Tootfinder

The space of multifurcating ranked tree shapes: enumeration, lattice structure, and Markov chains
Julie Zhang, Noah A. Rosenberg, Julia A. Palacios
https://arxiv.org/abs/2506.10856

The space of multifurcating ranked tree shapes: enumeration, lattice structure, and Markov chains
Coalescent models of bifurcating genealogies are used to infer evolutionary parameters from molecular data. However, there are many situations where bifurcating genealogies do not accurately reflect the true underlying ancestral history of samples, and a multifurcating genealogy is required. The space of multifurcating genealogical trees, where nodes can have more than two descendants, is largely underexplored in the setting of coalescent inference. In this paper, we examine the space of rooted…

Transformers as Multi-task Learners: Decoupling Features in Hidden Markov Models
Yifan Hao, Chenlu Ye, Chi Han, Tong Zhang
https://arxiv.org/abs/2506.01919

Transformers as Multi-task Learners: Decoupling Features in Hidden Markov Models
Transformer based models have shown remarkable capabilities in sequence learning across a wide range of tasks, often performing well on specific task by leveraging input-output examples. Despite their empirical success, a comprehensive theoretical understanding of this phenomenon remains limited. In this work, we investigate the layerwise behavior of Transformers to uncover the mechanisms underlying their multi-task generalization ability. Taking explorations on a typical sequence model, i.e, H…

On the Weak Error for Local Stochastic Volatility Models
Peter K. Friz, Benjamin Jourdain, Thomas Wagenhofer, Alexandre Zhou
https://arxiv.org/abs/2506.10817

On the Weak Error for Local Stochastic Volatility Models
Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for "calibration-on-the-fly", typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this limit is a well-known problem in the field; the general case is largely open, despite recent progress in Markovian situations. Our take is to start with a well-defined Euler approximation to the formal McKean-Vlasov equation, followed by a newly established hal…

Mean-Field-Type Game Theory with Rosenblatt Noise
Hamidou Tembine, Tyrone E. Duncan, Bozenna Pasik-Duncan
https://arxiv.org/abs/2506.08025 https://

Mean-Field-Type Game Theory with Rosenblatt Noise
We study the integration of Rosenblatt noise into stochastic systems, control theory, and mean-field-type game theory, addressing the limitations of traditional Gaussian and Markovian models. Empirical evidence from various domains, including water demand, e-commerce, power grid operations, wireless channels, and agricultural supply chains, demonstrates the prevalence of non-Gaussian characteristics such as skews, heavy tails and strong long-range dependencies. The Rosenblatt process, a non-Gau…

This https://arxiv.org/abs/2502.20799 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum-assisted variational Monte Carlo
Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry. Recent advancements in quantum hardware have opened new avenues for addressing this challenge. Inspired by the quantum-enhanced Markov chain Monte Carlo (QeMCMC) algorithm [Nature, 619, 282-287 (2023)], which was originally designed for sampling the Boltzmann distribution of classical spin models using quantum computers, we introduce a quantum-assisted variational Monte Carlo (QA-VMC)…

ProjMC$^2$: Scalable and Stable Posterior Inference for Bayesian Spatial Factor Models with Application to Spatial Transcriptomics
Lu Zhang
https://arxiv.org/abs/2506.01098

ProjMC$^2$: Scalable and Stable Posterior Inference for Bayesian Spatial Factor Models with Application to Spatial Transcriptomics
Factor models exhibit a fundamental tradeoff among flexibility, identifiability, and computational efficiency. Bayesian spatial factor models, in particular, face pronounced identifiability concerns and scaling difficulties. To mitigate these issues and enhance posterior inference reliability, this work proposes Projected Markov Chain Monte Carlo (ProjMC$^2$), a novel Markov Chain Monte Carlo (MCMC) sampling algorithm employing projection techniques and conditional conjugacy. ProjMC$^2$ is show…

Drawdowns, Drawups, and Occupation Times under General Markov Models
Pingping Zeng, Gongqiu Zhang, Weinan Zhang
https://arxiv.org/abs/2506.00552 https://…

Drawdowns, Drawups, and Occupation Times under General Markov Models
Drawdown risk, an important metric in financial risk management, poses significant computational challenges due to its highly path-dependent nature. This paper proposes a unified framework for computing five important drawdown quantities introduced in Landriault et al. (2015) and Zhang (2015) under general Markov models. We first establish linear systems and develop efficient algorithms for such problems under continuous-time Markov chains (CTMCs), and then establish their theoretical convergen…

Large Deviations for Markovian Graphon Processes and Associated Dynamical Systems on Networks
Shankar Bhamidi, Amarjit Budhiraja, Souvik Ray
https://arxiv.org/abs/2506.08333

Large Deviations for Markovian Graphon Processes and Associated Dynamical Systems on Networks
We consider temporal models of rapidly changing Markovian networks modulated by time-evolving spatially dependent kernels that define rates for edge formation and dissolution. Alternatively, these can be viewed as Markovian networks with $O(1)$ jump rates viewed over a long time horizon. In the regimes we consider, the window averages of graphon valued processes over suitable time intervals are natural state descriptors for the system. Under appropriate conditions on the jump-rate kernels, we e…

This https://arxiv.org/abs/2503.00772 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Bayesian inference for dynamic spatial quantile models with interactive effects
With the rapid advancement of information technology and data collection systems, large-scale spatial panel data presents new methodological and computational challenges. This paper introduces a dynamic spatial panel quantile model that incorporates unobserved heterogeneity. The proposed model captures the dynamic structure of panel data, high-dimensional cross-sectional dependence, and allows for heterogeneous regression coefficients. To estimate the model, we propose a novel Bayesian Markov C…

The Law of Large Numbers and CLT for Non-stationary Markov Jump Processes Exhibiting Time-of-Day Effects
Monte Fischer, Peter W. Glynn
https://arxiv.org/abs/2506.08282

The Law of Large Numbers and CLT for Non-stationary Markov Jump Processes Exhibiting Time-of-Day Effects
In this paper, we develop a general law of large numbers and central limit theorem for finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in service operations and manufacturing applications in which time-of-day, day-of-week, and secular effects are of first order importance in predicting system behavior. Our theorems allow for non-stationary reward environments that continuously accumulate reward, while including contributions from non-stationar…