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.
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 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.
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.
We consider a stochastic volatility model where the moment generating function of the logarithmic price is finite only on part of the real line. Using a new Tauberian result obtained in [1] and [2], we show that the knowledge of the moment generating function near its critical moment gives a sharp asymptotic expansion …
New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
In this paper we will study the statistics of the unit geodesic flow normal to the boundary of a hyperbolic manifold with non-empty totally geodesic boundary. Viewing the time it takes this flow to hit the boundary as a random variable, we derive a formula for its moments in terms of the orthospectrum. The first moment…
In this paper, we consider generalized moment maps for Hamiltonian actions on H-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness properties for generalized moment maps. We study Hamiltonian torus actions on compact H…
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.
The paper analyzes distances and volumes in lens spaces using recursion and formulas.
problem The problem of moments for distances between points on lens spaces.
method Derivation of recursion relations, formulas for moments and moment generating function, explicit formula for ball volumes.
result Explicit formulas for the volume of balls of all radii in lens spaces.
The paper derives formulas for moments of a Student t distribution and applies them to quantify Lp-quantiles.
problem Understanding the moments and quantiles of a Student t distribution.
method Developed formulas for partial and complete moments, and derived relationships between Lp-quantiles. result For a Student t distribution, the Ln−j+1-quantile and Lj-quantile coincide at any confidence level. New method unfolds distribution moments directly from data without binning.
problem Deconvolving detector distortions in particle physics.
method Uses machine learning, inspired by GANs, to unfold moments directly.
result More precise than bin-based approaches and comparable to unbinned methods.
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.
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.
We provide an approach for learning deep neural net representations of models described via conditional moment restrictions. Conditional moment restrictions are widely used, as they are the language by which social scientists describe the assumptions they make to enable causal inference. We formulate the problem of est…
Paper develops methods for inference on time series data using neural networks and sieves.
problem Inference on time series data with nonparametric conditional moment restrictions.
method GN-QLR based inference using general nonlinear sieves and multilayer neural networks.
result Optimally weighted GN-QLR statistic is asymptotically Chi-square distributed.
Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.
problem Time-inconsistent stochastic control problems with mean and higher-order moments.
method Developed closed-loop and open-loop Nash equilibrium controls using PDEs and maximum principles.
result Identical closed-loop and open-loop Nash equilibria controls, independent of state value and random path.
Q-MMR evaluates policies using reweighted rewards and moment matching.
problem Off-policy evaluation in finite-horizon MDPs.
method Q-MMR learns scalar weights for data points via a moment matching objective against a value-function discriminator class.
result Data-dependent finite-sample guarantee with a dimension-free error bound.
Develops efficient algorithms for learning latent-variable models using implicit moment tensor computation.
problem Learning latent-variable models with moment tensors of super-constant degree.
method Implicit moment tensor computation for general models, extending previous work on clustering mixtures of spherical Gaussians.
result First poly(d, k) time learning algorithms for various models including mixtures of linear regressions, spherical Gaussians, and positive linear combinations of non-linear activations.
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat's proof is an adaptation of Lojasiewicz's argument for analytic functions to functions which ar…
New SGMM algorithm for efficient estimation of moment restriction models.
problem Estimation and inference on overidentified moment restriction models.
method Stochastic Approximation to Generalized Method of Moments (SGMM).
result SGMM offers fast and scalable implementation with streaming dataset handling.
In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function) by matching moments of increasing order. Because, as shown in literature, the pri…
Method estimates observation functions in state-space models without supervision.
problem Unsupervised learning of non-invertible observation functions in nonlinear state-space models.
method Nonparametric generalized moment method using constrained regression.
result Estimates function space of identifiability from state process.
Framework generates causal probabilities from observational data.
problem Generating causal probabilities from observational data.
method Moment-matching graph-networks for causal inference.
result Automated sampling of latent space conditional probability distributions.
