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.
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.
A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff can be replicated exact…
Optimizes hedging strategy using Fourier-integration for variance-optimality.
problem Finding optimal hedging strategy under variance-optimality criterion.
method General representations and Fourier-integration for Heston model; sparse hedging selection.
result Sparse semi-static hedging strategy using Fourier-integration.
New Riemannian optimization improves variance estimation in mixed models.
problem Challenges in estimating variance parameters in linear mixed models due to constraints.
method Formulated as an optimization problem on a Riemannian manifold, using Riemannian gradient and Hessian.
result Yields higher quality variance parameter estimates compared to existing methods.
New process explains asset volatility patterns.
problem Explains statistical relationship between asset volatility and returns.
method Uses multiplicative Langevin process with adjustable coherence time.
result Exactly equivalent to Inverse Gamma distribution for volatility.
Two surfaces minimize variance of Gaussian curvature.
problem Minimizing the variance of Gaussian curvature on triply periodic minimal surfaces.
method Interpreting branch values of Gauss map, expressing variance as integrals of exponentials of Green's functions, analyzing Hessian.
result The P and D surfaces are local minimizers of the variance of Gaussian curvature.
Algorithm optimizes hedging in electricity markets by minimizing variance risk.
problem Hedging contracts in electricity markets due to liquidity and market characteristics.
method Developed an algorithm for mean variance hedging considering transaction costs and market depth.
result Algorithm effectively reduces residual risk in electricity market positions.
Optimizes portfolio variance without short selling, revealing a critical point.
problem Optimizing portfolio variance with no short selling constraints.
method Analytic solution with ℓ1 regularizer, numerical simulations. result Critical point r=2 for optimal portfolio weights, diverging sensitivity. New RFs reduce kernel approximation variance and improve Transformer performance.
problem Efficient approximation of Gaussian and softmax kernels for kernel methods and Transformers.
method Parameterized, positive, non-trigonometric RFs optimized for variance reduction.
result Significant variance reduction in practice, outperforming previous methods.
New theorem splits spaces with maximal variance of 1-Lipschitz functions.
problem Understanding the structure of metric measure spaces.
method Analyzing isoperimetric profiles and variance of 1-Lipschitz functions.
result Spaces with maximal variance are foliated by minimal geodesics.
New convergence rates for SGD under heavy-tailed noise with infinite variance.
problem Convergence analysis of SGD under heavy-tailed noise with infinite variance.
method Identifying a condition on the Hessian and providing a convergence rate for the distance to the global optimum.
result SGD can converge to the global optimum under heavy-tailed noise with infinite variance.
New insights into trend following strategies show strong convexity in CTA performance.
problem Explaining the positive convexity of CTA performance.
method Revisits trend following strategies and measures long-term and short-term realized variance.
result Shows strong convexity in CTA performance, stronger than anticipated.
A new algorithm reduces variance in Riemannian stochastic quasi-Newton methods.
problem Minimizing the average of many loss functions on Riemannian manifolds.
method R-SQN-VR algorithm with variance reduction for non-convex and retraction-convex functions.
result The algorithm outperforms existing methods on manifold computations.
Analytic method optimizes portfolio variance with asymmetric ℓ1 constraint.
problem Optimizing portfolio variance under budget and asymmetric ℓ1 constraints. method Replica method from disordered systems theory.
result Regularization extends optimization interval and suppresses large sample fluctuations.
This work explains the structural origins of attention sinks in LLMs.
problem Initial tokens disproportionately monopolize attention scores in LLMs.
method Traced to self-attention's value aggregation process and FFN layer activations.
result Attention sinks form due to variance discrepancy and dimension disparity.
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel κ, which translates naturally into kernels between histograms or clouds of points. We first cover the case where $\Xcal$ is Euclidian, and focus on kernels which take into account th…
In the recent years, banks have sold structured products such as worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correl…
Study examines factors influencing tail risk premia for long-term equity investors.
problem Determining factors affecting variance and higher-moment risk premia in equity markets.
method Empirical study using discretisation invariant swaps for log returns, focusing on skewness, kurtosis, and variance risk premia.
result Momentum is the dominant driver for skewness and kurtosis risk premia, while variance risk premium is influenced by size and growth.
