Empirical study finds variance swap rate is affine in spot variance for S&P500 data.
problem Investigating the relationship between variance swap rate and spot variance.
method Empirical analysis using S&P500 data from 2006-2018, testing different models.
result Affine relationship between variance swap rate and spot variance is supported.
This paper tackles variance issues in GNN training by proposing a method to reduce both embedding and gradient variances.
problem High variance in estimating stochastic gradients in GNN training, especially in large graphs.
method The paper proposes a decoupled variance reduction strategy that employs approximate gradient information to adaptively sample nodes with minimal variance.
result The proposed method achieves faster convergence and better generalization compared to existing sampling methods.
Study shows gradient variance increases during deep learning training, contrary to common belief.
problem Understanding and minimizing gradient variance in deep learning models.
method Gradient Clustering method using stratified sampling to minimize gradient variance.
result Gradient variance increases during training, and smaller learning rates coincide with higher variance.
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
The paper analyzes the bias-variance tradeoff for Bregman divergences.
problem Understanding the bias-variance tradeoff for Bregman divergences.
method Analyzes the bias-variance tradeoff through operations in dual space.
result Derives several results including a generalized law of total variance and ensembling operations.
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.
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.
Paper tackles unknown variances in best-arm identification.
problem Identifying the best arm with unknown variances in Gaussian distributions.
method Two approaches: empirical variance plugging or adapting transportation costs.
result The impact of unknown variances is small on sample complexity.
New algorithms improve best-arm identification with varying rewards.
problem Identifying the best arm with varying reward variances in fixed budget.
method Proposed two algorithms: SHVar for known variances, SHAdaVar for unknown variances; uses non-uniform budget allocation.
result Bounding misidentification probabilities for both algorithms.
Before training a neural net, a classic rule of thumb is to randomly initialize the weights so the variance of activations is preserved across layers. This is traditionally interpreted using the total variance due to randomness in both weights \emph{and} samples. Alternatively, one can interpret the rule of thumb as pr…
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. In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this kind of problem, we consider to minimize the variances of the investm…
Increasing variance of losses improves learning with noisy labels.
problem Learning with noisy labels and the need to penalize variance of losses.
method Designing regularizers based on the label noise transition matrix to increase variance of losses.
result Increasing variance of losses significantly improves generalization ability.
New method corrects Markowitz variance for trading volume fluctuations.
problem Incorrect risk estimates from Markowitz variance in trading environments.
method Modeling portfolio variance based on trade volume fluctuations.
result Market-based variance can significantly differ from Markowitz variance.
This study reviews techniques to estimate volatility and price Variance Swaps.
problem Estimating historical volatility and pricing Variance Swaps.
method Review of existing techniques.
result Discussion of various methods to estimate volatility and price Variance Swaps.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
New method reduces inference variance for faster optimization.
problem High variance in black-box variational inference.
method Joint control variate addressing both data subsampling and Monte Carlo noise.
result Significantly reduced gradient variance, leading to faster optimization.
This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
problem Pathwise gradient estimators in variational inference have high variance, leading to inefficient optimization.
method Apply zero-variance control variates to pathwise gradient estimators.
result Zero-variance control variates can significantly reduce the variance of pathwise gradient estimators without requiring complex assumptions.
VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
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.
A simple method treats heteroscedastic variance variatively, improving model calibration and sample quality.
problem Brittle optimization impacts model likelihoods for mean and variance estimation.
method Proposes a variational approach to heteroscedastic variance, improving predictive mean and variance calibration.
result The proposed method significantly improves parameter calibration and sample quality for regression and VAEs.
Improved LLM pre-training performance through better weight and variance control.
problem Improper weight and variance control in LLM pre-training affects downstream task performance.
method Introduced Layer Index Rescaling (LIR) and Target Variance Rescaling (TVR) techniques.
result Substantial improvements in downstream task performance (up to 4.6%) and reduced extreme activation values.
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…
MFVI can overestimate predictive variance compared to the exact posterior
problem MFVI underestimates posterior variance
method Analyzing conjugate Bayesian Linear Regression
result MFVI can overestimate predictive variance compared to the exact posterior
New algorithms reduce regret in both stochastic and deterministic environments.
problem Designing algorithms that perform well in both types of MDPs.
method Proposed new environment norms and algorithms with variance-dependent regret bounds.
result First algorithm with simultaneously optimal bounds for both stochastic and deterministic MDPs.
Memory-efficient algorithm reduces variance in off-policy RL.
problem High variance in off-policy policy optimization.
method Memory-efficient, stochastically variance-reduced algorithm using off-policy samples.
result Empirically validated effectiveness of the proposed algorithm.