This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we es…
Sharp comparison for sub-Gaussian random variables in convex order.
problem Comparing sub-Gaussian random variables in convex order.
method Proving dominance using moment generating functions and convex functions.
result Sharp comparison established between specific sub-Gaussian random variables.
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.
Sharp inequalities in unit ball with constraints on moments.
problem Establishing Sobolev trace inequalities with constraints.
method Constructing smooth test functions for higher order moments.
result Almost optimal Sobolev trace inequalities for 2nd and 4th orders.
In this paper we consider finite volume hyperbolic manifolds X with non-empty totally geodesic boundary. We consider the distribution of the times for the geodesic flow to hit the boundary and derive a formula for the moments of the associated random variable in terms of the orthospectrum. We show that the the first tw…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu f…
New real algebraic maps with prescribed images and compositions are constructed locally like moment maps.
problem Constructing real algebraic maps with specific properties and compositions.
method Explicit construction of real algebraic hypersurfaces and maps with prescribed images and compositions.
result Explicit families of functions represented as compositions of constructed maps with canonical projections.
Introduces generalized moment maps for almost Hermitian settings.
problem Extending classical moment map theory to almost Hermitian settings.
method Introduces momentumly closed forms and proves a variant of the Darboux-Weinstein theorem.
result Establishes convexity property and constructs reduction space for generalized moment maps.
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a give…
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncor…
Study on quadratic L-functions using hyperelliptic curves and homology.
problem Understanding moments of families of quadratic L-functions.
method Homological stability theorem and computations of homology.
result Confirmations of Conrey-Farmer-Keating-Rubinstein-Snaith predictions for large prime powers.
Let Phi : M --> g^* be a proper moment map associated to an action of a compact connected Lie group, G, on a connected symplectic manifold, (M,ω). A collective function is a pullback via Φof a smooth function on g^*. In this paper we present four new results about the relationship between the collective functions and t…
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…
The paper introduces new equations in Kähler geometry and proves their solutions and convexity.
problem Solving equations in Kähler geometry and understanding their geometric implications.
method Using moment map pictures to motivate and prove solutions for the equations.
result The Mabuchi functional for certain equations is shown to be convex.
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.
This study shows the moment-SOS hierarchy converges in polynomial optimization over product of spheres.
problem Minimizing multihomogeneous polynomials over product of spheres.
method Moment-SOS hierarchy, local optimality conditions, differential geometry, Morse theory.
result The moment-SOS hierarchy has finite convergence for generic multihomogeneous objective functions.
A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.
problem Nonlinear Bayesian filtering challenges in representing belief distributions.
method Combines score matching with Stein's identity to avoid partition function evaluation.
result The Score Kalman Filter (SKF) outperforms existing methods on nonlinear systems.
Proposes Moment Exchange to use moments in image recognition models, improving generalization.
problem Discarding moments in image recognition models reduces stability and training time.
method Moment Exchange: replaces moments of learned features with another image's moments and interpolates labels.
result Improves generalization of recognition models across multiple datasets.
The asymptotic behavior of the implied volatility associated with a general call pricing function has been extensively studied in the last decade. The main topics discussed in this paper are Lee's moment formulas for the implied volatility, and Piterbarg's conjecture, describing how the implied volatility behaves in th…
The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …
Classifies domains critical for heat content and exit-time moments.
problem Understanding critical domains for heat content and exit-time moments.
method First variation of heat content, constant flow property, isoparametric foliation.
result Domains critical for heat content at all times have constant flow property and isoparametric foliation.
The author studies regions foliated by 1D families of functions and their applications.
problem Understanding regions represented as foliated forms and natural smooth maps onto them.
method Investigates natural smooth maps respecting canonical projections and moment maps, focusing on foliated regions.
result Discusses the 1st derivative of functions and critical sets in foliated regions.
Study finds critical points of volume functionals on Sasaki manifolds.
problem Finding Kähler-Einstein metrics on Sasaki manifolds.
method Revisited moment polytopes, applied to volume minimization.
result Transverse coupled Kähler-Einstein metrics found as critical points.