Study long-only minimum variance portfolio in one-factor market with arbitrary sign betas.
problem Characterize the long-only minimum variance portfolio in a one-factor market with mixed-sign betas.
method Explicit solution for long-only minimum variance portfolio, explicit characterization of active set, asymptotic analysis in high-dimensional regime.
result Proportion of active assets in LOMV portfolio converges to F(β∗) in high-dimensional regime, with rate O(F(0)1/3) when F(0)>0. New method reduces variance and bias in approximating indefinite kernels.
problem Approximating non-stationary indefinite kernels with low variance and bias.
method Generalized orthogonal random features (GORF)
result GORF achieves lower variance and approximation error compared to existing methods.
The paper shows how shared random seeds can reduce variance in machine learning evaluations.
problem The statistical structure of comparative evaluation under shared random seeds is not well understood.
method An extended learning-based multi-agent economic simulator was used to demonstrate the effects of shared random seeds on variance reduction.
result Pairing seeds can reduce variance in machine learning evaluations, especially when outcomes are positively correlated at the seed level.
Improved outlier detection in hierarchical Gaussian Processes using Wasserstein-2 kernels.
problem Outlier detection limitations in stacked Gaussian Processes.
method Proposed a hybrid kernel combining Euclidean and Wasserstein-2 distances, emphasizing variance in Wasserstein-2 computations.
result Improved performance and enhanced out-of-distribution detection on various datasets.
Paper explains contrastive learning using cosine similarity and proposes mitigations for batch size effects.
problem Understanding and improving contrastive learning through batch size effects.
method Unified framework of cosine similarity, theoretical insights, and auxiliary loss.
result Performance improvement in small-batch settings through proposed auxiliary loss.
Investigates Bitcoin market risk, showing volatility and jumps impact future volatility.
problem Understanding and forecasting the risk dynamics of Bitcoin market.
method Comprehensive investigation using realized volatility and jumps analysis.
result Jumps, especially positive ones, reduce future realized variance; long-term realized variance benefits from modeling jumps.
The paper studies random systems of holomorphic sections on compact Kähler manifolds and proves equidistribution results.
problem Estimating the distribution of zeros of random holomorphic sections on compact Kähler manifolds.
method Asymptotic variance estimate for smooth linear statistics, equidistribution result derivation.
result Smooth positive closed form ω^k can be approximated by currents of integration along analytic subsets of X.
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.
Our paper improves uplift model evaluation on randomized controlled trials (RCT) data.
problem Variance in uplift evaluation metrics makes their signals arbitrary and unreliable.
method Theoretical analysis and statistical adjustment of the outcome to reduce variance.
result Variance reduction methods improve uplift evaluation metrics on RCT data.
Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant variance to all stocks; zero rate of growth to all stocks but the smallest; and positiv…
Paper improves efficiency in matrix computations for Gaussian processes.
problem Efficiency in matrix computations for Gaussian processes.
method Variance reduction via matrix factorization.
result Factorized estimator can be up to 1,000 times more efficient.
Paper proposes a new covariance estimator ensuring positive semi-definite matrices.
problem Estimating spot covariance matrices while maintaining positive semi-definiteness.
method Modification of the Fourier covariance estimator with a symmetric positive semi-definite constraint.
result The estimator is consistent and produces accurate positive semi-definite matrices.
Trading styles affect long-run variance of asset prices, increasing under trend-following and decreasing under mean-reverting.
problem Understanding how different trading styles impact the long-run variance of asset prices.
method Probabilistic models designed to capture the direction of trading were used.
result Trading styles increase long-run variance under trend-following and decrease it under mean-reverting conditions.
