Unified geometric framework for Brownian motion on various manifolds.
problem Modeling Brownian motion on complex Riemannian manifolds.
method Constructing stochastic differential equations with noise and drift terms aligned with Laplace-Beltrami operators.
result Geometrically transparent and mathematically consistent foundation for diffusion processes.
New method calculates geometric Brownian motion with affine drift and its integral.
problem Calculating the distribution of geometric Brownian motion with affine drift and its integral.
method Laplace transform approach and Heun differential equation.
result Joint distribution of geometric Brownian motion with affine drift and its integral can be determined.
A new geometric metric identifies true data changes from parametrization artifacts in high-dimensional representations.
problem Quantifying representation drift in high-dimensional data using Euclidean or cosine distances can misattribute changes due to arbitrary parametrizations.
method Introducing the Fubini Study metric to identify representations that differ only by gauge transformations.
result The Fubini Study metric isolates intrinsic evolution by remaining invariant under gauge-induced fluctuations, providing a diagnostic for meaningful structural changes.
Geometric stability predicts steerability and detects drift in language models.
problem Predicting steerability and detecting drift in language models.
method Supervised and unsupervised geometric stability measures.
result Supervised geometric stability predicts steerability with high accuracy and detects drift earlier.
Paper studies long-run risk optimization with dyadic impulses for unbounded processes.
problem Long-run risk optimization problem with unbounded and non-uniformly ergodic processes.
method Adapting weight norm approach, combining geometric drift and local minorization property.
result Existence of solution to Bellman equation for risk-averse parameters.
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential moment, we show that the equality is achieved if and only if the Gibbs density is…
Study geometric and analytical properties of ρ-Einstein solitons.
problem Characterize geometric and analytical features of ρ-Einstein solitons. method Analyze the spectrum of the drifted Laplacian operator and prove volume growth estimates.
result Establish new volume growth estimates for geodesic balls of complete noncompact ρ-Einstein solitons. This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters. They claimed that averages are inaccurate if they are incorrect or drift-outs. F…
Unified framework for Brownian motion distances on specific geometric manifolds.
problem Understanding Brownian motion distances on radially isoparametric manifolds.
method Developed a geometric framework and derived drift-window inequalities.
result Unified framework for coadapted Brownian couplings on RIM.
This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be ex…
We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the dri…
New budget quantifies drift in closed-loop learning, improving reproducibility.
problem Characterizing statistical learning under distributional drift in closed-loop settings.
method Introduces an intrinsic drift budget CT quantifying cumulative information-geometric motion of the data distribution. result Proves a drift-feedback bound of order T−1/2+CT/T for prequential reproducibility, up to controlled second-order remainder terms. In this paper we prove some spectral properties of the drifted Laplacian of self-shrinkers properly immersed in gradient shrinking Ricci solitons. Then we use these results to prove some geometric properties of self-shrinkers. For example, we describe a collection of domains in the ambient space that cannot contain sel…
The Lie group Sol(p,q) is the semidirect product induced by the action of the real numbers R on the plane R^2 which is given by (x,y) --> (exp{p z} x, exp{-q z} y), where z is in R. Viewing Sol(p,q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift …
Solves optimal liquidation problem for stock price following geometric Brownian motion.
problem Optimal liquidation problem for stock price process following geometric Brownian motion.
method Functional analysis tools; working in terms of cash.
result Explicit solution to the problem, extending to stochastic drift.
We consider cocycles of isometries on spaces of nonpositive curvature H. We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there…
Investment strategy in uncertain markets improved by learning and risk-ambiguity preferences.
problem Investment in financial markets with unknown drift coefficients.
method Optimization under KMM approach, considering risk and ambiguity preferences.
result Optimal investment strategy can be adjusted based on prior drift distribution.
We reformulate wealth taxation using Fokker-Planck equations to ensure tax neutrality.
problem Ensuring tax neutrality in wealth taxation frameworks.
method Reformulating the neutral wealth tax framework using stochastic dynamics and statistical physics, specifically Fokker-Planck equations.
result The framework clarifies when wealth taxation is a benign rescaling of dynamics and when it introduces new physics.
Paper extends transfer learning for decision rules, improving treatment rule estimation.
problem Estimating optimal individualized treatment rules under changing conditions.
method Bayes decision rules and low-dimensional empirical risk minimization.
result Consistent estimators and risk bounds established under mild conditions.
Quantum model investigates financial derivative price dynamics with quantum interference effects.
problem Investigate quantum drift in financial derivatives using Heisenberg Equation of Motion.
method Apply geometric techniques to integrate Heisenberg Equation of Motion, model financial market as quantum observable.
result Quantum interference effects can act as drag or boost on financial returns.
