We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death …
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48 results for “Birth-Death Process”
Bessel-like birth-death processphysics.soc-ph
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDE…
New method uses birth-death process and exploration component to accelerate sampling from multimodal distributions.
problem Sampling from multimodal probability distributions efficiently.
method Combines birth-death process and exploration component to accelerate sampling.
result Proves exponential asymptotic convergence under mild assumptions.
FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.
problem Global optimization of non-convex objective functions over measure space.
method Introduces Fast Spawn\&Prune (FS\&P) combining CPGD with birth-death process.
result First theoretical guarantee of global convergence for discrete-time stochastic algorithms.
Study birth-death dynamics for sampling Gibbs measures with nonconvex potentials.
problem Sampling Gibbs measures with nonconvex potentials.
method Birth-death dynamics, Kullback-Leibler divergence, divergence, kernel-based approximations, -convergence of gradient flows.
result Probability density converges exponentially fast to Gibbs equilibrium measure with a universal rate.
We consider probabilistic programming for birth-death models of evolution and introduce a new widely-applicable inference method that combines an extension of the alive particle filter (APF) with automatic Rao-Blackwellization via delayed sampling. Birth-death models of evolution are an important family of phylogenetic…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanis…
Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree models according to their posterior probabilities. The critical component of such an …
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 condition for linear graphs and prove the triviality of edge w…
Neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for the favorable training properties of "overparameterized" models. In this regime, gradient descent obeys a deterministic partial differential equation (PDE) that converges to a glo…
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.
problem Integrating high-dimensional multi-omic data for cancer subtyping.
method Mixed graphical model approach using Birth-Death MCMC algorithm.
result Our method outperforms LASSO and standard BDMCMC in computational efficiency and model selection accuracy.
Flow Matching for Count Datastat.ML
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
The paper develops a stationary-distribution theory for Random Forest ensemble size selection.
problem Determining the optimal number of trees in Random Forests.
method Modeling the ensemble size as a birth-death Markov chain and deriving its stationary distribution.
result The stationary ensemble size scales as as .
Reinforcement Learning in a Birth and Death Process: Breaking the Dependence on the State Spacecs.LG
New RL algorithm reduces regret in birth-death queueing problems.
problem Efficiency of reinforcement learning in MDPs with large state spaces.
method Modified Ucrl2 algorithm exploiting birth-death structure.
result Regret bound of independent of state space size.
Paper disproves conjecture about log-Sobolev constants.
problem Log-Sobolev constants and curvature bounds.
method Counterexample on birth-death chains.
result Conjecture about Ollivier curvature is incorrect.
USD algorithm transports distributions with or without mass conservation.
problem Transporting distributions with different masses.
method Particle descent algorithm using Sobolev-Fisher discrepancy.
result USD converges to target distribution in MMD sense.
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.
problem Proving modified logarithmic Sobolev inequalities for discrete Markov chains.
method Identifying and proving a curvature-dimension inequality , and showing its compatibility with diffusive settings.
result The condition preserves curvature bounds under tensorization and leads to Beckner inequalities.
In recent years, multi object tracking (MOT) problem has drawn attention to it and has been studied in various research areas. However, some of the challenging problems including time dependent cardinality, unordered measurement set, and object labeling remain unclear. In this paper, we propose robust nonparametric met…
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.
problem Comparing higher torsions from analytic and topological perspectives.
method Introduced fiberwise generalized Morse functions (GMFs) and excised neighborhoods around birth-death points.
result Established a generalized version of the higher Cheeger-Müller/Bismut-Zhang theorem.
Why Stake When You Can Borrow?q-fin.GN
New model assesses risks of staking and borrowing in smart contracts.
problem Security and efficiency of staking in smart contract platforms.
method Combines birth-death Pólya processes and credit derivatives models.
result Derivatives can reduce wealth concentration in staking networks.
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.
problem Optimizing multiple conflicting objectives in complex scenarios.
method Interacting particle method combining Langevin and birth-death dynamics with a dominance potential.
result Method effectively relocates dominated particles, improving Pareto optimality.
A (reactive) lattice-gas approach to economic cyclescond-mat.stat-mech
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.
problem Estimating hidden quantities in poorly characterized biochemical processes.
method Developed a Bayesian inference algorithm based on Markov chain Monte Carlo and sequential Monte Carlo methods.
result Numerical evaluation of the algorithm for a partially observed multi-scale birth-death process.
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.
problem Learning transition rates for complex stochastic systems.
method Neural networks to model nonlinear transition rates from observed data.
result Neural models outperform traditional methods in accuracy.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
This study investigates self-organizing dynamics in a stochastic exponential DAM model using Temporal Complexity.
problem Understanding self-organizing behavior in artificial neural systems.
method Investigation of a stochastic exponential DAM model through Temporal Complexity analysis.
result The model exhibits regimes of complex intermittency with nontrivial temporal correlations and scale-free behavior.
Classification of cryptocurrency coins and tokens by the dynamics of their market capitalisationsphysics.soc-ph
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.
problem Quantum cohomology of symplectic manifolds with -actions.
method Floer theory applied to -actions on symplectic manifolds.
result Constructs a family of filtrations on quantum cohomology for Conical Symplectic Resolutions.
This work develops sampling methods for differential privacy using SHK geometry.
problem Approximating sampling for the exponential mechanism in differential privacy.
method Develops perturbation theory for SHK gradient flows and applies to differential privacy.
result Derives time-dependent Pure-DP guarantees and Approximate-DP certificates.
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).
Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihoodstat.ME
Bayesian method learns graph structures from Gaussian data efficiently.
problem Scalability issue in Bayesian Gaussian graphical model inference.
method Marginal pseudo-likelihood, birth-death and reversible jump MCMC algorithms.
result Efficient graph structure learning for large graphs with over 1,000 nodes.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
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…
Deep Neyman-Scott Processesstat.ML
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
The study examines Hawkes processes and their long-term behavior.
problem Understanding the long-term behavior of Hawkes processes.
method Proving functional limit theorems under various conditions on the dispersion of child events.
result Functional limit theorems hold for Hawkes processes with different levels of child event dispersion.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
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…
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.
problem Efficient numerical methods for evaluating Lévy models.
method Defining SL-processes and sSL-processes, deriving properties of characteristic exponent, and showing all popular Lévy processes can be subordinated to Brownian motion.
result All crucial properties of characteristic exponent are consequences of a specific representation, and all popular Lévy processes are SL- or sSL-subordinated Brownian motion.
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…
A Technique for Determining Relevance Scores of Process Activities using Graph-based Neural Networkscs.LG
GRM uses graph neural networks to score process activity relevance.
problem Improving business processes with performance measures.
method Graph Relevance Miner (GRM) based on graph neural networks.
result Quantitatively evaluated relevance scores with four datasets.