Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.
problem Gradient-based methods for two-player games suffer from drift due to discrete update steps.
method Derived modified continuous dynamical systems to closely follow the discrete dynamics of games.
result Identified distinct components of discretization drift that can alter or destabilize game performance.
New algorithm learns changing discrete distributions with minimal drift error.
problem Learning discrete distributions that change over time with limited past samples.
method Adaptive algorithm using data-dependent bounds to balance statistical and drift errors.
result Tighter statistical error bounds for drifting distributions with or without finite support.
The paper develops a neural network-based classifier for diffusion process drifts.
problem Classifying diffusion processes with distinct drift functions from discrete observations.
method Derives a Bayes rule and constructs a plug-in classifier using neural networks to estimate drifts.
result Establishes convergence rates for misclassification risk, highlighting benefits of diffusion structure.
The paper develops a neural network method for estimating drift functions of diffusion processes from discrete observations.
problem Nonparametric estimation of drift function for diffusion processes from high-frequency discrete observations.
method Neural network-based estimator for drift function estimation.
result Derives a non-asymptotic convergence rate for the neural network estimator.
Study on the spectrum of drift Laplacian on Ricci expanders.
problem Analyzing the spectrum of the drift Laplacian on Ricci expanders.
method Investigation of discrete spectrum under proper potential function, asymptotic behavior of potential function, and computation of eigenvalues.
result Discrete spectrum of the drift Laplacian on Ricci expanders with bounded Ricci curvature.
Graphs approximate semigroups for diffusion on Riemannian manifolds.
problem Approximating semigroups for diffusion on Riemannian manifolds.
method Discretized approximation using random walks on proximity graphs.
result Quantitative error estimates for convergence of discrete semigroups to continuous semigroups.
New risk bound for drift estimator in stochastic models.
problem Theoretical guarantees for drift estimation in stochastic differential equations.
method Derives an explicit risk bound using diffusion model theory.
result Explicit decomposition of risk into multiple sources of error.
This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as an external source of information. For estimating the hidden drift it is crucial…
Study non-stationary distributions, proving risk bounds for density estimation.
problem Estimating current distribution under gradual changes.
method Proves tight minimax risk bounds for nonparametric density estimation under drift.
result Generalizes previous results on agnostic learning under drift.
Study approximates financial market with discrete-time models.
problem Approximating continuous-time financial market models with discrete-time.
method Constructs discrete-time market models with Markov switching and proves convergence.
result Discrete-time models converge to continuous-time Black-Scholes model with Markov switching.
Study scaling limits of utility indifference prices in discretized Bachelier model.
problem Analyzing utility indifference prices for path-dependent European options in a discretized Bachelier model.
method Purely probabilistic approach, including duality argument, optimal drift control problem, martingale techniques, and strong invariance principles.
result Obtained a scaling limit for utility indifference prices as the number of trading times increases.
Kernel-Gradient Drifting improves generative modeling for non-Euclidean data.
problem Challenges in generative modeling for non-Euclidean data.
method Replaces Euclidean displacement with kernel-induced directions, exposing score-based structure.
result Kernel-gradient drifting enables state-of-the-art one-step generation for non-Euclidean data.
We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the sho…
Study improves survival analysis for credit risk by accounting for data drift.
problem Survival analysis in credit risk assumes a stationary data-generating process, but real-world data drift affects model performance.
method Proposes a dynamic joint modelling framework integrating longitudinal behavioural markers and hazard formulations, combined with drift-adaptive techniques.
result Proposed model outperforms classical survival models and drift-adaptive learners in various data drift scenarios.
Geometric formalism views optimization algorithms as discrete connections, revealing their algebraic curvature and flatness properties.
problem Understanding and optimizing the behavior of iterative optimization algorithms.
method Introducing a geometric and operator-theoretic formalism where optimization algorithms are encoded by coupled channels (drift and diffusion) whose algebraic curvature measures the deviation from ideal reversibility.
result Flat connections correspond to methods whose updates commute up to higher order, achieving minimal numerical dissipation and preserving stability.
The paper compares PINN methods for solving drift-diffusion equations on metric graphs.
problem Solving drift-diffusion equations on metric graphs using machine learning.
method Comparison of physics-informed neural networks (PINNs) for solving drift-diffusion equations on metric graphs.
result PINNs offer a flexible and versatile tool for solving parameter identification or optimization problems on metric graphs.
I In this paper, first we study a complete smooth metric measure space (Mn,g,e−fdv) with the (∞)-Bakry-Émery Ricci curvature Ricf≥2ag for some positive constant a. It is known that the spectrum of the drifted Laplacian Δf for M is discrete and the first nonzero eigenvalue of $Δ…
Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.
problem Nonparametric estimation of Schrödinger bridge drifts from single time interval data.
method Direct Nadaraya-Watson plug-in estimator based on kernelized numerator and denominator terms.
result Uniform non-asymptotic bound, CLT under undersmoothing, and adaptive bandwidth selector.
This paper investigates optimal portfolio strategies in a financial market where the drift of the stock returns is driven by an unobserved Gaussian mean reverting process. Information on this process is obtained from observing stock returns and expert opinions. The latter provide at discrete time points an unbiased est…
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw learning curves in simplified situations. The performance for learning drifting concep…
In this paper, we study self-expanders for mean curvature flows. First we show the discreteness of the spectrum of the drifted Laplacian on them. Next we give a universal lower bound of the bottom of the spectrum of the drifted Laplacian and prove that this lower bound is achieved if and only if the self-expander is th…
Researchers tackle insider trading in incomplete markets using a discrete-time jump process approach.
problem Tackles insider trading in incomplete markets under the trinomial model.
method Uses a marked binomial process and stochastic analysis with Malliavin calculus.
result Identifies insider expected additional utility with Shannon entropy of extra information.
Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
problem Proving convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
method Differentiation-based approach to handle Z process, uniformly controlling Lipschitz continuity of decoupling fields.
result Proves convergence of Markovian iteration method for FBSDEs with fully coupled drift and Z process.
This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing stock returns and expert opinions. The latter provide unbiased estimates on the cu…
Study portfolio optimization with partial info and drawdown constraints using deep learning.
problem Optimizing portfolios with partial information and maximum drawdown constraints.
method Bayesian framework, dynamic programming, semi-explicit solutions, deep learning for stochastic control.
result Numerical solutions and performance analysis with deep learning, convergence to Merton problem.
The paper improves parameter estimation for interest rate models using the CIR and CKLS frameworks.
problem Improving parameter estimation for interest rate models.
method Employing Euler-Maruyama discretization to transform SDEs into linear regression problems.
result Established strong consistency and asymptotic normality of estimators for drift and volatility parameters.
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between…
Estimates roughness of volatility from discrete variance data.
problem Estimating roughness exponent of stochastic volatility from discrete observations of integrated variance.
method Pathwise estimator based on fractional Brownian motion with drift.
result Strong consistency theorems for rough volatility models.
This paper identifies a negative profit effect in limit order fills.
problem Profit drag in limit order fills due to adverse price movements.
method Discrete market model, empirical simulation of US Treasury Bond futures.
result Existence of negative drift in limit order fills.
Differentiable segmented models for non-stationary data.
problem Estimating change points in non-stationary sequential data.
method Formulated a relaxed variant of segmented models that enables gradient descent for all parameters, including segmentation.
result Successfully learned all tasks with standard gradient descent algorithms.
New bounds for MCMC on discrete spaces without dimension dependence.
problem High-dimensional statistical convergence analysis of MCMC methods.
method Combining multicommodity flow and single-element drift conditions.
result Informed Metropolis-Hastings algorithms achieve relaxation times independent of dimension.
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the…
We solve continuous-time latent SDE identifiability using diffusion shifts.
problem Identifiability of latent SDEs in continuous-time time series.
method Environment-induced shifts in diffusion covariance for additive-noise latent SDEs.
result Two diagonal diffusion regimes with distinct variance ratios identify latent coordinates up to permutation and scaling.
Study provides error estimates for approximating game options with diffusion asset prices.
problem Approximating fair prices of game options with diffusion asset prices.
method Error estimates for discrete approximations of diffusion processes, applied to game options.
result Effective tool for computing fair prices of game options in multi-asset markets.
First, we consider the problem of hedging in complete binomial models. Using the discrete-time Föllmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in incomplete trinomial models, we examine the extension of the sequential regression app…
This review covers learning under concept drift, including detection, understanding, and adaptation.
problem Unforeseeable changes in data distribution over time impact machine learning performance.
method Reviews and analyzes methodologies and techniques for concept drift detection, understanding, and adaptation.
result Establishes a framework for learning under concept drift with three main components.
New schemes improve error estimates for sampling from non-log-concave distributions.
problem Improving sampling from non-log-concave distributions with super-linear drift growth.
method Developed tamed Euler and randomized Euler schemes with error estimates.
result Near-optimal error bounds for sampling and optimization problems.
Paper analyzes stability and forgetting in score-based generative models.
problem Understanding the stability and long-time behavior of generative models.
method Quantitative bounds on sampling error using stability and forgetting properties of the Markov chain.
result Provides practical consequences of stability and contraction mechanism in sampling.
Identifies features most relevant to concept drift in data.
problem Identifying features most relevant to concept drift.
method Distinguishing between drift inducing and faithfully drifting features; deriving minimal subsets of features to characterize drift.
result Derives a detection algorithm for concept drift.
Paper explores how Rectified Flow adapts to low-dimensional data.
problem Improving sampling efficiency in low-dimensional data.
method Investigates Rectified Flow's adaptation to low-dimensional support and introduces a stochastic version.
result Shows improved sampling efficiency with O(k/ε) complexity. Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the L2 Wasserstein distance of sampling algorithms based on Euler discretisations of SDEs has been recently develop…
The paper examines the rigidity of eigenvalues in shrinking Ricci solitons.
problem Rigidity of eigenvalues in shrinking Ricci solitons.
method Analysis of the drifted Laplacian on shrinking Ricci solitons, showing eigenvalue bounds and rigidity results.
result If the nextth eigenvalue is close to a lower bound, the n-soliton must be the trivial Gaussian soliton. New method detects when models influence their own drift in real-time data streams.
problem Models can induce concept drift in real-time data streams.
method CheckerBoard Performative Drift Detection (CB-PDD)
result CB-PDD effectively detects performative drift in real-time data streams.
This research identifies flaws in drift detection methods and creates adversarial data streams to exploit them.
problem The challenge of detecting data distribution changes (drift) in real-time systems.
method Developed adversarial data streams to show weaknesses in existing drift detection schemes.
result Demonstrated that common drift detection methods can be fooled by adversarial data streams.
We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic dif…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and formulated in various degrees of abstraction and mathematical coherence. In this contribu…
A new drift detection method based on autoregressive models.
problem Concept drift in real-world data leads to decreased model performance.
method Autoregressive based drift detection method (ADDM).
result ADDM outperforms state-of-the-art drift detection methods.
Neural Jump ODEs model Itô processes without adversarial training.
problem Generating samples from Itô processes with irregular data.
method Neural Jump ODEs framework for drift and diffusion approximation.
result NJODEs can recover true parameters of Itô processes in the limit.