arXiv subjects

Johannes Textor

Publications and source records attributed to Johannes Textor.

14 recordsLinked to original sources

arXiv2023

A parallelized cellular Potts model that enables simulations at tissue scale

The Cellular Potts Model (CPM) is a widely used simulation paradigm for systems of interacting cells that has been used to study scenarios ranging from plant development to morphogenesis, tumour growth and cell migration. Despite their wide use, CPM simulations are considered too computationally intensive for three-dimensional (3D) models at organ scale. CPMs have been difficult to parallelise because of their inherently sequential update scheme. Here, we present a Graphical Processing Unit (GPU)-based parallelisation scheme that preserves local update statistics and is up to 3-4 orders of magnitude faster than serial implementations. We show several examples where our scheme preserves simulation behaviors that are drastically altered by existing parallelisation methods. We use our framework to construct tissue-scale models of liver and lymph node environments containing millions of cells that are directly based on microscopy-imaged tissue structures. Thus, our GPU-based CPM framework enables in silico studies of multicellular systems of unprecedented scale.

q-bio.TO↗

arXiv2023

Fitting Stochastic Lattice Models Using Approximate Gradients

Stochastic lattice models (sLMs) are computational tools for simulating spatiotemporal dynamics in physics, computational biology, chemistry, ecology, and other fields. Despite their widespread use, it is challenging to fit sLMs to data, as their likelihood function is commonly intractable and the models non-differentiable. The adjacent field of agent-based modelling (ABM), faced with similar challenges, has recently introduced an approach to approximate gradients in network-controlled ABMs via reparameterization tricks. This approach enables efficient gradient-based optimization with automatic differentiation (AD), which allows for a directed local search of suitable parameters rather than estimation via black-box sampling. In this study, we investigate the feasibility of using similar reparameterization tricks to fit sLMs through backpropagation of approximate gradients. We consider four common scenarios: fitting to single-state transitions, fitting to trajectories, inference of lattice states, and identification of stable lattice configurations. We demonstrate that all tasks can be solved by AD using four example sLMs from sociology, biophysics, image processing, and physical chemistry. Our results show that AD via approximate gradients is a promising method to fit sLMs to data for a wide variety of models and tasks.

nlin.CG↗

arXiv2023

Implementing Immune Repertoire Models Using Weighted Finite State Machines

The adaptive immune system's T and B cells can be viewed as large populations of simple, diverse classifiers. Artificial immune systems (AIS) $\unicode{x2013}$ algorithmic models of T or B cell repertoires $\unicode{x2013}$ are used in both computational biology and natural computing to investigate how the immune system adapts to its changing environments. However, researchers have struggled to build such systems at scale. For string-based AISs, finite state machines (FSMs) can store cell repertoires in compressed representations that are orders of magnitude smaller than explicitly stored receptor sets. This strategy allows AISs with billions of receptors to be generated in a matter of seconds. However, to date, these FSM-based AISs have been unable to deal with multiplicity in input data. Here, we show how weighted FSMs can be used to represent cell repertoires and model immunological processes like negative and positive selection, while also taking into account the multiplicity of input data. We use our method to build simple immune-inspired classifier systems that solve various toy problems in anomaly detection, showing how weights can be crucial for both performance and robustness to parameters. Our approach can potentially be extended to increase the scale of other population-based machine learning algorithms such as learning classifier systems.

cs.NE↗

arXiv2023

pgmpy: A Python Toolkit for Bayesian Networks

Bayesian Networks (BNs) are used in various fields for modeling, prediction, and decision making. pgmpy is a python package that provides a collection of algorithms and tools to work with BNs and related models. It implements algorithms for structure learning, parameter estimation, approximate and exact inference, causal inference, and simulations. These implementations focus on modularity and easy extensibility to allow users to quickly modify/add to existing algorithms, or to implement new algorithms for different use cases. pgmpy is released under the MIT License; the source code is available at: https://github.com/pgmpy/pgmpy, and the documentation at: https://pgmpy.org.

cs.LG↗

arXiv2023

Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models

Measurement error is ubiquitous in many variables - from blood pressure recordings in physiology to intelligence measures in psychology. Structural equation models (SEMs) account for the process of measurement by explicitly distinguishing between latent variables and their measurement indicators. Users often fit entire SEMs to data, but this can fail if some model parameters are not identified. The model-implied instrumental variables (MIIVs) approach is a more flexible alternative that can estimate subsets of model parameters in identified equations. Numerous methods to identify individual parameters also exist in the field of graphical models (such as DAGs), but many of these do not account for measurement effects. Here, we take the concept of "latent-to-observed" (L2O) transformation from the MIIV approach and develop an equivalent graphical L2O transformation that allows applying existing graphical criteria to latent parameters in SEMs. We combine L2O transformation with graphical instrumental variable criteria to obtain an efficient algorithm for non-iterative parameter identification in SEMs with latent variables. We prove that this graphical L2O transformation with the instrumental set criterion is equivalent to the state-of-the-art MIIV approach for SEMs, and show that it can lead to novel identification strategies when combined with other graphical criteria.

stat.ME↗

arXiv2022

A Simple Unified Approach to Testing High-Dimensional Conditional Independences for Categorical and Ordinal Data

Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform simple independence tests in each stratum, and combine the results. Unfortunately, the statistical power of this approach degrades rapidly as the number of conditioning variables increases. Here we propose a simple unified CI test for ordinal and categorical data that maintains reasonable calibration and power in high dimensions. We show that our test outperforms existing baselines in model testing and structure learning for dense directed graphical models while being comparable for sparse models. Our approach could be attractive for causal model testing because it is easy to implement, can be used with non-parametric or parametric probability models, has the symmetry property, and has reasonable computational requirements.

stat.ML↗

arXiv2021

Reply to Comment on "Inverse Square Lévy Walks are not Optimal Search Strategies for d \geq 2 "

We refute here the concernes raised in the Comment of our letter. This reply states clearly the validity range of our results and shows that the optimality of inverse-square Levy walks at the basis of the Levy flight foraging hypothesis is generically unfounded. We also give the precise set of conditions for which inverse-levy square Levy walks turn to be optimal, conditions which are unlikely to be verified biologically.

cond-mat.stat-mech↗

arXiv2020

Inverse square Lévy walks are not optimal search strategies for $d\ge 2$

The Lévy hypothesis states that inverse square Lévy walks are optimal search strategies because they maximise the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret a wealth of experimental data at various scales, from molecular motors to animals looking for resources, putting forward the conclusion that many living organisms perform Lévy walks to explore space because of their optimal efficiency. Here we provide analytically the dependence on target density of the encounter rate of Lévy walks for any space dimension $d$ ; in particular, this scaling is shown to be {\it independent} of the Lévy exponent $α$ for the biologically relevant case $d\ge 2$, which proves that the founding result of the Lévy hypothesis is incorrect. As a consequence, we show that optimizing the encounter rate with respect to $α$ is {\it irrelevant} : it does not change the scaling with density and can lead virtually to {\it any} optimal value of $α$ depending on system dependent modeling choices. The conclusion that observed inverse square Lévy patterns are the result of a common selection process based purely on the kinetics of the search behaviour is therefore unfounded.

cond-mat.stat-mech↗

arXiv2019

Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework

Principled reasoning about the identifiability of causal effects from non-experimental data is an important application of graphical causal models. This paper focuses on effects that are identifiable by covariate adjustment, a commonly used estimation approach. We present an algorithmic framework for efficiently testing, constructing, and enumerating $m$-separators in ancestral graphs (AGs), a class of graphical causal models that can represent uncertainty about the presence of latent confounders. Furthermore, we prove a reduction from causal effect identification by covariate adjustment to $m$-separation in a subgraph for directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs). Jointly, these results yield constructive criteria that characterize all adjustment sets as well as all minimal and minimum adjustment sets for identification of a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results extend several existing solutions for special cases of these problems. Our efficient algorithms allowed us to empirically quantify the identifiability gap between covariate adjustment and the do-calculus in random DAGs and MAGs, covering a wide range of scenarios. Implementations of our algorithms are provided in the R package dagitty.

cs.AI↗

arXiv2018

Complete Graphical Characterization and Construction of Adjustment Sets in Markov Equivalence Classes of Ancestral Graphs

We present a graphical criterion for covariate adjustment that is sound and complete for four different classes of causal graphical models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our criterion unifies covariate adjustment for a large set of graph classes. Moreover, we define an explicit set that satisfies our criterion, if there is any set that satisfies our criterion. We also give efficient algorithms for constructing all sets that fulfill our criterion, implemented in the R package dagitty. Finally, we discuss the relationship between our criterion and other criteria for adjustment, and we provide new soundness and completeness proofs for the adjustment criterion for DAGs.

math.ST↗

arXiv2015

Drawing and Analyzing Causal DAGs with DAGitty

DAGitty is a software for drawing and analyzing causal diagrams, also known as directed acyclic graphs (DAGs). Functions include identification of minimal sufficient adjustment sets for estimating causal effects, diagnosis of insufficient or invalid adjustment via the identification of biasing paths, identification of instrumental variables, and derivation of testable implications. DAGitty is provided in the hope that it is useful for researchers and students in Epidemiology, Sociology, Psychology, and other empirical disciplines. The software should run in any web browser that supports modern JavaScript, HTML, and SVG. This is the user manual for DAGitty version 2.3. The manual is updated with every release of a new stable version. DAGitty is available at dagitty.net.

cs.AI↗

arXiv2015

Learning from Pairwise Marginal Independencies

We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully explain a given set of independencies, and derive algorithms to efficiently enumerate such structures. Our results map out the space of faithful causal models for a given set of pairwise marginal independence relations. This allows us to show the extent to which causal inference is possible without using conditional independence tests.

cs.AI↗

arXiv2015

A Complete Generalized Adjustment Criterion

Covariate adjustment is a widely used approach to estimate total causal effects from observational data. Several graphical criteria have been developed in recent years to identify valid covariates for adjustment from graphical causal models. These criteria can handle multiple causes, latent confounding, or partial knowledge of the causal structure; however, their diversity is confusing and some of them are only sufficient, but not necessary. In this paper, we present a criterion that is necessary and sufficient for four different classes of graphical causal models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our criterion subsumes the existing ones and in this way unifies adjustment set construction for a large set of graph classes.

math.ST↗

arXiv2012

Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective

Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.

cs.AI↗