Dual moments replace primal moments for measuring risk aversion.
problem Traditional risk aversion measures using mean and variance are insufficient in non-EU models.
method Introduced dual moments as a new measure for absolute risk aversion.
result Dual moments provide an equivalent index of absolute risk aversion in non-EU models.
Moment polytope of toric exponential families is a projection of a simplex.
problem Understanding the geometry of exponential families in finite sample spaces.
method Toric torification and projection of higher-dimensional simplices.
result Moment polytope is a projection of a higher-dimensional simplex.
Expands newsvendor model with moment constraints using Wasserstein distance.
problem Optimizing order quantity under distributional ambiguity.
method Formulates infinite dimensional primal problem, derives finite dimensional dual problem using problem of moments duality.
result Distributional ambiguity affects optimal order quantity and profits/costs.
We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg symplectic cross-section theorem and of convexity properties of the moment map. …
Study moment maps coupled with convex functions to find critical points.
problem Understanding critical points of moment maps coupled with convex functions.
method Develop a theory of moment maps coupled with an Ad_K-invariant convex function f on k*.
result Interpret Kähler-Ricci solitons as a special case of generalized extremal metrics.
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 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.
A dual pair is constructed for contact groups, linking submanifolds and orbits.
problem Understanding the geometry of contact manifolds and their diffeomorphisms.
method Constructing an infinite-dimensional non-linear Stiefel manifold with a symplectic structure, and using equivariant moment maps.
result An EPContact dual pair is established, providing a geometric description of coadjoint orbits and solutions to geodesic equations.
The article provides formulas for the number of terms in connected sums of sphere products associated with dual-neighborly polytopes.
problem Understanding the number of terms in the connected sums of sphere products associated with dual-neighborly polytopes.
method Combinatorial operations and formulas for the number of terms in the connected sums of sphere products.
result Formulas for the number of terms in the connected sums of sphere products associated with dual-neighborly polytopes.
New formulas for geometric measures in vector spaces.
problem Local additive kinematic formulas for vector spaces.
method Introducing dual area measures and proving their convolution product.
result Local additive kinematic formulas in hermitian vector spaces.
A theorem of E.Lerman and S.Tolman, generalizing a result of T.Delzant, states that compact symplectic toric orbifolds are classified by their moment polytopes, together with a positive integer label attached to each of their facets. In this paper we use this result, and the existence of "global" action-angle coordinat…
In [29], Plebanski reformulated the anti-self-dual Einstein equations with non-zero scalar curvature as a first order PDE for a connection in an SO(3)-bundle over the four-manifold. The aim of this article is to place this differential equation in a new framework, in which it is both elliptic and a stationary point of …
Polynomial processes in Banach spaces via infinitesimal generator and ODEs.
problem Modeling polynomial processes in infinite-dimensional spaces.
method Infinitesimal generator, martingale problem, ODE representations of moments.
result Moment formulas for polynomial processes in Banach spaces.
Let G¶ be a compact simple Poisson-Lie group equipped with a Poisson structure ¶ and (M,ø) be a symplectic manifold. Assume that M carries a Poisson action of G¶ and there is an equivariant moment map in the sense of Lu and Weinstein which acts to the dual Poisson-Lie group G¶∗, $\m: M\rightarrow G^*_¶…
A new method for neural networks adapts to different domains without labeled data.
problem Adapting neural networks to new domains without labeled data.
method Metric-based regularization to maximize similarity of domain-specific activation distributions by aligning moments.
result The method achieves higher classification accuracies than existing approaches.
Analogous to 4D, new Ansatz for quaternionic Kähler spaces with a free action.
problem Describing the geometry of quaternionic Kähler spaces with a free action.
method Gibbons-Hawking-like Ansatz based on quaternionic Kähler moment map.
result Explicit equivariant completion of twistor space construction.
A new algorithm uses IVs to learn optimal policies from observational data.
problem Learning optimal policies from unobserved variable confounded data.
method IV-aided Value Iteration (IVVI) algorithm based on conditional moment restrictions.
result First provably efficient algorithm for instrument-aided offline RL.
The paper examines the failure of Brunn-Minkowski inequality for certain convex bodies.
problem Brunn-Minkowski inequality for q-th dual quermassintegrals with q>n. method Second variation argument, dimension reduction, Hadwiger's inequality, singular weighted Reilly formula, coordinate-slice Hardy inequality.
result Established the inequality for unconditional convex bodies in the full range 0<q≤n+1. New method finds closest martingale to Brownian motion.
problem Finding optimal martingale interpolating marginals.
method Martingale Sinkhorn algorithm, iterative scheme.
result Algorithm yields Bass potential in arbitrary dimension.
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.
Extending a result of He to the non-integrable case of K-contact manifolds, it is shown that transverse Hermitian scalar curvature may be interpreted as a moment map for the strict contactomorphism group. As a consequence, we may generalize the Sasaki-Futaki invariant to K-contact geometry and establish a number of ele…
In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with a polyhedral norm, its horofunction compactification is homeomorphic to the dual u…
A2-SBNN models spatial data with copulas for non-Gaussian dependencies.
problem Capturing complex spatial relationships and extreme dependencies in non-Gaussian data.
method Embedding A2 copula into a Bayesian neural network, trained with Wasserstein loss and moment matching.
result A2-SBNN consistently delivers high accuracy across various dependency strengths.
