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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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92184275367 · Jun 202019922001200920172026
48 results for Adaptive Discretization

ADCMs adaptively discretize CMs for efficient training.

problem Manual discretization schemes cause repeated adjustments for different noise schedules and datasets.
method Unified framework with optimization problem, local and global consistency constraints, and Gauss-Newton method.
result Significantly improve training efficiency and generative performance of CMs.

New algorithm improves online learning with reduced discretization.

problem Improving adaptive online learning with refined discretization.
method Continuous time approach to online learning, followed by a new discretization argument.
result Optimal regret bound with O(VT)O(\sqrt{V_T}) dependence on gradient variance.

Algorithm tackles adaptive discretization in adversarial Lipschitz bandits for dynamic pricing and auctions.

problem Adaptive discretization in adversarial Lipschitz bandits.
method Adversarial Zooming algorithm for adaptive discretization.
result First algorithm for adversarial Lipschitz bandits with instance-dependent regret bounds.

Ada-BKB optimizes black-box functions on continuous domains with adaptive discretization.

problem Optimizing functions with continuous domains using Gaussian process optimization.
method Adaptive discretization of the function domain to avoid non-convex optimization costs.
result Ada-BKB algorithm runs in O(T2dexteff2)O(T^2 d_ ext{eff}^2), significantly faster than existing methods.

Locally-verifiable conditions ensure exactness of spline discrete de Rham complex.

problem Ensuring cohomological equivalence of spline discrete complex to continuous de Rham complex.
method Theoretical analysis and locally-verifiable sufficient conditions for exactness.
result Locally-verifiable conditions guarantee exactness of hierarchical B-spline discrete de Rham complex.

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.

Algorithm identifies Pareto optimal designs efficiently for noisy, multi-objective functions.

problem Optimizing multi-objective functions with noisy data and large design spaces.
method Adaptive discretization and tree-based approach to identify Pareto optimal designs.
result Algorithm identifies Pareto optimal designs with fewer evaluations than exhaustive search.

GBS uses machine learning to design products based on consumer preferences.

problem Designing products to meet consumer preferences.
method GBS is a discrete choice experiment that uses machine learning to adaptively construct paired comparison questions.
result GBS outperforms existing methods in accuracy and sample efficiency.

The paper analyzes sampling efficiency of discrete diffusion models, providing sharp and adaptive guarantees.

problem Theoretical foundations of discrete diffusion models, especially sampling efficiency.
method Continuous-time Markov chain (CTMC) formulation, ττ-leaping-based samplers, effective total correlation.
result The ττ-leaping algorithm achieves an iteration complexity of order ildeO(d/ε) ilde O(d/\varepsilon) for uniform discrete diffusion, improving existing bounds by a factor of dd.

A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is disc…

1998-02-27abs ↗pdf ↗

Unified analysis of tree-based methods for online reinforcement learning.

problem Designing efficient algorithms for online reinforcement learning with low sample complexity, storage, and computational burden.
method Unified theoretical analysis of tree-based hierarchical partitioning methods for online reinforcement learning.
result Our algorithms provide guarantees that scale with respect to the 'zooming dimension', improving upon ambient dimension scaling.

In this paper, I present VQ-DRAW, an algorithm for learning compact discrete representations of data. VQ-DRAW leverages a vector quantization effect to adapt the sequential generation scheme of DRAW to discrete latent variables. I show that VQ-DRAW can effectively learn to compress images from a variety of common datas…

2020-03-03abs ↗pdf ↗

A new method for learning function parameters in operators using data-adaptive RKHS.

problem Learning function parameters in operators with robustness to noise and numerical error.
method Data Adaptive RKHS Tikhonov Regularization (DARTR) method.
result DARTR leads to an accurate estimator robust to noise and numerical error, converging at a consistent rate as data refines.

Improved Markov models learn from their mistakes and adapt to problem complexity.

problem Limitations of standard masked discrete diffusion models in reasoning tasks.
method Learning a Markov transition kernel trained on its own outputs, allowing remasking and adaptation.
result Significant improvement in solving reasoning problems, especially Sudoku-Extreme and Countdown-4.

Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three disadvantages: 1) the predefined similarity graph is often fixed and may not be optimal f…

2019-04-25abs ↗pdf ↗

New algorithm improves OT map estimation for semi-discrete settings.

problem Improving estimation of OT maps in semi-discrete settings.
method Stochastic Gradient Descent with adaptive entropic regularization and averaging acceleration.
result Achieves nearly minimax rate of O(t1)\mathcal{O}(t^{-1}) for OT map estimation.

