arXiv research

Method approximates first passage times for birth-death processes.

Proposes a new birth-death process for better modeling of population dynamics.

New method uses birth-death process and exploration component to accelerate sampling from multimodal distributions.

FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.

New birth-death dynamics accelerates convergence in neural networks.

New method improves phylogenetic model inference by 30x.

Study birth-death dynamics for sampling Gibbs measures with nonconvex potentials.

A new sampling algorithm speeds up Langevin sampling for multimodal distributions.

New MCMC algorithm improves convergence of Bayesian regression trees.

In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery's $CD(K,n)$ condition for linear graphs and prove the triviality of edge w…

Near a birth-death critical point in a one-parameter family of gradient flows, there are precisely two Morse critical points of index difference one on the birth side. This paper gives a self-contained proof of the folklore theorem that these two critical points are joined by a unique gradient trajectory up to time-shi…

Paper proposes scalable method for analyzing multi-omic data.

Flow Matching for count data improves sample quality and efficiency.

The paper develops a stationary-distribution theory for Random Forest ensemble size selection.

New RL algorithm reduces regret in birth-death queueing problems.

Paper disproves conjecture about log-Sobolev constants.

USD algorithm transports distributions with or without mass conservation.

The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In t…

The study establishes a curvature-dimension condition for discrete Markov chains.

Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics' distribution and popularity are time-evolving. Several mode…

Paper compares higher torsions and removes fiberwise Morse function assumption.

Bayesian nonparametric models improve multi-object tracking robustness and flexibility.

New model assesses risks of staking and borrowing in smart contracts.

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the drift and diffusion depends on the volume present on both sides of the spread. "J…

New method optimizes multiple objectives using particle dynamics and gradient flow.

A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth-death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is nu…

Bayesian inference for biochemical reaction networks using jump-diffusion approximations.

According to Kiyoshi Igusa a generalized Morse function on an n-dimensional manifold M is a smooth function with only Morse and birth-death singularities and a framed function is a generalized Morse function with an additional structure: a framing of the negative eigenspace at each critical point of the function f. In …

We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that saddle cobordisms can be computed in terms of maps in a decorated skein exact triangle that extends the oriented skein exact triangle in knot…

Neural models learn continuous-time Markov chain transition rates from data.

Unified framework for analyzing gradient flows of measures with exponential decay of entropy.

This study investigates self-organizing dynamics in a stochastic exponential DAM model using Temporal Complexity.

We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simpl…

Floer theory constructs filtrations on quantum cohomology for symplectic manifolds.

This work develops sampling methods for differential privacy using SHK geometry.

Stein transport improves Bayesian inference with faster convergence and reduced variance.

Bayesian method learns graph structures from Gaussian data efficiently.

Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.

This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…

We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and a…

A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.

The study examines Hawkes processes and their long-term behavior.

Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…

SNP extends Neural Processes to handle temporal dependencies in sequences.

We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…

Efficient methods for Lévy models using SINH-regular processes.

The aim of process discovery, originating from the area of process mining, is to discover a process model based on business process execution data. A majority of process discovery techniques relies on an event log as an input. An event log is a static source of historical data capturing the execution of a business proc…