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Leveraging the group structure of hypotheses for more powerful multiple testing with FDR control for the filtered rejection set
Marina Bogomolov, Shinjini Nandi
https://arxiv.org/abs/2509.15444

Leveraging the group structure of hypotheses for more powerful multiple testing with FDR control for the filtered rejection set
Modern biological studies often involve testing many hypotheses organized in a group or a hierarchical structure, such as a directed acyclic graph (DAG). In these studies, researchers often wish to control the false discovery rate (FDR) after filtering the discoveries to obtain interpretable results. For addressing this goal, Katsevich, Sabatti, and Bogomolov (2023, Journal of the American Statistical Association, 118(541), 165-176) developed a general method, Focused BH, that guarantees FDR co…

Using Medical Algorithms for Task-Oriented Dialogue in LLM-Based Medical Interviews
Rui Reis, Pedro Rangel Henriques, Jo\~ao Ferreira-Coimbra, Eva Oliveira, Nuno F. Rodrigues
https://arxiv.org/abs/2510.12490

Using Medical Algorithms for Task-Oriented Dialogue in LLM-Based Medical Interviews
We developed a task-oriented dialogue framework structured as a Directed Acyclic Graph (DAG) of medical questions. The system integrates: (1) a systematic pipeline for transforming medical algorithms and guidelines into a clinical question corpus; (2) a cold-start mechanism based on hierarchical clustering to generate efficient initial questioning without prior patient information; (3) an expand-and-prune mechanism enabling adaptive branching and backtracking based on patient responses; (4) a t…

M\"obius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs
Patrick Forr\'e, Abel Jansma
https://arxiv.org/abs/2510.05786

Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs
We generalize the concept of Möbius inversion and Shapley values to directed acyclic multigraphs and weighted versions thereof. We further allow value functions (games) and thus their Möbius transforms (synergy function) and Shapley values to have values in any abelian group that is a module over a ring that contains the graph weights, e.g. vector-valued functions. To achieve this and overcome the obstruction that the classical axioms (linearity, efficiency, null player, symmetry) are not str…

Flow polytopes for extensions of bipartite graphs
Benjamin Braun, Kaitlin Bruegge, Robert Davis, Derek Hanely
https://arxiv.org/abs/2509.26445 https://arxi…

Flow polytopes for extensions of bipartite graphs
The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph $G$ with minimum degree at least two, we construct two associated acyclic directed graphs: the extension of $G$ and the almost-degree-whiskered graph of $G$. We prove that the normalized volume of the flow polytope for the extension of $G$ is equal to the number of matchings in the almost-degree-whiskered graph of $G$. Further, we refine this result by …

Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models
Daniel Bartl, Stephan Eckstein
https://arxiv.org/abs/2510.09270 https://…

Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models
Using i.i.d. data to estimate a high-dimensional distribution in Wasserstein distance is a fundamental instance of the curse of dimensionality. We explore how structural knowledge about the data-generating process which gives rise to the distribution can be used to overcome this curse. More precisely, we work with the set of distributions of probabilistic graphical models for a known directed acyclic graph. It turns out that this knowledge is only helpful if it can be quantified, which we forma…

The chanciness of time
John M. Myers, Hadi Madjid
https://arxiv.org/abs/2511.08611 https://arxiv.org/pdf/2511.08611 https://arxiv.org/html/2511.08611
arXiv:2511.08611v1 Announce Type: new
Abstract: Digital network failures stemming from instabilities in measurements of temporal order motivate attention to concurrent events. A century of attempts to resolve the instabilities have never eliminated them. Do concurrent events occur at indeterminate times, or are they better seen as events to which the very concept of temporal order cannot apply? Logical dependencies of messages propagating through digital networks can be represented by marked graphs on which tokens are moved in formal token games. However, available mathematical formulations of these token games invoke "markings"-- global snapshots of the locations of tokens on the graph. The formulation in terms of global snapshots is misleading, because distributed networks are never still: they exhibit concurrent events inexpressible by global snapshots. We reformulate token games used to represent digital networks so as to express concurrency. The trick is to replace global snapshots with "local snapshots." Detached from any central clock, a local snapshot records an action at a node during a play of a token game. Assemblages of local records define acyclic directed graphs that we call history graphs. We show how history graphs represent plays of token games with concurrent motions, and, importantly, how history graphs can represent the history of a network operating while undergoing unpredictable changes.
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Restrictions of PCBNs for integration-free computations
Alexis Derumigny, Niels Horsman, Dorota Kurowicka
https://arxiv.org/abs/2510.03518 https://arxiv.or…

Restrictions of PCBNs for integration-free computations
The pair-copula Bayesian Networks (PCBN) are graphical models composed of a directed acyclic graph (DAG) that represents (conditional) independence in a joint distribution. The nodes of the DAG are associated with marginal densities, and arcs are assigned with bivariate (conditional) copulas following a prescribed collection of parental orders. The choice of marginal densities and copulas is unconstrained. However, the simulation and inference of a PCBN model may necessitate possibly high-dimen…

Minimal Trails in Restricted DAGs
Alexis Derumigny, Niels Horsman, Dorota Kurowicka
https://arxiv.org/abs/2510.02113 https://arxiv.org/pdf/2510.02113

Minimal Trails in Restricted DAGs
In this paper, the properties of minimal trails in a directed acyclic graph that is restricted not to contain an active cycle are studied. We are motivated by an application of the results in the copula-based Bayesian Network model developed recently. We propose a partial order on the set of trails activated by a certain subset of nodes, and show that every minimal trail, according to such an order, has a simple structure.