Paper introduces a new fat-tail test using conditional second moments.
problem Measuring and assessing the impact of fat-tails on data dispersion.
method Constructs a goodness-of-fit statistic based on conditional second moments.
result Shows superior performance of the new test compared to existing methods.
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.
New adaptive stepsize method for stochastic approximation converges to target point.
problem Finding optimal step sizes for stochastic approximation algorithms.
method Adaptive block-coordinate stepsizes using online estimates of second moment.
result New method converges almost surely to a small neighborhood of the target point.
Proof of a simpler orthogonal double machine learning method.
problem Consistency and asymptotic normality of machine learning estimates.
method Alternative proof for Z-estimator in simpler setting.
result Orthogonal moments and consistency imply asymptotic normality.
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.
A new portfolio optimization method using the Sherman-Morrison identity.
problem Portfolio optimization with covariance and variance.
method Sherman-Morrison identity applied to replace covariance with second moment matrix.
result Sherman-Morrison-Markowitz portfolio solves standard portfolio optimization problems.
A new method for uncertainty estimation in neural networks using existing optimization steps.
problem Uncertainty quantification in deep neural networks.
method L2M: Practical posterior Laplace approximation with optimization-driven second moment estimation.
result L2M method yields reasonable results without requiring changes in models or extra computational steps.
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.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
We tackle causal inference under conditional moment restrictions using importance weighting.
problem Challenges in causal inference under conditional moment restrictions, especially in high-dimensional settings.
method Transform conditional moment restrictions to unconditional moment restrictions through importance weighting.
result Successfully estimate nonparametric functions defined under conditional moment restrictions.
JME continually estimates data moments privately and accurately.
problem Private and accurate continual estimation of data moments.
method Uses matrix mechanism and joint sensitivity analysis.
result Improves accuracy in estimating mean and covariance with reduced noise.
New method uses machine learning to improve statistical inference.
problem Performing inference on conditional functionals with scarce labeled data.
method Combines localization with prediction-based variance reduction.
result Valid and sharp confidence intervals for conditional functionals.
A new method for estimating causal parameters from observables reduces the need for finite moment conditions.
problem Estimating causal parameters from observational data with unknown or infinite moment conditions.
method Variational Method of Moments (VMM) for a general class of estimators, including kernel and neural net-based methods.
result VMM estimators are consistent, asymptotically normal, and semiparametrically efficient.
Study detects edge correlation between unlabeled random graphs.
problem Detect edge correlation between unlabeled random graphs.
method Hypothesis testing, conditional second-moment method, pseudoforest structure, enumeration of subpseudoforests.
result Sharp threshold for phase transition in testing error probability.
Article proves effective conditions for existence of Kähler metrics.
problem Existence of extremal Kähler metrics on fibrations.
method Weighted uniform K-stability conditions derived from moment polytopes.
result Various effective conditions for K-stability verified.
Develops a new method for estimating models with conditional moment restrictions.
problem Estimating models with conditional moment restrictions, especially non-parametric instrumental variable regression.
method Introduces a min-max criterion function to solve a zero-sum game between modeler and adversary, analyzing estimation rates for various hypothesis spaces.
result Shows that with regularization and rich test function spaces, estimation rates scale with the critical radius of hypothesis and test function spaces.
A new method of moments estimator goes beyond data reweighting.
problem Estimation of moment restrictions and conditional moment restrictions.
method Kernel Method of Moments (KMM) based on maximum mean discrepancy.
result KMM achieves competitive performance on conditional moment restriction tasks.
Paper proposes a novel spectral approach to learn binary latent variable models.
problem Learning binary latent variable models with hidden binary units in noisy data.
method Spectral approach based on eigenvectors of second and third order moment matrices.
result Consistently estimates model parameters at optimal rate under mild conditions.
We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a family of smooth densities and conditional densities by second order exponential mo…
The paper tackles matrix completion in ultra-sparse sampling, improving imputation accuracy.
problem Matrix completion in ultra-sparse sampling, where each row has only a few entries.
method Estimate row span of matrix or averaged second-moment matrix, normalize and impute missing entries.
result Gradient descent method normalizes and imputes missing entries, achieving low variance and unbiased estimation.
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. New method improves estimation of complex models from conditional moment restrictions.
problem Estimation of complex models from conditional moment restrictions.
method Functional Generalized Empirical Likelihood (GEL) with a practical method.
result The method achieves state-of-the-art performance on two problems.
New KCM tests improve specification testing via RKHS.
problem Improving specification tests for econometric models.
method Kernel conditional moment (KCM) tests based on RKHS.
result KCM tests have better finite-sample performance than existing tests.
DML-CMR estimator reduces bias in CMR problems using deep neural networks.
problem Solving conditional moment restrictions with deep neural networks.
method Double/debiased machine learning framework for unbiased estimation.
result Achieves minimax optimal convergence rate of O(N−1/2). Bayesian method reduces dimensions for small datasets.
problem Dimension reduction for small datasets with limited data.
method Bayesian approach using Gaussian process regression.
result Effective for small datasets, especially.
A method learns representations for conditional moment models with controlled ill-posedness.
problem Efficient estimation of nonparametric conditional moment models with flexible models is challenging.
method Proposes a procedure that learns spectral representations with controlled measures of ill-posedness.
result The proposed method can efficiently estimate representations from data and is L2 consistent.
