arXiv research

It is well-known that irreversible MCMC algorithms converge faster to their stationary distributions than reversible ones. Using the special geometric structure of Lie groups $\mathcal G$ and dissipation fields compatible with the symplectic structure, we construct an irreversible HMC-like MCMC algorithm on $\mathcal G…

Unified framework for MCMC algorithms simplifies their design and application.

Novel geometry-informed irreversible perturbation accelerates Langevin dynamics convergence.

Study measures irreversibility in crypto trends using Kullback-Leibler divergence.

Study of irreversible metric-measure spaces, proving convergence and stability results.

Recover simple irreversible Finsler geometry from travel time data

The relation between time series irreversibility and entropy production has been recently investigated in thermodynamic systems operating away from equilibrium. In this work we explore this concept in the context of financial time series. We make use of visibility algorithms to quantify in graph-theoretical terms time …

Study optimal investment under uncertain conditions.

The paper analyzes strategic irreversible investments with novel dynamic strategies.

Study on reinsurance decisions using mean-variance criterion with irreversible contracts.

Bayesian inference over admissible histories leads to irreversible kinetics.

The abstract discusses financial irreversibility using quantum mechanics and projective geometry.

Optimal dividend strategy with irreversible reinsurance constraints.

Sharp Hardy and spectral gap inequalities found on special irreversible Finsler manifolds.

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficienc…

Study links cognitive effort to thermodynamic principles, optimizing decision-making.

Investment decision triggered by a convex curve in a two-factor uncertainty model.

In the recent paper \cite{LoD1}, we classified closed geodesics on Finsler manifolds into rational and irrational two families, and gave a complete understanding on the index growth properties of iterates of rational closed geodesics. This study yields that a rational closed geodesic can not be the only closed geodesic…

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to …

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property…

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general…

In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (including Riemannian) manifold of dimension not less than 2.

Framework selects real estate redevelopment uses by integrating value, risk, complexity, and irreversibility.

Investment decisions shift earlier as patience decreases, with implications for pasting conditions.

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets…

We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every move of the sequence. This conditional setting leads to a possibility of irreve…

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …

Unified framework for MCMC and machine learning problems.

JaxSGMC simplifies SG-MCMC for Bayesian deep learning.

We introduce a new geometric approach that constructs a transition kernel of Markov chain. Our method always minimizes the average rejection rate and even reduce it to zero in many relevant cases, which cannot be achieved by conventional methods, such as the Metropolis-Hastings algorithm or the heat bath algorithm (Gib…

Paper proposes first unlearning algorithm for MCMC models.

In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-$σ$-fields as a flexi…

Paper applies theorem to find optimal investment boundary in stochastic capacity expansion.

We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in $α'$ in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we…

TensorFlow Probability MCMC toolkit improves MCMC efficiency for modern hardware.

We prove that for every $\Q$-homological Finsler 3-sphere $(M,F)$ with a bumpy and irreversible metric $F$, either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.

Stochastic EM with biased MCMC improves inference stability.

PDHAMS improves sampling for discrete distributions with quadratic potential functions.

It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel conce…

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, s…

In this paper, we derive a new handy integral equation for the free-boundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion $X$. The new integral equation allows to explicitly find the free-boundary $b(\cdot)$ in s…

Cyclical MCMC tackles high-dimensional multimodal distributions, showing convergence under certain conditions.

Paper compares MCMC-based copula methods for exchange option pricing.

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform no…

Nonlinear MCMC improves Bayesian machine learning sampling.

Model predicts stationary equilibrium in investment decisions of firms in fluctuating markets.

Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods …

Online method selects candidates from data streams, ensuring irreversible decisions.