Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.
Optimizes MCMC chains with neural control variates.
problem Reducing variance in Markov Chain Monte Carlo (MCMC) simulations.
method Uses neural networks as control variates to minimize asymptotic variance.
result Derives optimal convergence rate under various ergodicity assumptions.
UCB-V algorithm improves on UCB for MAB problems with variance estimates.
problem Optimizing arm selection in MAB problems with variance information.
method Asymptotic and high probability analysis of UCB-V algorithm.
result UCB-V can exhibit instability in arm-pulling rates but achieves refined regret bounds.
Study improves variance calculation for random zero sets on complex manifolds.
problem Improving the variance calculation for random zero sets on complex manifolds.
method Deriving an asymptotic expansion for the variance of linear statistics of zero divisors of random holomorphic sections.
result Sharpens leading-order asymptotics for the variance of random zero sets.
Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.
problem Analyzing the behavior of short-maturity options on realized variance in local-stochastic volatility models.
method Large deviations theory and variational problems to solve rate functions for different cases.
result Explicit solutions for the rate function in the uncorrelated case and upper/lower bounds and expansions for the correlated case.
Estimates Markov chain variance efficiently without storing samples.
problem Estimating the asymptotic variance of Markov chain functions.
method Linear stochastic approximation of Poisson equation solution.
result Optimal MSE convergence rate with finite sample guarantees.
In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce th…
New strategy optimally identifies best arm in unknown variance Gaussian bandits.
problem Identifying the best arm in two-armed Gaussian bandits with unknown variances.
method Proposes a Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW) strategy to estimate variances and draw arms adaptively.
result Demonstrates asymptotic optimality of the proposed strategy in the small-gap regime.
There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence method, pseudo-likelihood, Monte Carlo maximum likelihood, and noise contrastive…
Large batch sizes reduce gradient variance in DP-SGD, improving privacy.
problem Understanding why large batch sizes work in DP-SGD.
method Decomposed total gradient variance into subsampling and noise-induced variances, proving batch size independence in the limit.
result Large batch sizes reduce effective total gradient variance, improving privacy in DP-SGD.
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by Lévy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Usin…
This paper is concerned with the asymptotics for Greeks of European-style options and the risk-neutral density function calculated under the constant elasticity of variance model. Formulae obtained help financial engineers to construct a perfect hedge with known behaviour and to price any options on financial assets.
The paper provides concentration inequalities for Markov chain variance estimators.
problem Estimating the variance of Markov chains with concentration properties.
method Martingale decomposition method for uniformly geometrically ergodic Markov chains.
result Explicit control of the p-th moment of the OBM estimator difference and dependence on p and mixing time.
We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull-White and Schobel-Zhu stochastic volatility models we give simple explicit expressions (improving Broadie and Jain (2008a) in the case of the Heston model). We give condi…
In this note we provide detailed derivations of two versions of small-variance asymptotics for hierarchical Dirichlet process (HDP) mixture models and the HDP hidden Markov model (HDP-HMM, a.k.a. the infinite HMM). We include derivations for the probabilities of certain CRP and CRF partitions, which are of more general…
We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic …
The paper studies stochastic gradient descent with infinite variance gradients.
problem Theoretical properties of SGD with infinite variance gradients.
method Establish asymptotic behavior of SGD with infinite variance gradients.
result Asymptotic distribution of SGD is characterized as a stationary distribution of an Ornstein-Uhlenbeck process driven by a stable Lévy process.
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
The paper analyzes V-statistics and variance estimation under varying kernel sizes.
problem Analyzing V-statistics and variance estimation under varying kernel sizes. method Develops a general framework for asymptotics of V-statistics, reducing to U-statistics and providing a unified variance estimation method. result Demonstrates asymptotic normality of V-statistics when kernel size grows with sample size. This paper shows how to carry out efficient asymptotic variance reduction when estimating volatility in the presence of stochastic volatility and microstructure noise with the realized kernels (RK) from [Barndorff-Nielsen et al., 2008] and the quasi-maximum likelihood estimator (QMLE) studied in [Xiu, 2010]. To obtain …
We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors k may depend on and diverge with sample size n. In addition to the case of known error variance, we define and study versions of the estimators when…
Improved statistical inference for adaptive Thompson Sampling.
problem Statistical inference challenges in Thompson Sampling.
method Inflating posterior variance in Thompson Sampling.
result Asymptotically normal estimates of arm means with logarithmic regret increase.
Study variance-reduced method for estimating fixed points in Banach spaces.
problem Estimating fixed points of contractive operators in Banach spaces with noisy evaluations.
method Variance-reduced stochastic approximation scheme in Banach spaces.
result Establish non-asymptotic bounds for operator defect and estimation error.
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{é}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating t…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved incl…
Study on variance of Laplace eigenfunctions on manifolds.
problem Investigating the variance of Laplace eigenfunctions on compact manifolds.
method Combining Kac-Rice formula, Wiener-Itô chaos decompositions, and pointwise Weyl law analysis.
result Established a quantitative bound for the fluctuations of nodal volumes, improving existing results.
