This paper identifies and bounds ICE central moments using PO marginal central moments.
problem Identifying and characterizing treatment effect heterogeneity.
method Using only marginal central moments of potential outcomes, the paper identifies and bounds central moments of individual causal effects.
result Identification and bounding of central moments of ICE using marginal moments of POs.
New bounds on machine learning model generalization error moments.
problem Understanding the performance of machine learning models.
method Information-theoretic bounds on the moments of the generalization error of learning algorithms.
result Proposed bounds on generalization error moments and their high-probability bounds.
The paper improves PAC-Bayes bounds for losses with finite moments.
problem Bounding generalization for losses with heavy tails and finite moments.
method Truncation method and PAC-Bayes bounds for unbounded losses with heavy tails and bounded variance.
result Bounds interpolate between slow and fast rates depending on the moment.
This paper examines how data affects risk measures in uncertain distributions.
problem How does distributional ambiguity affect risk measures?
method Formulated and derived simpler dual problems for infinite and finite dimensional robust moment problems.
result Developed theory and conducted experiments in inventory control and portfolio management.
New bounds on generalization error using information density moments.
problem Bounding the generalization error of randomized learning algorithms.
method Derives bounds on average and tail probabilities of generalization error using mth central moments of the information density.
result Explicit bounds on generalization error are derived, showing better dependence on confidence level with higher-order information density moments.
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …
Study differentially private linear regression with heavy-tailed data.
problem Differentially private ℓ1-norm linear regression with heavy-tailed data. method Exponential mechanism for ℓ2-norm bounded second moment; relaxation to ℓ2-norm bounded θ-th moment; coordinate-wise bounded moments. result Achieved upper bounds for privacy-preserving linear regression under various moment conditions.
The paper examines higher moments in insurance, focusing on coskewness and its impact on actuarial quantities.
problem The impact of higher-order moments on actuarial applications, particularly expected shortfall and life annuity valuation.
method Derives analytical bounds for mixed moments under unspecified dependence structure, applies copula-based mixture model.
result Coskewness and odd-order mixed moments exhibit a monotonic relationship with expected shortfall and annuity premiums.
The paper improves generalization bounds for domain adaptation.
problem Improving generalization bounds for domain adaptation under practical conditions.
method Derives generalization bounds for domain adaptation based on finitely many moments and smoothness conditions.
result Obtains generalization bounds for domain adaptation.
We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions…
We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an associated ordinary differential equation (ODE). We obtain finite-time bounds on t…
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…
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.
This thesis studies domain adaptation under minimal distribution similarity assumptions using moments.
problem Learning from samples with distributions different from training samples.
method Uses minimal similarity assumptions modeled by moments.
result Establishes learning bounds and algorithms for domain adaptation.
The paper sets limits on the accuracy of macroeconomic forecasts based on statistical moments and trade volumes.
problem Uncertainty in predicting macroeconomic variables like prices and returns.
method Defines theoretical lower bounds of uncertainty and upper limits on forecast accuracy based on statistical moments and trade volumes.
result Accuracy of forecasts of probabilities of macroeconomic variables doesn't exceed Gaussian approximations.
Paper tackles moment estimation under covariate shift with a two-stage algorithm.
problem Estimating moments under covariate shift when source and target distributions differ.
method Proposes a two-stage algorithm: first, an optimal estimator for the source distribution; second, likelihood ratio reweighting for calibration.
result Achieves minimax optimal bound for moment estimation.
Study resolvent convergence for random matrices with general covariance profiles.
problem Analyzing resolvent convergence for random matrices with non-identically distributed columns.
method Using moments of quadratic forms and deterministic equivalents, the study provides bounds on the trace of matrix products.
result The trace of matrix products is close to the trace of a deterministic equivalent, controlled by matrix norms.
We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our u…
PMT uses public data moments to make DP feasible for unbounded data.
problem Applying differential privacy to unbounded data distributions.
method Public-moment-guided Truncation (PMT) using second-moments from public data.
result PMT improves the accuracy and stability of DP models.
Improved bounds on moments of word measures on unitary groups.
problem Analyzing the moments of word measures on unitary groups.
method Using Haar-uniform sampling and algebraic invariants to study asymptotic behavior.
result Found a new algebraic invariant related to the moments of word measures.
New method tightens sub-Gaussian concentration inequalities.
problem Estimating variance-type parameters of sub-Gaussian distributions.
method Using sub-Gaussian intrinsic moment norm to maximize normalized moments.
result Provides tighter sub-Gaussian concentration inequalities.
Empower efficient representation of distributions through moment-preserving methods.
problem Representing high-dimensional probability measures efficiently and accurately.
method Empower efficient representation of distributions through moment-preserving methods.
result Empowers efficient and accurate representation of high-dimensional probability measures.
New stability framework relaxes boundedness assumptions for generalization bounds.
problem Overly restrictive assumptions for modern learning settings with heavy-tailed or unbounded losses.
method Develops a stability-based framework requiring only finite Lp moment conditions. result Sharp generalization bounds derived for various learning paradigms.
New SQ lower bounds for NGCA without requiring chi-squared condition.
problem Proving SQ hardness for NGCA under moment-matching conditions.
method General SQ lower bound methodology applied to NGCA under moment-matching conditions.
result Proved near-optimal SQ lower bounds for NGCA without chi-squared condition.
