↗

arXiv2020

Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values

In this article, we describe the algorithms for causal structure learning from time series data that won the Causality 4 Climate competition at the Conference on Neural Information Processing Systems 2019 (NeurIPS). We examine how our combination of established ideas achieves competitive performance on semi-realistic and realistic time series data exhibiting common challenges in real-world Earth sciences data. In particular, we discuss a) a rationale for leveraging linear methods to identify causal links in non-linear systems, b) a simulation-backed explanation as to why large regression coefficients may predict causal links better in practice than small p-values and thus why normalising the data may sometimes hinder causal structure learning. For benchmark usage, we detail the algorithms here and provide implementations at https://github.com/sweichwald/tidybench . We propose the presented competition-proven methods for baseline benchmark comparisons to guide the development of novel algorithms for structure learning from time series.

stat.ML↗