Machine learning reduces variance in online experiment results.
problem Reducing variance in randomized controlled trials.
method Machine learning regression-adjusted treatment effect estimator (MLRATE).
result MLRATE reduces estimator variance by over 70% in A/A tests.
New methods for handling confounding in observational studies.
problem Handling confounding variables in observational studies.
method Generalized coarsened procedures for clustering confounding variables, followed by estimation of treatment effects and variance.
result Developed a general asymptotic framework for the average causal effect estimator and variance formulae.
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) appr…
Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-…
This paper optimizes importance sampling for rare-event options pricing under the Heston model.
problem Efficiently pricing European call options with short maturity and deep out-of-the-money strikes.
method Asymptotic importance sampling schemes leveraging the large deviation principle and state-dependent change of measure.
result Proposed IS methods achieve logarithmic efficiency in short-maturity and deep OTM regimes, significantly reducing variance.
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options…
Paper proves robust M-estimators' coordinates' normality in high dimensions.
problem High-dimensional robust M-estimators' asymptotic normality.
method Develops Stein formulae for high-dimensional random vectors on the sphere.
result Asymptotic normality holds for most coordinates of robust M-estimators with convex penalty.
A method for efficient statistical inference from online algorithms.
problem Computational constraints in online algorithms make traditional variance estimation difficult.
method HulC method that wraps around online algorithms to produce valid confidence regions.
result The HulC method produces asymptotically valid confidence regions for online algorithms.
A new estimator for evaluating policies in unknown environments.
problem Evaluating policies when both logging policy and value function are unknown.
method Doubly-Robust (DR) off-policy evaluation (OPE) estimator, DRUnknown, that estimates both the logging policy and value function.
result DRUnknown achieves the smallest asymptotic variance and is optimal when both models are correctly specified.
Optimal feature transfer identified through bias-variance analysis.
problem Optimizing feature transfer in transfer learning.
method Simple linear model with fine-grained bias-variance decomposition.
result Optimal pretrained feature transform is naturally sparse.
Paper introduces new risk measures for Kelly criterion.
problem Aggressive Kelly criterion investment strategy.
method Unified approach to risk assessment in Kelly criterion.
result Two new measures for quantifying risk.
The paper develops asymptotic theory for QRF variable importance, revealing a bias-variance trade-off.
problem Challenges in statistical inference for QRF variable importance due to non-smoothness and bias-variance trade-off.
method Developed asymptotic theory using pinball loss and Knight's identity, uncovered phase transition phenomenon, derived asymptotic bias.
result Theoretical foundation for understanding QRF inference limitations in high-dimensional settings.
Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.
problem Violation of constant error variance in high-dimensional regression.
method HDBEN framework using hierarchical Bayesian priors with ℓ1 and ℓ2 penalties. result Achieves posterior concentration, variable selection consistency, and asymptotic normality.
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently…
New methods improve temporal difference learning for policy evaluation in Markov decision processes.
problem Improving temporal difference learning for policy evaluation in Markov decision processes.
method Introduced variance-reduced forms of stochastic approximation to achieve non-asymptotic, instance-dependent optimality.
result Temporal difference learning is strictly suboptimal, but variance-reduced forms achieve optimality up to logarithmic factors.
Optimal tuning for estimating ECC in proportional asymptotics.
problem Estimating Expected Conditional Covariance (ECC) under proportional asymptotics.
method Debiased ridge regression estimators for nuisance functions, sample splitting strategies, and asymptotic variance analysis.
result Prediction-optimal tuning parameters may not minimize asymptotic variance of ECC estimator.
New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.
problem Estimating first-and total-orders Sobol' indices accurately.
method Comparing two Monte Carlo estimators for Sobol' indices.
result New method outperforms current approach in accuracy.
In the context of the Heston model, we establish a precise link between the set of equivalent martingale measures, the ergodicity of the underlying variance process and the concept of asymptotic arbitrage proposed in Kabanov-Kramkov and in Follmer-Schachermayer.
Federated learning method improves covariate shift adaptation for missing target values.
problem Missing target values in federated learning.
method Federated covariate shift adaptation algorithm for missing target output values.
result Asymptotically unbiased and efficient algorithm for federated learning.
This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.
problem Analyzing the distribution of genera in 2-bridge knots.
method Proving asymptotic normality through median, mode, and variance calculations.
result The distribution of genera of 2-bridge knots is asymptotically normal.
We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by α-stable processes with α∈(1,2]. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. Furthermore, we examine the jump clus…
Study on geodesics on random hyperbolic surfaces, showing variance asymptotic to X log X.
problem Distribution of closed geodesics on random hyperbolic surfaces.
method Viewing surfaces as random points in moduli space, studying weighted counting function.
result Variance in large genus limit is asymptotic to X log X, with exceptions.