arXiv research

Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.

In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this context, one is interested in computing certain quantities of interest such as th…

Study solves HJB equations for time-inconsistent control problems.

The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic response to various types of stimulation. We show that an ensemble of deterministic le…

Identifies most probable flows for Kunita SDEs in fluid dynamics.

Unified analysis for deterministic samplers in diffusion models.

Unified quadrature framework for large-scale kernel machines.

Efficient methods accelerate diffusion model sampling.

We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In…

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates across the action when estimating the gradient, instead of relying only on the action in the sampled trajectory. We es…

The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal processing: It is a member of the broader class of $f$-divergences, and it is related to …

Research integrates sentiment analysis with reinforcement learning for better trading strategies.

TT-DAC-PS: A deterministic actor-critic approach for optimal trade execution

In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possible non-gaussian distributions of the underlying object. We adapt to our probl…

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field …

The paper analyzes the stationarity of stochastic Volterra integral equations and introduces fake stationary regimes.

Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…

Gaussian processes are an important regression tool with excellent analytic properties which allow for direct integration of derivative observations. However, vanilla GP methods scale cubically in the amount of observations. In this work, we propose a novel approach for scaling GP regression with derivatives based on q…

New model predicts dynamic tax evasion with audits and imitation.

New method ensures consistent inference across different tensor parallel sizes for large language models.

The stochastic exponential $Z_t=\exp\{M_t-M_0-(1/2) <M,M>_t\}$ of a continuous local martingale $M$ is itself a continuous local martingale. We give a necessary and sufficient condition for the process $Z$ to be a true martingale in the case where $M_t=\int_0^t b(Y_u)\,dW_u$ and $Y$ is a one-dimensional diffusion drive…

Proposes a multi-fidelity machine learning strategy integrating low-fidelity deterministic and high-fidelity Bayesian models.

Study compares deterministic and probabilistic ML for precise AM component dimensions.

PS-IG improves feature attribution by reducing noise and variance.

The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly …

Study on complexity of random polynomials with deterministic spikes, identifying phase transitions.

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory…

This research improves deep neural networks for parameter identification and prediction in stochastic Volterra integral equations.

New algorithm speeds up MCMC for complex distributions.

We introduce a new recursive aggregation procedure called Bernstein Online Aggregation (BOA). The exponential weights include an accuracy term and a second order term that is a proxy of the quadratic variation as in Hazan and Kale (2010). This second term stabilizes the procedure that is optimal in different senses. We…

Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated as Lagrangians. Assumptions of integrability of Lagrangians and dynamics are im…

Itô maps provide a method for any-step SDE integration.

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly dete…

LLMs produce volatile sentence-level sentiment classifications that affect financial decision-making.

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we …

A new method for estimating uncertainties in neural ODEs without numerical integration.

The study characterizes straight-line flows in dynamic measure transport.

Developed mlf-core for deterministic machine learning.

Random number generators (RNGs) that are crucial for cryptographic applications have been the subject of adversarial attacks. These attacks exploit environmental information to predict generated random numbers that are supposed to be truly random and unpredictable. Though quantum random number generators (QRNGs) are ba…

Study on regret minimization in deterministic MDPs.

ProGen improves spatiotemporal forecasting with SDEs and diffusion models.

Bayesian neural networks improve likelihood-free inference efficiency.

CGAN fails to improve deterministic sequence predictions, revealing a theoretical limitation.

Deep actor-critic learning optimizes power control in mobile networks.

Reinforcement learning algorithms such as the deep deterministic policy gradient algorithm (DDPG) has been widely used in continuous control tasks. However, the model-free DDPG algorithm suffers from high sample complexity. In this paper we consider the deterministic value gradients to improve the sample efficiency of …

ETGL-DDPG improves DDPG for sparse reward control with new exploration and replay techniques.

In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon b…

We convert deterministic flow models to stochastic samplers.