Four geometries govern sequential and distribution-free inference.
problem Sequential and distribution-free inference challenges.
method Four distinct admissibility geometries.
result Four classes of admissible procedures are pairwise non-nested.
On-device research index
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “Blackwell dominance”
N-discount optimality was introduced as a hierarchical form of policy- and value-function optimality, with Blackwell optimality lying at the top level of the hierarchy Veinott (1969); Blackwell (1962). We formalize notions of myopic discount factors, value functions and policies in terms of Blackwell optimality in MDPs…
Blackwell's theorems influence modern AI through information compression and decision making.
problem Information compression and decision making under uncertainty.
method Theorems developed in the 1940s and 1950s, applied to modern AI.
result Blackwell theorems remain relevant and influence modern AI subfields.
New truthful calibration errors improve model ranking in multiclass prediction.
problem Non-truthful calibration errors can mislead model comparisons.
method Introduced perfectly truthful calibration errors for multiclass predictions.
result Truthful calibration errors preserve decision-theoretic dominance and stabilize model rankings.
New approach for adaptive conformal inference using Blackwell's theory.
problem Non-exchangeable environments in sequential conformal inference.
method Reinterpretation of ACI as a game, construction of coverage and efficiency objectives, approachability strategy.
result Algorithm achieves strong theoretical guarantees and practical insights.
Study extends binary omniprediction to multiclass setting with improved sample complexity.
problem Suboptimality bounds for each loss function against infinite comparator family in multiclass prediction.
method Design of a framework for solving Blackwell approachability problems with coupled actions.
result Sample complexity of for -omniprediction in a -class problem.
Transforms offline greedy algorithms to online algorithms for combinatorial problems.
problem Online decision-making in time-varying combinatorial environments.
method General framework using Blackwell approachability and Bandit Blackwell approachability.
result Achieves regret in full information setting and regret in bandit setting.
Paper improves Gumbel-Softmax estimator variance reduction.
problem Challenges in gradient estimation for models with discrete latent variables.
method Rao-Blackwellization applied to straight-through Gumbel-Softmax estimator.
result Reduces mean squared error and variance of Gumbel-Softmax estimator.
New algorithms minimize regret with global costs in online learning.
problem Minimizing regret in online learning with global costs.
method Extended FTRL algorithms for Blackwell's approachability.
result First bounds on regret minimization with explicit dependence in and .
A game-theoretic approach to multi-criteria ranking from ordinal data.
problem Ranking objects from ordinal data with multiple criteria.
method Generalizing von Neumann winner to multi-criteria setting using Blackwell's approachability.
result The Blackwell winner can be computed as a convex optimization problem and achieves near-optimal sample complexity.
Derives new equations for stochastic volatility models.
problem Modeling local-stochastic-volatility models and their derivatives.
method Conditional forward equation, Dupire stochastic PDE, rolling expiry vanilla option SPDE.
result New equations for LSV models and their derivatives.
We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market …
Paper explores rate-preserving reductions between Blackwell approachability and no-regret learning.
problem Tackles rate-preserving reductions between Blackwell approachability and no-regret learning.
method Studies fine-grained reductions and optimal rates of convergence.
result Shows that rate-preserving reductions do not always hold, but provides conditions for when they do.
Unified approach to fair online learning with stochastic contexts.
problem Fairness in online learning with unknown sensitive contexts.
method Adapting Blackwell's approachability theory to handle unknown contexts' distributions.
result Characterization of optimal trade-off between fairness and performance objectives.
We wish to compute the gradient of an expectation over a finite or countably infinite sample space having categories. When is indeed infinite, or finite but very large, the relevant summation is intractable. Accordingly, various stochastic gradient estimators have been proposed. In this paper, we de…
Proposes a method to stabilize Black Box Variational Inference using the James-Stein estimator.
problem Stability issues and fine-tuning required in basic Black Box Variational Inference.
method Reframe stochastic gradient ascent as multivariate estimation problem using James-Stein estimator.
result Provides a simpler method with consistent performance in terms of model fit and convergence time.
DSM on manifolds removes singularities and computes small-noise expansions.
problem DSM on manifolds with singular noise.
method Rao-Blackwellized score matching, nearest-point projection, intrinsic Riemannian score.
result Canonical target equals intrinsic Riemannian score up to a small correction.
A new variational method for SSMs improves inference efficiency.
problem Hard variational inference for state space models.
method Proposes variational marginal particle filter (VMPF) based on Rao-Blackwellization.
result VMPF provides tighter variational bounds and sometimes benefits from unbiased reparameterization.
Differential privacy is a statistical concept that can be explained through hypothesis testing.
problem Formalizing differential privacy as a statistical concept.
method Using David Blackwell's informativeness theorem, the paper shows differential privacy can be understood through hypothesis testing.
result The definition of -differential privacy provides a unified framework for analyzing privacy bounds.
New sampler reduces MCMC complexity for Bayesian variable selection.
problem High-dimensional Bayesian variable selection with high computation complexity.
method Variable-complexity subset weighted-Tempered Gibbs Sampler (wTGS) with Rao-Blackwellized estimator.
result Variances of Rao-Blackwellized estimator are smaller than those of subset wTGS.
New estimator reduces variance in discrete random variables.
problem Estimating gradients for discrete random variables with reduced variance.
method Sampling without replacement and Rao-Blackwellization.
result Our estimator is the most consistent gradient estimator across different entropy settings.
Improves survey sampling with unbiased machine learning methods.
problem Design-consistent model-assisted estimation lacks a general theory for machine learning.
method Proposes a subsampling Rao-Blackwell method for design-unbiased estimation.
result Yields efficiency gains over standard methods while ensuring valid estimation.