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…
The paper explores the trade-off between bias and variance in high-dimensional models.
problem Understanding the unavoidable trade-off between bias and variance in high-dimensional statistical models.
method Proposes a general strategy to obtain lower bounds on the variance of estimators with a specified bias, and applies it to various statistical models.
result Shows the extent to which the bias-variance trade-off is unavoidable and quantifies the performance loss for methods that do not balance it.
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high vari…
A new QHR model extends HR model with a quadratic variance function.
problem Modeling volatility with greater flexibility and stationarity.
method Introducing a quadratic variance function to the HR model, maintaining Markovian property.
result Stationary distribution of the QHR model is Pearson type IV.
We quantify predictive uncertainty using the posterior predictive variance.
problem Quantifying uncertainty in predictive models.
method Using the law of total variance, we generate expansions for the posterior predictive variance.
result Identify the main contributors to prediction intervals and quantify term-wise uncertainty.
Neural SDEs reduce variance in stochastic simulations.
problem Efficiency of Monte Carlo simulations in finance.
method Use neural SDEs with control variates parameterized by neural networks.
result Prove optimality conditions for variance reduction in SDEs with infinite activity.
The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models, for which it is often observed that larger models generalize better. We provide …
NP-PROV separates mean and variance spaces to improve function uncertainty.
problem Neural Processes fail on out-of-domain tasks due to shared latent space uncertainty.
method Separates mean and variance into function-value-related and position-related latent spaces.
result NP-PROV achieves state-of-the-art likelihood with bounded variance in drifts.
Improved regret bounds for contextual bandits considering variance sequences.
problem Establishing lower bounds for contextual bandits with variance-dependent regret.
method Developed variance-dependent lower bounds for linear contextual bandits under two settings: fixed and adaptive variance sequences.
result Lower bounds match upper bounds of SAVE algorithm up to logarithmic factors.
Deep learning models show bias and variance are aligned, not in trade-off.
problem The classical bias-variance trade-off in deep learning models.
method Empirical evidence and theoretical analysis of bias and variance in deep learning models.
result Squared bias is approximately equal to variance for correctly classified sample points in deep learning models.
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.
New formulas derived for variance gamma model option pricing.
problem Option pricing for the variance gamma model.
method Combining randomization method and fractional derivatives.
result Closed-form formulas for European options.
In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy, we use a Fourier approach in a general multidime…
Paper improves confidence intervals and variance estimation for deep learning models.
problem Improving confidence intervals and variance estimation in deep learning models.
method Residual-based framework for conditional variance estimation; robust bootstrap procedure for confidence intervals.
result First non-asymptotic bounds for variance estimation using ReLU networks.
The article prices exchange options using variance gamma-like models.
problem Pricing exchange options under specific stochastic processes.
method Derives formulas for variance gamma and variance gamma++ processes, constructs multidimensional versions, calibrates parameters with real data.
result Closed formulas and numerical methods for evaluating exchange options.
Data balancing reduces variance in machine learning models.
problem Reduction of variance in machine learning models.
method Non-asymptotic statistical bound and eigenvalue decay of Markov operators.
result Data balancing across modalities and sources reduces variance.
Enhances neural network regression performance by modeling weight and variance uncertainty.
problem Improving predictive performance of neural networks for regression tasks.
method Extended Blundell's framework to include variance uncertainty, using a full posterior distribution over variance parameters.
result Explicitly modeling variance uncertainty improves generalization of Bayesian neural networks.
In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is optimal for a large family of kernels, including cubic splines and Gaussian ker…
A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.
problem Simplifying mean-variance portfolio theory.
method Introducing the Hansen ratio and extending mean-variance theory.
result The Hansen ratio provides a parsimonious description of the mean-variance efficient frontier.
Paper tackles bias-variance trade-off in missing data, proposing a dynamic framework.
problem Missing data in practical applications deteriorates model performance.
method Develops a fine-grained dynamic learning framework to jointly optimize bias and variance.
result Theoretical and empirical validation of joint bias-variance optimization.
Meta-learning variance reduced via Laplace approximation for regression tasks.
problem High variance in meta-learning due to limited support data for each task.
method Laplace approximation to estimate posterior variance and reduce gradient estimate variance.
result Effective variance reduction in meta-learning, improving generalization performance.
Market-based portfolio variance measures risks using trade data.
problem Measuring portfolio risks using traditional methods ignores trade volume randomness.
method Uses time series of trades with securities and portfolio to assess variance.
result Portfolio variance can be decomposed into securities' contributions, accounting for trade volume randomness.