A geometric theory explains loss functions for robust representation learning.
problem Treats robustness, domain adaptation, and sensor drift as separate literatures.
method Estimates covariance Sigma_task and uses it to pin Jacobian penalties.
result Proves optimality and necessity of range coverage for penalty matrices.
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract underlying asset follows a geometric Brownia…
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.
Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.
problem Queue peak laws in stochastic networks with geometric thresholds.
method Self-normalization mechanism
result Logarithmic scaling of queue peaks after geometric thresholds.
Paper offers a fast method to assess DeFi liquidation risk.
problem Assessing liquidation risk in DeFi stablecoin lending.
method Modeling collateral exchange rate as zero-drift geometric Brownian motion.
result Derives an exact formula for liquidation probability.
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.
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
problem Proving geometric ergodicity of SGLD in nonconvex, log-concave settings.
method Reflection coupling technique to handle SGLD's time discretization and minibatch issues.
result SGLD has an invariant distribution and geometric ergodicity in W1 distance. New framework for detecting data drift in continuous time.
problem Drift in data distribution over time.
method Probability theoretical framework for continuous time drift.
result New efficient drift detection method and decomposition of data.
We study space-like self-shrinkers of dimension n in pseudo-Euclidean space $\ir{m+n}_m$with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove a rigidity results under minor growth conditions interms of the mean curv…
Novel drift detection method using deformation analysis in ML models.
problem Detecting subtle changes in data that affect model performance.
method Quantifying deformation using eigenvalue analysis, KDE, KL divergence, and strain tensor analogy.
result Demonstrated effectiveness in detecting context shifts in Generative AI and healthcare.
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.
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.
Paper proposes a semi-supervised method for detecting concept drift in streaming environments.
problem Detecting concept drift in streaming environments with limited labeled data.
method Utilizes density estimation of posterior probabilities in partially labeled streaming data.
result Demonstrates superior concept drift detection in streaming environments with limited labeled data.
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.
Geometric approach combines asset returns and investor views for better portfolio optimization.
problem Optimizing portfolios with investor-specific views.
method Generalized Wasserstein barycenter (GWB) to integrate statistical asset returns and investor views.
result The geometric approach offers more flexibility and rewards for correct investor views.
Adaptive sampling detects local concept drift with limited labels.
problem Detecting local concept drift in dynamic environments with scarce labels.
method Combines residual-based exploration and exploitation with EWMA monitoring.
result Superior performance in label efficiency and drift detection accuracy.
Algorithm detects concept drift and adapts models in streaming data.
problem Concept drift in streaming data renders models inaccurate.
method Adaptive learning algorithm that detects drifts and reacts to them.
result Risk competitive to an algorithm with perfect drift knowledge.
Classifiers operating in a dynamic, real world environment, are vulnerable to adversarial activity, which causes the data distribution to change over time. These changes are traditionally referred to as concept drift, and several approaches have been developed in literature to deal with the problem of drift handling an…
Classifies polynomial growth solutions to drift-harmonic equations on asymptotically paraboloidal manifolds.
problem Classifying polynomial growth solutions to drift-harmonic equations on specific types of manifolds.
method Inductive argument that alternates between constructing and asymptotically controlling drift-harmonic functions.
result All drift-harmonic functions with polynomial growth asymptotically separate variables and dimensions of spaces are computed.
This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Dr…
New method detects drift in high-dimensional data.
problem Understanding and localizing concept drift in learning systems.
method Conformal predictions for drift localization.
result Our approach outperforms existing methods on image datasets.
Detects drifts in data for classification tasks using constrained embeddings.
problem Drifts in data affect model performance; unsupervised methods ignore label information.
method Task-sensitive semi-supervised drift detection with constrained low-dimensional embedding.
result Successfully detects real drifts affecting classification performance.
PDD detects concept drift using explainable AI, improving model performance in dynamic environments.
problem Detecting and adapting to concept drift in predictive models.
method Profile Drift Detection (PDD) using Partial Dependence Profiles (PDPs).
result PDD outperforms existing methods in detecting concept drift and maintaining high predictive performance.
This paper studies concept drift detectors for financial time series.
problem Improving accuracy on financial time series with concept drifts.
method Three simple concept drift detectors tailored to financial time series.
result Two of the detectors are as effective as state-of-the-art detectors.
Paper proposes a framework to detect adversarial concept drifts under poisoning attacks.
problem Adversarial concept drift in data streams.
method Augmented Restricted Boltzmann Machine with improved gradient computation and energy function.
result High robustness and efficacy of the proposed drift detection framework in adversarial scenarios.
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.
Study a financial market with singular drift and no arbitrage, considering jumps and delays.
problem Model a financial market with singular drift and no arbitrage, considering jumps and delays.
method Use geometric Itô-Lévy process with singular drift term, incorporate jumps and delays, and apply white noise calculus.
result No arbitrage in the market when delay θ > 0, maximal value finite.