The paper shows incorrect mean-variance analysis methods should be avoided.
problem Incorrect ex post mean-variance analysis methods in financial studies.
method Illustrates incorrect methods using 2014 biotech ETF data.
result Ex post mean-variance analysis should not be done as generally practiced.
The paper tackles mean-variance analysis in Bayesian optimization under uncertainty.
problem Optimizing decisions in uncertain environments considering trade-offs between average and variance of risk.
method Developed bounds for mean and variance risk measures in Gaussian Process models and proposed AL algorithms for multi-task, multi-objective, and constrained optimization scenarios.
result Proposed AL algorithms effectively address the mean-variance trade-off in uncertain optimization scenarios.
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
Improved SVRPG analysis for faster convergence in reinforcement learning.
problem Finding faster convergence in reinforcement learning algorithms.
method Improved convergence analysis of SVRPG method, focusing on variance reduction and epoch length/batch size parameters.
result Improved convergence to ε-approximate stationary point with reduced sample complexity.
Significant improvements in regret analysis for adaptive online learning problems.
problem Exploiting low variance in online learning problems without known variances.
method Novel peeling-based regret analysis leveraging elliptical potential `count` lemma.
result Significant improvements in regret bounds for linear bandits and linear mixture MDPs.
New methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
This paper analyzes the posterior variance of Gaussian processes and derives a new bound.
problem Lack of suitable analysis of posterior variance for finite and infinite training data.
method Derives a novel bound for posterior variance requiring only local information.
result Proves sufficient conditions for the convergence of posterior variance to zero and demonstrates improved average learning bound.
Improved bounds for adversarial bandits with variance analysis.
problem Optimizing decision-making in adversarial environments with varying gaps.
method First-order bounds, variance analysis, gap-dependent bounds for follow the regularized leader.
result Improved bounds for adversarial bandits with a factor of log(n)/log(log(n)) improvement.
BS-VAE separates decoder variance and beta to improve VAE performance.
problem Blurriness in VAE outputs and difficulty in analyzing model performance.
method Explicitly separates beta and decoder variance in Beta-Sigma VAE.
result Superior performance in natural image synthesis and controllable parameters.
The paper identifies the minimum mean-variance spanning set and its importance in asset evaluation.
problem Estimating the minimum subset of assets that span the efficient frontier.
method Established identification conditions and developed a novel procedure for MSS estimation and inference.
result The MSS estimator accurately covers the true MSS and converges to it at any desired confidence level.
New clustering algorithms capture time-evolving clusters using Markov models.
problem Capturing time-evolving clusters in data.
method Small-variance asymptotic analysis of Markov chain mixture models.
result Two clustering algorithms (D-Means and SD-Means) outperform existing methods in accuracy and computational cost.
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
Unified analysis of SVRG and Katyusha using dissipativity theory.
problem Accelerating variance reduction in stochastic optimization.
method Dissipativity theory applied to SVRG and Katyusha.
result Unified convergence analysis of SVRG and Katyusha.
Enhances sensitivity analysis for correlated inputs.
problem Estimating sensitivity indices in models with correlated inputs.
method Proposes an extension of Sobol' estimator using a linear correlation model.
result Improves accuracy in variance-based sensitivity analysis.
Efficient variance estimation for kernel ridge regression.
problem Estimating variance in kernel ridge regression efficiently.
method Random projection approach to estimate variance.
result Optimal variance estimator for various kernels.
Simplified analysis of diffusion models using discrete random variables.
problem Theoretical analysis of diffusion models is complex and requires rigorous proofs.
method Simplified framework for analyzing Euler--Maruyama discretization of VP-SDEs using Grönwall's inequality.
result Standard Gaussian noise can be replaced by discrete random variables without sacrificing convergence guarantee.
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.
A new statistical concept, lepto-variance, is defined for stock returns using Regression Trees.
problem Understanding the underlying structure of stock returns using statistical methods.
method Defining lepto-variance as the variance that cannot be removed by any regression tree of a specific depth and analyzing stock returns with 1- and 2-bit Regression Trees.
result Lepto-variance quantifies the resolving power of Regression Trees for stock returns, decomposing total variance into lepto-variance and macro-variance.
The paper calculates factor loading and unique variance covariances for various factor analysis methods.
problem Estimating the asymptotic covariances of unrotated factor loading and unique variance estimates.
method Explicit formulas derived from sample covariances or correlations, using least square, principal, iterative principal component, alpha, or image factor analysis.
result The formulas produce reasonable standard errors for rotated loading estimates in multivariate normal populations.
Paper analyzes bias-variance tradeoff in graph Laplacian regularization.
problem Understanding the optimal regularization parameter for graph Laplacian.
method Spectral graph properties and signal-to-noise ratio parameter used to determine optimal regularization.
result Selecting mediocre regularization is often suboptimal, suggesting near-optimal performance.
Unified framework speeds up SMF algorithms via variance reduction.
problem Improving convergence speed and accuracy in stochastic matrix factorization.
method Unified framework using variance reduction for SMF.
result Consistently faster convergence and more accurate output.
A new Riemannian algorithm reduces variance in manifold optimization.
problem Optimizing functions on manifolds with stochastic gradient descent.
method Riemannian stochastic variance reduction with retraction and vector transport.
result The proposed algorithm outperforms standard methods on SPD and Grassmann manifolds.
The paper develops variance-reduced methods to solve complex optimization problems.
problem Non-convex composition optimization with many inner functions.
method Variance-reduced techniques applied to SGD and SVRG.
result Significant improvement in query complexity for large inner function numbers.
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.