A new L-BFGS algorithm for Riemannian optimization converges fast without linesearch.
problem Optimization on Riemannian manifolds with fast convergence.
method Stochastic variance reduction, minibatching, constant step sizes, correction pairs.
result Convergence proof for strongly convex functions, convergence discussion for nonconvex functions.
To any positive number ε and any nonnegative even Schwartz function w:R→R we associate the random function uε on the m-torus Tεm:=Rm/(ε−1Z)m defined as the real part of the random Fourier series $$ \sum_{ν\in\mathbb{Z}^m} X_…
The paper connects semi-parametric estimates to European option pricing.
problem Estimating European option prices using semi-parametric methods.
method Connecting estimates by de la Peña, Ibragimov and Jordan, Scarf, and Lo.
result The estimates imply European option prices.
This study optimizes neural networks for doubly robust ATE estimation to balance bias and variance.
problem Balancing bias and variance in doubly robust estimators with neural networks.
method Investigates two neural network architectures and their hyperparameters in the presence of confounders and IVs.
result Optimal hyperparameters for neural networks reduce bias-variance tradeoff for ATE estimators.
Hybrid model combines risk measures for better portfolio allocation.
problem Optimizing portfolios with various risk measures.
method Mean-variance hybrid model combining spectral risk measure and quantile optimization.
result Hybrid model outperforms classical mean-variance model in risk allocation.
We show that stochastic recovery always leads to counter-intuitive behaviors in the risk measures of a CDO tranche - namely, continuity on default and positive credit spread risk cannot be ensured simultaneously. We then propose a simple recovery variance regularization method to control the magnitude of negative credi…
The replica method solves mean-variance portfolio optimization without symmetry assumptions.
problem Mean-variance portfolio optimization for a generic covariance matrix.
method Replica method from statistical physics applied to optimization problem.
result Replica symmetry emerges as the unique solution of the optimization problem.
CVTMLE improves statistical inference in settings of positivity or Donsker class violations.
problem Inference issues in causal inference due to data sparsity or near-positivity violations.
method Cross-validation of TMLE (CVTMLE) to improve performance in settings of positivity or Donsker class violations.
result CVTMLE vastly improves confidence interval coverage without affecting bias, especially in small sample sizes and near-positivity violations.
Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.
problem Implied volatility constraints under finite log-moments.
method Analyzes stock price martingale with finite log-moments, derives new bounds and proof.
result New bounds on implied volatility growth, relaxes moment assumptions.
Bayesian framework improves variance component estimation in MET data.
problem Inaccurate estimation of variance components in MET data.
method Proposes a Bayesian updating framework using historical data.
result Stabilizes variance component estimation and quantifies uncertainty.
Proposes ENVAR for causal discovery in structural VAR models with equal noise variance.
problem Challenges in causal discovery from multivariate time series with contemporaneous effects.
method Introduces observational equivalence and the observational alignment discrepancy for structural VAR models with equal noise variance.
result Shows that multiple structural VAR parameterizations can induce the same stationary observed process law.
Paper analyzes high-dimensional portfolio risks and finds empirical out-of-sample relative loss is more reliable.
problem Analyzing risks in high-dimensional portfolios using empirical variance.
method Derives asymptotic behavior of out-of-sample variance and relative loss in high-dimensional settings.
result Empirical out-of-sample relative loss is more reliable than variance in high-dimensional portfolios.
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.
New algorithm for contextual combinatorial bandits with probabilistic arm triggering.
problem Optimizing decisions in dynamic environments with probabilistic arm availability.
method C^2-UCB-T and VAC^2-UCB algorithms with TPM and VM conditions.
result Achieved improved regret bounds for contextual combinatorial bandits.
We show that the efficient frontier for a portfolio in which short positions precisely offset the long ones is composed of a pair of straight lines through the origin of the risk-return plane. This unique but important case has been overlooked because the original formulation of the mean-variance model by Markowitz as …
Study the averaging estimator on graphs with labeled nodes.
problem Understanding the quality of averaging estimators on graph data.
method Rigorously study concentration properties, variance bounds, and risk bounds.
result Contributes to theoretical understanding of graph learning.