New method estimates log-determinant using trace powers, avoiding classical limitations.
problem Estimating log-determinant of large matrices efficiently and accurately.
method Interpolating moment-generating function and its derivative at zero using trace powers.
result No continuous estimator using finite moments can be uniformly accurate over unbounded conditioning.
We improve bounds for stochastic processes, especially those with heavy tails.
problem Bounding the concentration of sub-ψ processes with heavy tails. method Variational approach to concentration, focusing on sub-Gaussian and other tail conditions.
result First dimension-free self-normalized empirical Bernstein inequality.
Study finds the minimum number of finite Gaussian mixtures for best approximation.
problem Finding the minimum number of finite Gaussian mixtures for best approximation.
method Local moment matching for upper bound and spectral analysis for lower bound.
result Corrects a previous lower bound in the case of Gaussian mixing distributions.
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, an…
The paper introduces a new method for tail bounds of random vectors and matrices.
problem Estimating norms of random vectors and matrices under moment assumptions.
method Variational tail bounds for norms of random vectors and matrices.
result Dimension-free concentration inequalities for various norms of random vectors and matrices.
Unified framework for imitation learning via moment matching.
problem Closing the gap between imitation and real-world performance.
method Classifying imitation learning algorithms based on reward or action-value moment matching, considering adversarial divergences.
result Derivation of bounds on policy performance for all algorithms in each class, and introduction of moment recoverability.
Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.
problem Well-posedness of parabolic Anderson model on Riemannian manifolds with rough initial conditions.
method Construct intrinsic Gaussian noises, explore global geometry, use Feynman-Kac formula.
result Show well-posedness with non-positive curvature and conditions on α. The paper analyzes extreme risk measures with limited distributional information.
problem Investigating risk measures under partial knowledge of distribution moments and shape.
method Employing probability inequalities and modified Schwarz inequality to derive bounds on distortion risk measures.
result Unified framework for calculating best- and worst-case scenarios of distortion risk measures.
In this paper, we the improve the bound for the moment map derivative proved by Donaldson in his recent proof of the Hilbert-Mumford stability of complex manifolds with constant scalar curvature. The proof depends on the identification of Donaldson's symplectic form with the curvature of a certain Deligne pairing.
A new UCB algorithm for heavy-tailed bandits with near-optimal regret.
problem Sequential decision making in uncertain environments with heavy-tailed rewards.
method Data-driven, distribution-free UCB algorithm combining resampled median-of-means and UCB.
result Near-optimal regret bound for heavy-tailed distributions.
The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation…
Robustly estimates linear regression coefficients with adversarial and noisy data.
problem Estimating robust linear regression coefficients with adversarial and noisy data.
method Adversarial robust weighted Huber regression with polynomial computational complexity.
result Derives an estimation error bound that depends on the stable rank and condition number of the covariance matrix.
Study compares eigenvalues and moment spectra of geodesic balls in Riemannian manifolds.
problem Comparing eigenvalues and moment spectra of geodesic balls in Riemannian manifolds.
method Explicit upper and lower bounds for Poisson hierarchy and torsional rigidity.
result Equality of eigenvalues and moment spectra characterizes the model space.
New bounds for neural networks without loss boundedness assumption.
problem Generalization error bounds for two-layer neural networks.
method Wasserstein distance estimates and moment bounds for stochastic gradient method.
result Dimension-free rate of order O(n−1/2) for independent test data. The paper optimizes estimating high-dimensional Gaussian mixtures without separation conditions.
problem Estimating the mixing distribution in high-dimensional Gaussian mixtures without separation conditions.
method The method of moments and careful application of moment tensors.
result The minimax rate of estimating the mixing distribution in Wasserstein distance is Θ((d/n)1/4+n−1/(4k−2)). We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained in recent works of Diakonikolas et al, Lai et al, and Charikar et al. We also sho…
Efficiently estimates mean of symmetric distributions without moments.
problem Estimating mean of symmetric distributions without moment assumptions.
method Generalization of filtering technique, Huber-loss-based techniques, SoS proofs.
result Achieves optimal error bounds for various symmetric distributions.
Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g., AdaGrad, AdaDelta, and Adam, eases the job slightly. However, such methods have also …
Enhances DP linear regression using public data moments.
problem Limited utility of traditional DP methods in linear regression.
method Transform private data using public second-moment matrix for a better OLSE.
result Improved accuracy and robustness of OLSE in DP linear regression.
Paper proposes a new method for density estimation using squared Hellinger distance.
problem Density estimation using moment methods is sensitive to the choice of functions.
method Proposes a non-classical parametrization using squared Hellinger distance for density estimation.
result The proposed method does not require choosing functions and can be solved by convex optimization.
The paper analyzes the performance of empirical risk minimization for p-norm linear regression.
problem Empirical risk minimization on p-norm linear regression. method Analyzes performance under various conditions and moment assumptions.
result High probability excess risk bounds for empirical risk minimizer, matching asymptotic rates.
We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for sum-of-squares and related to the method of moments. Our focus is on sample complexity bo…
New algorithm for risk-sensitive reinforcement learning with natural policy gradients.
problem Risk-sensitive reinforcement learning with downside risk constraints.
method Introduce a new Bellman equation to estimate the lower partial moment of returns, use natural policy gradients, and extend Reward Constrained Policy Optimization.
result Sample-efficient estimation of partial moments and effective risk-sensitive control.