Improved TD learning reduces variance and bias errors.
problem Inefficient optimization variance in TD learning.
method Proposed a mathematically solid analysis of VRTD, showing linear convergence rate and reduced variance and bias errors.
result VRTD converges to a fixed-point solution with reduced variance and bias errors compared to vanilla TD.
Unified analysis of stochastic gradient methods for convex and smooth optimization.
problem Minimizing composite convex and smooth functions.
method Unified convergence analysis of various stochastic gradient methods.
result Unified convergence rates for a variety of methods including proximal SGD, variance reduced methods, quantization, and coordinate descent.
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situa…
Paper proposes variance reduction for Markov chains, especially useful in MCMC.
problem Reducing variance in Markov chain additive functionals.
method Minimizes asymptotic variance of functionals over control variates.
result Significantly reduces overall finite sample variance in simulations.
Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.
problem Minimizing regret in Gaussian process bandits with unknown reward functions.
method New upper bound on maximum posterior variance, refined MVR and PE algorithms.
result Optimal regret bounds for noiseless, varying noise, and RKHS norms.
VAEs analyzed using harmonic analysis, showing how variance controls frequency content and robustness.
problem Understanding and optimizing VAEs for robustness and frequency control.
method Viewing VAE latent space as Gaussian space, deriving results on variance and frequency content, and demonstrating soft Lipschitz constraints.
result Increasing encoder variance reduces high frequency content and improves adversarial robustness.
Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -…
A new method detects anomalies in multivariate streams without unit dependence.
problem Detect anomalies in multivariate streams without unit dependence.
method Proposes SigMahaKNN combining variance norm and path signature.
result SigMahaKNN detects anomalies better than existing methods.
The paper analyzes the variance of different shuffling methods in stochastic gradient descent.
problem Understanding the variance of different shuffling methods in stochastic gradient descent.
method Power spectral density analysis to study the noise sequences of stochastic gradients.
result The stationary variances of iterates decrease in the order of SGD, SGD-RR, and SGD-SO.
The paper analyzes how larger minibatch sizes in SG-MCMC lead to faster convergence.
problem Theoretical analysis of impact of minibatch size on SG-MCMC convergence rate.
method Proposes a variance-reduction technique for SG-MCMC and proves its faster convergence rate.
result The proposed variance-reduction technique leads to a faster convergence rate than standard SG-MCMC.
New approach combines PCA and t-sne for better data analysis.
problem Multiscale complexity in high-dimensional data.
method Multiscale joint characterization using PCA and t-sne.
result Joint characterization detects signals not seen by PCA or t-sne alone.
Closed pricing formulas for Variance Gamma model payoffs.
problem Pricing path-independent payoffs in the Variance Gamma model.
method Mellin transform theory and multidimensional complex analysis.
result Closed-form pricing formulas with accelerated convergence for short-term options.
Paper presents ZO-SVRG for faster nonconvex optimization.
problem Gradient-free optimization challenges in nonconvex settings.
method Comprehensive theoretical analysis, novel ZO-SVRG algorithm, accelerated versions.
result ZO-SVRG achieves best rate for ZO stochastic optimization.
A new measure k-variance captures local distributional shape.
problem Summarizing distributional shape with local information.
method Random bipartite matchings and stochastic approximation.
result Easily approximated k-variance measures capture local distributional properties. Two derivations of PCA for distributional data.
problem PCA for datasets of distributions.
method Two derivations: variance maximization and reconstruction error minimization.
result Closed-form solution for distributional PCA.
Fourier analysis improves REINFORCE for binary models.
problem Improving gradient estimation for binary latent variable models.
method Connecting Fourier spectrum of Boolean functions to REINFORCE and developing low-variance unbiased gradient estimators.
result REINFORCE estimates degree-1 Fourier coefficients of a Boolean function.
Action-dependent baselines reduce policy gradient variance in deep RL.
problem High variance in policy gradient methods, especially in long-horizon or high-dimensional action spaces.
method Derive a bias-free action-dependent baseline that fully exploits policy structure without additional assumptions.
result Demonstrates and quantifies the benefit of action-dependent baselines through theoretical and numerical results.
New method optimizes PCA for better prediction and variance.
problem Improve PCA for better prediction and variance.
method Jointly optimize prediction error and variance explained.
result Our method outperforms existing approaches in both prediction and variance.
Improved variance reduction for Riemannian non-convex optimization with adaptive batch size.
problem Optimizing non-convex functions on Riemannian manifolds.
method Batch size adaptation in R-SVRG, R-SRG, and R-SPIDER.
result Achieves lower total complexities for various non-convex functions.
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.
Proposes a novel MTL approach based on bias-variance analysis.
problem Improving multi-task learning performance through shared knowledge.
method Two-phase iterative aggregation of targets and features using bias-variance analysis.
result Validation on synthetic and real-world datasets demonstrates the effectiveness of the proposed method.
New algorithm improves convergence of AUC maximization.
problem Optimizing AUC for imbalanced classes with stochastic methods.
method Variance Reduced Stochastic Proximal Algorithm for AUC Maximization (VRSPAM).
result VRSPAM converges faster than previous methods.
Adaptive PCA algorithms for changing environments.
problem Static adversarial regret is not suitable for changing environments.
method Online adaptive algorithms for PCA and variance minimization with sub-linear adaptive regret guarantees.
result The proposed algorithms adapt to changing environments.
Simplified analysis of SGD for linear regression with weight averaging.
problem Understanding SGD optimization in linear regression models.
method Simplified analysis using linear algebra tools, bypassing complex operator manipulations.
result Recovery of bias and variance bounds for SGD in linear regression.