Jonas Wahl
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View article: Causal discovery on vector-valued variables and consistency-guided aggregation
Causal discovery on vector-valued variables and consistency-guided aggregation Open
Causal discovery (CD) aims to discover the causal graph underlying the data generation mechanism of observed variables. In many real-world applications, the observed variables are vector-valued, such as in climate science where variables a…
View article: When Counterfactual Reasoning Fails: Chaos and Real-World Complexity
When Counterfactual Reasoning Fails: Chaos and Real-World Complexity Open
Counterfactual reasoning, a cornerstone of human cognition and decision-making, is often seen as the 'holy grail' of causal learning, with applications ranging from interpreting machine learning models to promoting algorithmic fairness. Wh…
View article: Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery
Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery Open
Causal discovery aims to extract qualitative causal knowledge in the form of causal graphs from data. Because causal ground truth is rarely known in the real world, simulated data plays a vital role in evaluating the performance of the var…
View article: Internal Incoherency Scores for Constraint-based Causal Discovery Algorithms
Internal Incoherency Scores for Constraint-based Causal Discovery Algorithms Open
Causal discovery aims to infer causal graphs from observational or experimental data. Methods such as the popular PC algorithm are based on conditional independence testing and utilize enabling assumptions, such as the faithfulness assumpt…
View article: The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications
The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications Open
Causal discovery aims to automatically uncover causal relationships from data, a capability with significant potential across many scientific disciplines. However, its real-world applications remain limited. Current methods often rely on u…
View article: Sortability of Time Series Data
Sortability of Time Series Data Open
Evaluating the performance of causal discovery algorithms that aim to find causal relationships between time-dependent processes remains a challenging topic. In this paper, we show that certain characteristics of datasets, such as varsorta…
View article: Asymptotic Uncertainty in the Estimation of Frequency Domain Causal Effects for Linear Processes
Asymptotic Uncertainty in the Estimation of Frequency Domain Causal Effects for Linear Processes Open
Structural vector autoregressive (SVAR) processes are commonly used time series models to identify and quantify causal interactions between dynamically interacting processes from observational data. The causal relationships between these p…
View article: Causal Inference on Process Graphs, Part II: Causal Structure and Effect Identification
Causal Inference on Process Graphs, Part II: Causal Structure and Effect Identification Open
A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an…
View article: Impacts of Climate Change on Small Island Nations: A Data Science Framework using Remote Sensing and Observational Time Series
Impacts of Climate Change on Small Island Nations: A Data Science Framework using Remote Sensing and Observational Time Series Open
Small Island Developing States (SIDS) comprise a group of 58 nations identified by the United Nations as facing unique sustainability challenges. These challenges include high exposure to climate change and a lack of data and limited resou…
View article: Separation-based distance measures for causal graphs
Separation-based distance measures for causal graphs Open
Assessing the accuracy of the output of causal discovery algorithms is crucial in developing and comparing novel methods. Common evaluation metrics such as the structural Hamming distance are useful for assessing individual links of causal…
View article: Foundations of causal discovery on groups of variables
Foundations of causal discovery on groups of variables Open
Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for …
View article: Invariance & Causal Representation Learning: Prospects and Limitations
Invariance & Causal Representation Learning: Prospects and Limitations Open
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variable…
View article: Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions
Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions Open
The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various assump…
View article: Projecting infinite time series graphs to finite marginal graphs using number theory
Projecting infinite time series graphs to finite marginal graphs using number theory Open
In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the pas…
View article: Vector Causal Inference between Two Groups of Variables
Vector Causal Inference between Two Groups of Variables Open
Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-base…
View article: Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery
Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery Open
Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather unrea…
View article: Foundations of Causal Discovery on Groups of Variables
Foundations of Causal Discovery on Groups of Variables Open
Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for …
View article: Causal Inference on Process Graphs, Part I: The Structural Equation Process Representation
Causal Inference on Process Graphs, Part I: The Structural Equation Process Representation Open
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent comp…
View article: Vector causal inference between two groups of variables
Vector causal inference between two groups of variables Open
Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-base…
View article: Traces on diagram algebras II: centralizer algebras of easy groups and new variations of the Young graph
Traces on diagram algebras II: centralizer algebras of easy groups and new variations of the Young graph Open
In continuation of our recent work [39], we classify the extremal traces on infinite diagram algebras that appear in the context of Schur–Weyl duality for Banica and Speicher’s easy groups [3]. We show that the branching graphs of these al…
View article: Traces on diagram algebras I: Free partition quantum groups, random lattice paths and random walks on trees
Traces on diagram algebras I: Free partition quantum groups, random lattice paths and random walks on trees Open
We classify extremal traces on the seven direct limit algebras of noncrossing\npartitions arising from the classification of free partition quantum groups of\nBanica-Speicher (arXiv:0808.2628) and Weber (arXiv:1201.4723). For the\ninfinite…
View article: Traces on diagram algebras II: Centralizer algebras of easy groups and new variations of the Young graph
Traces on diagram algebras II: Centralizer algebras of easy groups and new variations of the Young graph Open
In continuation of our recent work arXiv:2006.07312, we classify the extremal traces on infinite diagram algebras that appear in the context of Schur-Weyl duality for Banica and Speicher's easy groups. We show that the branching graphs of …
View article: The Fourier algebra of a rigid $C^{\ast}$-tensor category
The Fourier algebra of a rigid $C^{\ast}$-tensor category Open
Completely positive and completely bounded mutlipliers on rigid $C^{\ast}$-tensor categories were introduced by Popa and Vaes. Using these notions, we define and study the Fourier-Stieltjes algebra, the Fourier algebra and the algebra of c…
View article: A note on reduced and von Neumann algebraic free wreath products
A note on reduced and von Neumann algebraic free wreath products Open
In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix quantum group. Based on recent result on the…