Adversarial method learns deep models from conditional moment restrictions.
problem Learning deep neural net representations of models with conditional moment restrictions.
method Formulate as a zero-sum game between modeler and adversary, using adversarial training.
result Effective adversarial training methods, including k-means and random forests.
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.
Derives derivatives of risk measures for various types of portfolio losses.
problem Calculating precise risk measures for portfolio losses.
method Analyzes first and second order derivatives of risk measures for both continuous and discrete portfolio loss scenarios.
result Provides asymptotic results for conditional moments of heavy-tailed portfolio losses.
A new method calculates fractional moments using the moment-generating function.
problem Computing fractional moments from probability densities.
method Integral framework based on moment-generating function.
result Exact integral expressions for various types of moments.
Method estimates posterior model for boundary value problems with uncertain constraints.
problem Estimating posterior probability model for stochastic boundary value problems with uncertain constraints.
method Probabilistic learning inference using Kullback-Leibler divergence and MCMC.
result Method successfully estimates posterior probability measure with constraints.
Proposes a new method for big portfolio selection using graph-based conditional moments.
problem Challenges in selecting portfolios for thousands of stocks.
method Graph-based Conditional Moments (GRACE) method: learns quantiles, means, variances, skewness, and kurtosis of stock returns.
result Shows superior performance compared to competitors, especially in measures of conditional variance, skewness, and kurtosis.
New estimator tackles multi-task linear regression with outliers, avoiding eigenvalue lower bounds.
problem Multi-task linear regression with contaminated tasks and eigenvalue lower bounds failure.
method Matrix-weighted norm regularization and relative balancedness condition.
result Prediction MSE bounds match Duan and Wang (2023) under weaker spectral assumptions.
RAME adapts learning rates using recent first moment of gradients.
problem Training deep neural networks efficiently and adaptively.
method RAME computes individual learning rates using the most recent first moment of gradients.
result RAME outperforms SHB, Adam, and RMSprop in convergence speed and generalization performance.
Efficiently simulates SABR model with novel sampling methods.
problem Sampling integrated variance and terminal forward price in SABR model.
method Moment-matched shifted lognormal approximation for integrated variance, CEV approximation for terminal forward price.
result Enhanced simulation scheme is highly efficient, accurate, and reliable.
New optimizer Eve uses examplewise gradients for better second-moment estimates.
problem Improving optimization methods for machine learning.
method Adaptive optimization with examplewise gradients.
result Eve optimizer slightly outperforms Adam on small scale benchmarks.
Method learns moments for large implicit models, improving image generation quality.
problem Difficulty in defining and selecting moments for training large implicit models.
method Introduced moment network and used asymptotic theory to define and learn better moments.
result MoLM-trained generators outperform other methods in quality and diversity of generated images.
Corrected moment-based methods improve inference in topic model regression.
problem Inferential difficulties in topic model plug-in workflow for regression.
method Corrected spectral moment methods for LDA, response-weighted word moments.
result Direct identification of regression coefficients without estimating topic shares.
A new memory-efficient Adam variant reduces second moments when feasible.
problem Memory constraints in training machine learning models.
method Signal-to-Noise Ratio (SNR) analysis to identify dimensions where second moments can be replaced by means.
result Memory-efficient Adam variant (SlimAdam) matches performance and stability of Adam while saving up to 98% of second moments.
Paper relaxes symmetry conditions for universal feature selection in noisy data.
problem Feature selection in noisy data with weak symmetry.
method Developed a universal feature selection framework using singular value decomposition of canonical dependence matrix.
result Selected features achieve asymptotically optimal error exponents up to a residual term.
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
Independent component analysis (ICA) is the problem of efficiently recovering a matrix A∈Rn×n from i.i.d. observations of X=AS where S∈Rn is a random vector with mutually independent coordinates. This problem has been intensively studied, but all existing efficient algorithms w…
The paper defines useful model simplifications and calibration methods for predictive uncertainty.
problem Quantifying predictive uncertainty in models that simplify data and predictions.
method Defines conditions for useful model simplifications and calibration schemes.
result Conditions for when simplified models can be used and when they should be ignored.
Huber regression assessed for robustness in statistical learning.
problem Understanding Huber regression in nonparametric statistical learning.
method Assessment from statistical learning perspective, focusing on risk consistency, adaptive tuning, and convergence rates.
result Huber regression can be asymptotically mean regression calibrated under (1+ε)-moment conditions, justifying its robustness. Generalizes moment-matching for exponential families with conditioning or hidden data.
problem Generalizing moment-matching conditions for exponential families with conditioning or hidden data.
method First-principles explanation and self-contained derivation of generalized moment-matching conditions.
result Derives generalized moment-matching conditions for conditional exponential families and hidden data.
New topic modeling method scales to large datasets.
problem Large-scale topic modeling with high co-occurrence data.
method Introduced Full Dependence Mixture (FDM) model for direct topic learning.
result FDM model performs comparably or better than benchmarks on large datasets.
Adafactor optimizes neural networks with less memory and similar performance.
problem Memory constraints in adaptive optimization methods.
method Adafactor uses row and column sums of moving averages to estimate per-parameter second moments, reducing memory usage.
result Adafactor achieves similar performance to Adam with minimal auxiliary storage.
Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each step, which is a simple multiplication between the inverse of the we…