We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk aware and the filtration is general, and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations. An example application to hydropower …

2019-10-09abs ↗pdf ↗

Paper proposes adaptive control for unknown systems using reinforcement learning.

problem Adaptive control for unknown, linearizable systems.
method On-policy reinforcement learning for discrete-time, stochastic systems.
result Stability and tracking errors concentrate near zero with high probability.

In this study, we propose a new definition of multivariate conditional value-at-risk (MCVaR) as a set of vectors for discrete probability spaces. We explore the properties of the vector-valued MCVaR (VMCVaR) and show the advantages of VMCVaR over the existing definitions given for continuous random variables when adapt…

2017-08-03abs ↗pdf ↗

This paper develops a discrete theory of real Riemann surfaces using quad-graphs and linear discretization.

problem Constructing a discrete theory of real Riemann surfaces.
method Using quad-graphs and linear discretization of Cauchy-Riemann equations, constructing a symplectic homology basis.
result The discrete period matrix has the same canonical decomposition as in the smooth setting.

Study nonparametric covariance function estimation for noisy data.

problem Estimating covariance function from discrete noisy data in high dimensions.
method Adaptive learning-based estimators, including deep learning.
result Established oracle inequality and convergence rates for deep learning estimators.

In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under consideration can be solved in terms of associated adaptive robust Bellman equa…

2017-06-07abs ↗pdf ↗

Discrete diffusion models improve data generation for discrete data like language and graphs.

problem Adapting diffusion models to discrete state spaces for better data generation.
method Formulated as CTMCs, used uniformization of continuous Markov chains for sampling.
result Derive guarantees for sampling from any distribution on a hypercube, aligning with state-of-the-art achievements.

Discrete integration in a high dimensional space of n variables poses fundamental challenges. The WISH algorithm reduces the intractable discrete integration problem into n optimization queries subject to randomized constraints, obtaining a constant approximation guarantee. The optimization queries are expensive, which…

2019-10-13abs ↗pdf ↗

Proposes an automatic cyclical scheduling for gradient-based discrete sampling.

problem Gradient-based sampling in high-dimensional models can get stuck in local modes.
method Cyclical step size and balancing schedules with automatic hyperparameter tuning.
result Proves non-asymptotic convergence and inference guarantees for general discrete distributions.

Discrete structure rules for validating molecular structures are usually limited to fulfillment of the octet rule or similar simple deterministic heuristics. We propose a model, inspired by language modeling from natural language processing, with the ability to learn from a collection of undirected molecular graphs, en…

2019-11-26abs ↗pdf ↗

Enhances gradient-based discrete samplers with parallel tempering for multimodal distributions.

problem Local minima in high-dimensional, multimodal discrete distributions.
method Combines parallel tempering with discrete Langevin proposal, using Metropolis criterion for swaps.
result Significantly faster mixing and better sampling from complex distributions.

Proposes a new method for two-dimensional data discretization.

problem Discretization of multi-dimensional data, especially when dimensions are dependent.
method PALM algorithm, which alternately partitions and merges regions using the MDL principle.
result PALM accurately reveals ground truth partitions and approximates well outside the model class.

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show tha…

2004-08-20abs ↗pdf ↗

Develops deep jump learning for continuous treatment OPE.

problem Estimating mean outcomes under new treatment rules using historical data from different rules.
method Adaptive deep discretization of continuous treatment space using deep learning and multi-scale change point detection.
result Validated method through theoretical results, simulations, and real application to Warfarin Dosing.

A new method for anomaly detection adapts to local non-stationarity in low-data regimes.

problem Adapting conformal anomaly detection to handle distribution shifts in real-world data.
method Proposes a continuous inference relaxation using continuous weighted kernel density estimation to decouple local adaptation from tail resolution.
result Restores detection capabilities and statistical power in low-data regimes while maintaining valid error control.

Enhances CEV model pricing with high-order scheme and adaptive time stepping.

problem Improving accuracy in pricing American CEV models with irregularities.
method High-order time adapted scheme, local mesh refinement, adaptive time stepping, fifth-order 5(4) Dormand-Prince method.
result Highly accurate solution with reduced computational runtime.