Paper introduces Lambda EVaR, a new risk measure.
problem Risk management, especially in finance.
method Lambda extension of Rényi entropic value-at-risk (Λ-EVaR). Defines properties and provides axiomatic characterization.
result Λ-EVaR bridges adaptive risk tolerance and moment-sensitive risk assessment.
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.
SRL embeds combinatorial optimization into RL for better decision-making.
problem Challenges of standard RL in complex, structured decision-making problems.
method Structured Reinforcement Learning (SRL) with combinatorial optimization layers in actor neural network.
result SRL outperforms unstructured RL and imitation learning by up to 92% on dynamic problems.
This paper analyzes M-estimators under infinite-variance noise in high dimensions.
problem High-dimensional M-estimation with infinite-variance noise.
method Study of the Fenchel conjugate domain and its impact on risk.
result Exact risk of M-estimators under infinite-variance noise is derived.
This work tackles resource allocation in asynchronous and stochastic systems.
problem Distributed resource allocation in asynchronous and stochastic settings.
method Approximate stochastic primal-dual approach with asynchronous updates.
result The Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm converges to the saddle point solution at a rate of O(1/t). Kernel DRO uses RKHS to optimize under distributional uncertainty.
problem Optimizing under distributional uncertainty with limited knowledge.
method Kernel DRO using RKHS ambiguity sets and duality theory.
result Unified approach to robust and stochastic optimization.
A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of the direct sum of V with its dual. We show how to associate to any Dirac structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of C*-algebras with typical fiber the compact operators on a Hilbert space. The construction has good f…
Study explores geometric structure and prior for beta-logistic distribution.
problem Understanding the geometric structure and prior distributions of the beta-logistic distribution.
method Exploring dual geometric structure and uncovering α-parallel prior. result The beta-logistic distribution admits an α-parallel prior for any real number α. New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.
problem Challenges in generative modeling on convex domains with heavy-tailed targets.
method Mirror Flow Matching with regularized mirror maps and Student-t priors.
result Empirically outperforms baselines and achieves competitive sample quality.
Study robust utility maximization with uncertain endowments.
problem Optimal strategy under nondominated model uncertainty.
method General representation result, Choquet's capacitability theorem, medial limits.
result Existence of optimal strategy and dual representation for optimal utility.
New algorithm samples constrained distributions efficiently.
problem Sampling from distributions with statistical constraints.
method Primal-dual Langevin Monte Carlo (PD-LMC) using gradient descent-ascent dynamics.
result PD-LMC algorithm successfully samples constrained distributions.
DeepMartingale uses deep learning to solve complex optimal stopping problems efficiently.
problem Optimal stopping problems in high-dimensional continuous-time models.
method Leverages martingale representation and deep learning to directly optimize over parameterized martingales.
result DeepMartingale can approximate the true value function to any desired accuracy with neural networks of manageable size.
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-li…
Framework approximates 2-Wasserstein distance for GANs training.
problem Training GANs with improved metrics and analysis.
method Approximates 2-Wasserstein distance via restricted convex potentials.
result Improved training for GANs with moment-matching property.
Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
problem Optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
method Martingale optimal principle and quadratic BSDEs with exponential moment.
result Establishes optimal strategies for consumption and investment.
Let U(n) be the unitary group, and u(n)∗ the dual of its Lie algebra, equipped with the Kirillov Poisson structure. In their 1983 paper, Guillemin-Sternberg introduced a densely defined Hamiltonian action of a torus of dimension (n−1)n/2 on u(n)∗, with moment map given by the Gelfand-Zeitlin coordinates. A few …
We find the exact worst-case tail probability for bounded kurtosis.
problem Determining the worst-case tail probability under bounded kurtosis constraints.
method AI-guided search and certificate verification around the certifying pipeline.
result A four-regime map of tail probabilities with explicit formulas and dual certificates.
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…
Analyzes GJR-GARCH moments for efficient predictive distributions.
problem Estimating moments of GARCH processes for accurate predictions.
method Derives analytic expressions for GJR-GARCH moments and their limits.
result Analytic moments provide excellent approximate predictive distributions.
Maps asymptotically embed conic transforms from circle bundles.
problem Embedding conic transforms from circle bundles.
method Asymptotic embeddings using equivariant Szegő projectors.
result Maps embed conic transforms from circle bundles.
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.
Study compares weak and homotopy moment maps in multisymplectic geometry.
problem Existence and equivariance of moment maps in multisymplectic geometry.
method Comparison of weak and homotopy moment maps.
result Analysis of existence and equivariance phenomena.
The paper applies Fisher-Rao geometry to beta distributions for moment analysis.
problem Comparing and analyzing moments of probability distributions.
method Derived geodesic equations and sectional curvature on beta distributions' parameter space. Used Fisher-Rao geometry to map canonical moments to beta distributions.
result Uniqueness of Riemannian centroid in beta distributions' parameter space.
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.
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.