New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
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.
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…
The paper establishes a connection between minimal surfaces and a family of stationary surfaces via inversions.
problem The problem of finding minimal surfaces and their properties.
method Using inversions, the paper establishes a one-to-one correspondence between α-stationary surfaces and −(α+4)-stationary surfaces, focusing on −4-stationary surfaces which are minimal surfaces. result The paper solves the Börling problem and provides results of uniqueness for −4-stationary surfaces. In this work, we show an injectivity result and support theorems for integral moments of a m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of m-tensor field were first introduced by Sharafutdinov. At first we generalize a Helgason type support theorem proven by Krishnan and Stefanov in …
The paper uses moment matching method for pricing spread options under Lévy models.
problem Pricing spread options under Lévy models with mean-variance mixture.
method Moment matching method applied to Lévy models with mean-variance mixture.
result Obtains semi-closed form formulas for spread option prices.
DualAdam improves generalization of Adam by integrating its update mechanisms.
problem Adam's tendency to converge to sharp minima leading to suboptimal generalization.
method DualAdam combines Adam and inverse Adam's update mechanisms to enhance generalization.
result DualAdam outperforms Adam and state-of-the-art variants in generalization performance.
Research on random matrices and machine learning consistency.
problem Understanding consistency in machine learning and random matrix theory.
method Analytical and theoretical approaches to Laguerre matrices, Wishart matrices, and machine learning algorithms.
result Derived necessary and sufficient conditions for inverse moments of matrices and consistency of machine learning algorithms.
Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.
problem Slower convergence of ICA in high-dimensional data with high-order moments.
method High-dimensional ODE analysis of ICA algorithm under controlled moment structure.
result Critical learning rate threshold for effective ICA when moments are high.
Study nearly parallel G2-structures with torus symmetry using multi-moment maps.
problem Characterize and construct nearly parallel G2-structures with torus symmetry.
method Use multi-moment map techniques and analyze the geometry of the base spaces.
result Locally, the construction may produce examples with four-torus symmetry.
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.
Examining orbits ending in binary collisions for three equal masses under an inverse cube force.
problem Analyzing orbits ending in binary collisions for three equal masses under an inverse cube force.
method Reparametrizing orbits as geodesics on a negatively curved metric on a pair of pants.
result Visibility properties of negatively curved surfaces describe orbits beginning or ending in binary collisions.
New methods for Z-transform inversion and Wiener-Hopf factorization.
problem Efficient numerical inversion of Z-transforms and factorization of functions. method Sinh-deformations of contours, variable changes, and simplified trapezoid rule.
result High precision and speed in evaluating moments and constructing filters.
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.
The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
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.
Two classification results for stationary surfaces of least moment of inertia.
problem Classifying stationary surfaces in Euclidean space based on their energy.
method Analyzing ruled and foliated surfaces, using critical point theory.
result Classification of stationary surfaces including vector planes, elongated helicoids, and specific types of surfaces.
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian quasi-Poisson manifolds fit into this framework by constructing an ``inversion'' procedur…
DeepGMM tackles complex causal effects with high-dimensional instruments.
problem Estimating causal effects with complex, high-dimensional instruments and confounders.
method DeepGMM algorithm based on variational reformulation of GMM with optimal inverse-covariance weighting.
result DeepGMM efficiently controls many moment conditions and matches best tuned methods in standard settings.
Determinantal averaging corrects inversion bias in distributed Newton's method.
problem Inverting a sum of distributed matrices is biased; local averages are incorrect.
method Reweighting local estimates of the Newton's step proportionally to the determinant of the local Hessian estimate, then averaging them.
result Determinantal averaging provides the first known asymptotically consistent distributed Newton step.
Unified geometric approach to image reconstruction from incomplete data.
problem Reconstruction of hidden structures from incomplete data.
method Geometric decomposition of configuration spaces into invariant foliations and moment maps, combining Vaisman and Neifeld's insights.
result Noise-resistant framework for robust computational reconstruction in imaging and structural analysis.
In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails,…
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using the tree-reweighted approximation, we can optimize the rigorous lower bound of th…
Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution (Δ) becomes small. They include all correlations within the system of particles and represent integral characteristics of any correlation between these particles. In this letter, we sh…
We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinit…
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
problem Avoiding moment explosions and preserving stock price martingale property in stochastic volatility models.
method Introduces a one-factor stochastic volatility model with quadratic drift and a linear dispersion function, showing that the quadratic term is crucial.
result The model prevents moment explosions and preserves the martingale property of the stock price process.
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.
