Abstract: A possibilistic portfolio choice problem using expected utility operators.
problem A possibilistic portfolio choice problem in the framework of expected utility operators.
method Using expected utility operators, the paper formulates a possibilistic choice problem and derives two approximate calculation formulas for optimization.
result Two approximate calculation formulas for optimization of possibilistic portfolio choice problem.
In this paper two portfolio choice models are studied: a purely possibilistic model, in which the return of a risky asset is a fuzzy number, and a mixed model in which a probabilistic background risk is added. For the two models an approximate formula of the optimal allocation is computed, with respect to the possibili…
Paper compares two possibilistic segmentation methods for SAS imagery.
problem Segmenting synthetic aperture sonar images into different seafloor environments.
method Comparison of Possibilistic Fuzzy Local Information C-Means (PFLICM) and Possibilistic K-Nearest Neighbors (PKNN) algorithms.
result PKNN outperforms PFLICM in segmentation performance on SAS images.
Develops possibilistic VI using maxitive Donsker-Varadhan formulation.
problem Adapting VI to possibilistic framework to handle uncertainty.
method Maxitive Donsker-Varadhan formulation for possibilistic VI.
result CBOpt optimizers achieve competitive performance in image classification.
New validity index for fuzzy-possibilistic c-means clustering.
problem Conflicting results in determining the optimal number of clusters due to noisy data points and outliers.
method Introducing a new validity index (FP index) for fuzzy-possibilistic c-means clustering.
result FP index works well in datasets with varying cluster shapes and densities.
This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, object's membership values should sum to 1. Hence, any object may obtain full membership in at most one cluster. Possibilistic clustering…
BFPM improves machine learning accuracy by considering object types and memberships flexibly.
problem Inaccurate learning due to missing important parameters.
method BFPM relaxes fuzzy and possibilistic constraints, allowing arbitrary object memberships and movement analysis.
result BFPM enhances object movement analysis and provides flexible search space.
In the study of investment problem, aside from the investment risk the background risk appears. Both the investment risk and the background risk are probabilistically described by random variables. This paper starts from the hypothesis that the two types of risk can be represented both probabilistically (by random vari…
This paper proposes two mixed models to study a consumer's optimal saving in the presence of two types of risk.
Categorical d-separation criterion simplifies probability graph analysis.
problem Detecting causal relationships in probability distributions.
method Introducing categorical definitions for causal models and d-separation.
result Abstract version of d-separation criterion applies to various probability theories.
This paper solves a coinsurance problem using fuzzy numbers and expected utility operators.
problem Formulating a coinsurance problem in the possibilistic setting of expected utility operators.
method Developed a framework using expected utility operators to model risk aversion and solve the coinsurance problem.
result Various formulas for the optimal T-coinsurance rate are derived for specific utility functions and fuzzy numbers. We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain classifiers that optimize the cross-entropy function. In the possibilistic framework, we …
A new method combines classifiers using possibility distributions and adaptive t-norms.
problem Aggregating predictions from multiple classifiers trained on overlapping datasets.
method Proposes a new approach to aggregate classifier predictions using possibility theory and adaptive t-norms.
result Proves the proposed approach possesses desirable robustness properties.
In this paper, we take a new look at the possibilistic c-means (PCM) and adaptive PCM (APCM) clustering algorithms from the perspective of uncertainty. This new perspective offers us insights into the clustering process, and also provides us greater degree of flexibility. We analyze the clustering behavior of PCM-based…
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.
For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time hori…
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.
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.
Enhanced Adam uses higher-order moments for better performance.
problem Improving the performance of Adam optimization algorithm.
method Proposes HAdam, an extension of Adam using higher-order moments of the stochastic gradient.
result Higher-order moments of the stochastic gradient can lead to better performance than vanilla Adam.
Developed moment estimators for affine stochastic volatility models.
problem Estimating parameters of affine stochastic volatility models.
method Introduced recursive equations for moments and proposed moment estimators.
result Established a central limit theorem and derived asymptotic covariance matrix.
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.
Stiefel-Whitney classes of moment-angle manifolds are trivial.
problem Analyzing the topological properties of moment-angle manifolds.
method Proving triviality of Stiefel-Whitney classes for moment-angle manifolds, including partial quotients.
result Stiefel-Whitney classes of moment-angle manifolds are trivial.
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.
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.
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.
Constructs a moment map flow for isotropic maps on surfaces.
problem Understanding isotropic maps on surfaces and their properties.
method Develops a Kähler moment map geometry and a modified moment map flow.
result Polyhedral modified moment map flow induces a strong deformation retraction.
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.
Moment Pooling reduces latent space dimensions in machine learning models.
problem High-dimensional latent spaces in machine learning models are hard to interpret.
method Moment Pooling extends Deep Sets networks to arbitrary multivariate moments.
result Latent dimensions as small as 1 can achieve similar performance to higher dimensions.
Deformation quantization yields a new moment map on symplectic diffeomorphisms.
problem Formalizing moment maps on diffeomorphism groups of symplectic manifolds.
method Deformation quantization framework applied to extrmDiff0(M). result Obtained a deformation of the Donaldson moment map.
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. We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specif…
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use …
Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.
problem Uniqueness of smooth structures on real moment-angle manifolds.
method Arguments from calculus applied to results from complex moment-angle manifolds.
result Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.
Deform quantization recovers scalar curvature in complex structures.
problem Recovering scalar curvature in complex structures.
method Formal moment map construction on almost complex structures.
result Formal moment map deforms scalar curvature moment map in integrable cases.
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.
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.
Paper reviews and proves the uniqueness of multipole moments for stationary spacetimes.
problem Characterizing the gravitational field in stationary spacetimes.
method Geroch's asymptotic flatness definition and one-point conformal completion.
result Revised uniqueness result for multipole moments in stationary spacetimes.
Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variet…
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.
We introduce features for massive data streams. These stream features can be thought of as "ordered moments" and generalize stream sketches from "moments of order one" to "ordered moments of arbitrary order". In analogy to classic moments, they have theoretical guarantees such as universality that are important for lea…
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.
Extends moment map concept to locally conformally Kähler manifolds.
problem No specific problem stated; extends existing concept.
method Extends classical moment map interpretation to locally conformally Kähler geometry.
result Scalar curvature as moment map in locally conformally Kähler geometry.
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.
Investigates properties of moment maps and stratifications on Lie groups.
problem Understanding moment maps and stratifications on real reductive Lie groups.
method Functorial, algebraic approach to moment map and Kirwan-Ness stratification.
result Properties and properties of moment maps and stratifications established.
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.