Fibonacci Ensembles use Fibonacci weights to improve ensemble learning, inspired by natural growth patterns.
problem Improving ensemble learning methods to enhance model performance and interpretability.
method Introduces Fibonacci weights and a recursive ensemble dynamic to reduce variance and enrich representational depth.
result Fibonacci weighting can match or improve upon uniform averaging in ensemble learning experiments.
Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliar…
New algorithm improves on static methods in Active Simple Hypothesis Testing.
problem Optimizing Active Simple Hypothesis Testing with active sampling.
method Game-theoretic formulation, differential games, PDEs, Blackwell Approachability.
result Proposes an efficient algorithm that outperforms static methods in ASHT.
We consider Blackwell approachability, a very powerful and geometric tool in game theory, used for example to design strategies of the uninformed player in repeated games with incomplete information. We extend this theory to "generalized quitting games" , a class of repeated stochastic games in which each player may ha…
New method compares DP mechanisms beyond pairs.
problem Current DP mechanism comparisons overlook substantial differences.
method Introduces -divergence for robust comparison.
result Demonstrates gaps in current DP-SGD practices.
New gradient estimators for discrete variables improve model training.
problem Training models with discrete latent variables is challenging due to high gradient variance.
method Introduced novel gradient estimators based on importance sampling and statistical couplings, extending to categorical variables.
result Proposed gradient estimators outperform previous methods in systematic experiments.
The paper introduces Robust Correlated Equilibrium for games with time-varying costs and proposes an algorithm to achieve it.
problem Games with time-varying costs and disturbances.
method Proposes Robust Correlated Equilibrium and a decentralized algorithm to learn optimal strategies.
result The algorithm converges to the Robust Correlated Equilibrium, showing no regret for each controller.
New methods for CI testing under model misspecification.
problem Challenges in CI testing with misspecified models.
method Proposes new approximations and upper bounds for testing errors of regression-based CI tests.
result Introduces the Rao-Blackwellized Predictor Test (RBPT) robust against misspecified inductive biases.
We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locally-optimal pr…
Optimizes predictions by recalibrating online forecasts with minimal error.
problem Tackles the challenge of recalibrating online predictions to be more accurate.
method Uses an imbalanced extension of the Blackwell approachability reduction framework to achieve -recalibration.
result Achieves -recalibration for Lipschitz proper losses in rounds.
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and …
Derives new equations for volatility models and option pricing.
problem Modeling and pricing options in local-stochastic-volatility models.
method Develops conditional forward equations and Dupire stochastic PDEs.
result Derives new SPDE for vanilla options.
Achieving Optimal Static and Dynamic Regret Simultaneously in Bandits with Deterministic Lossescs.LG
New algorithm achieves both static and dynamic regret optimally against an oblivious adversary for deterministic losses.
problem Achieving optimal static and dynamic regret simultaneously in adversarial bandits.
method Extends impossibility result to deterministic losses, uses negative static regret and Blackwell approachability.
result First algorithm achieving optimal static and dynamic regret simultaneously against an oblivious adversary.
Calibrated strategies can be obtained by performing strategies that have no internal regret in some auxiliary game. Such strategies can be constructed explicitly with the use of Blackwell's approachability theorem, in an other auxiliary game. We establish the converse: a strategy that approaches a convex -set can be…
Connected domination numbers found for plane triangulations up to 13 vertices.
problem Finding connected domination numbers for plane triangulations.
method Analyzing triangulations of up to 13 vertices and proving the difference between connected and regular domination numbers can be arbitrarily large.
result Connected domination numbers for triangulations up to 13 vertices and upper bound for larger triangulations.
Policy optimization on high-dimensional continuous control tasks exhibits its difficulty caused by the large variance of the policy gradient estimators. We present the action subspace dependent gradient (ASDG) estimator which incorporates the Rao-Blackwell theorem (RB) and Control Variates (CV) into a unified framework…
Manifolds can be dominated by hypersurfaces in a sphere.
problem Dominating manifolds with hypersurfaces.
method Proving any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
result Any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
New RL method improves on standard discounted RL for operations research.
problem Applying RL to operations research problems, especially with non-zero rewards.
method Near-Blackwell-optimal RL algorithm that assesses average reward per step.
result Proves viability on challenging queuing system problems.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
Formulae for 1-3 handle attachments in 4-manifolds.
problem Understanding handle attachments in 4-dimensional manifolds.
method Developed general formulae for 1-3 handle attachments using skein modules.
result Derived complete description of gluing homomorphism on skein modules.
New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function to replace the fixed parameter in fractional SD.
result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
Research examines when 4-manifolds are dominated by geometric ones.
problem When is an orientable closed 4-manifold dominated by another?
method Focuses on geometric or fibred cases.
result Characterizes conditions for domination.
3-manifolds can virtually dominate others with positive simplicial volume.
problem Domination of 3-manifolds with positive simplicial volume.
method Proving existence of finite covers with degree-1 maps.
result Virtual domination of 3-manifolds with positive simplicial volume.
On Experimentsstat.ML
Paper outlines a new mathematical language for experiments.
problem Formalizing the scientific process for automation.
method Formulates the scientific process in precise mathematical language.
result Novel contributions in data processing, bias variance, and deficiency.
Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.
problem Domination problem between non-Fuchsian representations of closed surface groups.
method Analysis of branched harmonic immersions and construction of anti-de Sitter 3-manifolds.
result Found that representations admitting branched harmonic immersions dominate other representations, and constructed large families of branched anti-de Sitter 3-manifolds.