We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimat…
Extends Euler's problem to Lorentz-Minkowski plane.
problem Finding critical points of moment of inertia in Lorentz-Minkowski space.
method Explicit solutions for stationary curves, symmetries, inversions, and energy maximization.
result Explicit solutions for stationary spacelike and timelike curves, and methods to transform between them.
This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Under fairly general assumptions for the distribution of the total net assets of a set of firms we show that retaining the first few moments of the por…
Bias correction improves language model training performance.
problem Stochastic update bias in preconditioned optimizers.
method Cross-fitted preconditioning and variance-corrected inversion.
result Reduces held-out pretraining loss by 0.15 nats.
Study uses machine learning to optimize seismic design parameters.
problem Optimizing seismic design parameters for performance-based design.
method Implementing explainable machine learning models to map design variables and performance metrics, integrated into a genetic optimization algorithm.
result Highly accurate surrogate models (R2> 90%) across diverse building types and hazards, identifying optimal member properties.
Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator acting on smooth functions on (O,g) determines the moment polytope of O, and hence by Delzant's theorem det…
In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For …
New method improves robustness of neural network-based debiasing.
problem Improving robustness of neural network-based debiasing.
method Moment-constrained learning for neural networks.
result Improved performance compared to state-of-the-art benchmarks.
Efficient policy learning from observational data using weighted classification reductions.
problem Efficient policy evaluation does not necessarily lead to efficient estimation of policy parameters.
method Proposed an estimation approach based on generalized method of moments, efficient for policy parameters.
result Demonstrated empirical efficiency and regret benefits of a proposed method.
New method for adaptive estimation and inference in econometric models without knowing smoothness.
problem Adaptive estimation and inference in ill-posed linear inverse problems with unknown smoothness.
method Discrepancy principle-based framework for adaptive hyperparameter selection.
result Achieves optimal rates in weak and strong metrics for linear functionals.
Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…
Develops a multilevel Monte Carlo framework with dropout for efficient uncertainty quantification.
problem Efficiently quantify uncertainty in complex models using dropout.
method Integrates multilevel Monte Carlo with Monte Carlo dropout, creating coupled estimators to reduce variance.
result Demonstrates significant variance reduction and efficiency gains over single-level Monte Carlo dropout.
Paper introduces STSL, a second-order Tweedie sampler for efficient posterior sampling in inverse problems.
problem Computational challenges in sampling from posterior distributions using latent diffusion models.
method Introduces STSL, a novel second-order Tweedie sampler with tractable reverse process.
result STSL achieves 4X and 8X reduction in neural function evaluations compared to state-of-the-art solvers.
Predict cell loads in cellular networks using statistical learning of geometric marks.
problem Predicting cell loads in cellular networks using geometric marks.
method Statistical regression model and scattering moments of random measures.
result Scattering moments can capture similar geometry information as baseline approach and improve performance.
Invariants for surfaces up to rigid transformations, with a comeagre subset retrieval algorithm.
problem Identifying compact surfaces up to rigid transformations.
method Degree four polynomials in moments of delta function, effective inversion algorithm.
result Invariants and retrieval algorithm work on a comeagre subset of surfaces.
Unified approach for estimating quantiles of potential outcomes using inverse estimating equations.
problem Estimating quantiles of potential outcomes for causal inference.
method Inverse estimating equations and moment function.
result Unified approach to estimate mean and quantiles of potential outcomes.
FM4PDE learns PDE solutions from sparse data.
problem Reconstructing PDE solutions from limited observations.
method Flow-matching generative framework that learns PDE coefficients and solutions.
result Error guarantees for guided procedures, including deterministic and stochastic samplers.
Statistical inference for misspecified contextual bandits is challenging due to adaptivity issues.
problem Statistical inference for misspecified contextual bandits
method Inverse-probability-weighted Z-estimation framework
result Consistent and asymptotically normal estimator with sandwich variance estimator
Enhances reinforcement learning uncertainty estimation with a generalized Gaussian error model.
problem Inaccurate error representations and compromised uncertainty estimation in conventional uncertainty-aware TD learning.
method Introduces a novel framework for generalized Gaussian error modeling in deep reinforcement learning, incorporating higher-order moments, particularly kurtosis, to improve uncertainty estimation and mitigation.
result Significant performance gains in policy gradient algorithms with the proposed framework.
Study nearly Kähler 6-manifolds with 2-torus symmetry, proving geometric properties and constructing new manifolds.
problem Characterize nearly Kähler 6-manifolds with 2-torus symmetry.
method Use multi-moment map and Laplace operator eigenfunctions, analyze quotient geometry, and construct new manifolds.
result Prove T2-action is free on level sets and determine the geometry of quotients. Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced w…