Efficient EP algorithm improves smoothing distribution inference in financial models.
problem Computational intractability of smoothing distribution in high dimensions.
method Adapted expectation propagation (EP) algorithms for the unified skew-normal family.
result Accuracy gains in financial illustrations over existing approximate algorithms.
Optimizes recommendation models using skew normal distribution.
problem Improving personalized recommendation systems.
method Develops a new optimization criterion based on skew normal distribution.
result Significantly outperforms state-of-the-art models.
The paper improves asset allocation using a skew-normal distribution in the Black-Litterman model.
problem Improving asset allocation under skewed return distributions.
method Using the Black-Litterman model with hidden truncation skew-normal distribution and Simaan's three-moment risk model.
result Optimal portfolios have less risk and higher skewness compared to classical BL model.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard …
SkewPNN uses probabilistic neural networks with skew-normal kernels to improve classification of imbalanced data.
problem Imbalanced data distribution leading to biased predictions for minority classes.
method Probabilistic neural networks with skew-normal kernel function and Bat optimization algorithm for hyperparameter tuning.
result SkewPNN and BA-SkewPNN outperform other methods in both balanced and imbalanced datasets.
Researchers develop a new spatial process model for non-Gaussian data.
problem Non-Gaussian spatial data with asymmetry and heavy-tailedness.
method Re-parameterized Unified Skew-Normal (SUN) distribution, GSUN process, neural Bayes inference with GATs.
result GSUN process captures non-Gaussian spatial data properties and outperforms conventional models.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
EP method speeds up Bayesian probit regression in high dimensions.
problem Computational challenges in high-dimensional Bayesian probit regression.
method Adapting EP approximation to multivariate Gaussian prior and skew-normal distribution.
result EP routine is computationally feasible in high-dimensional settings.
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution.…
We characterize convolutional neural networks with respect to the relative amount of features per layer. Using a skew normal distribution as a parametrized framework, we investigate the common assumption of monotonously increasing feature-counts with higher layers of architecture designs. Our evaluation on models with …
The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.
problem Examining skewness and kurtosis measures for skew-elliptical distributions.
method Deriving exact expressions for skewness and kurtosis measures for skew-elliptical distributions, constructing test statistics, and comparing measures through simulations and real data analysis.
result Exact expressions and test statistics for skewness and kurtosis measures for various skew-elliptical distributions.
SkewD robustly discovers causal relationships in skewed noise models.
problem Distinguishing cause from effect in skewed noise models.
method SkewD extends normal-distribution framework to skew-normal setting for reliable inference.
result SkewD remains robust under high skewness, improving reliability.
New conjugate priors improve Bayesian inference for multinomial probit models.
problem Lack of tractable conjugate priors for efficient Bayesian inference in multinomial probit models.
method Unified skew-normal (SUN) distributions as conjugate priors, leading to improved posterior inference and classification.
result Improved computational methods for posterior inference and classification, especially in high dimensions.
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
In Divide & Recombine (D&R), big data are divided into subsets, each analytic method is applied to subsets, and the outputs are recombined. This enables deep analysis and practical computational performance. An innovate D\&R procedure is proposed to compute likelihood functions of data-model (DM) parameters for big dat…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability, which extends from the previous work of Nguyen [2013] and Chen [1995] to address…
A new method tracks market performance without active management.
problem Active portfolio management does not outperform benchmarks.
method Developed a hybrid PCA-based tracking portfolio strategy.
result The hybrid PCA strategy outperforms optimization-based approaches.
As all physical adaptive quantum-enhanced metrology schemes operate under noisy conditions with only partially understood noise characteristics, so a practical control policy must be robust even for unknown noise. We aim to devise a test to evaluate the robustness of AQEM policies and assess the resource used by the po…
Paper develops Bayesian inference for discrete-choice mnp models with Gaussian priors.
problem Estimating parameters of discrete-choice multinomial probit models with Gaussian priors.
method Adapts Fasano and Durante's results to a specific mnp model with zero mean and independent Gaussian priors, simplifying posterior distribution parameters and providing a new variational algorithm.
result Simplified expressions for posterior distribution parameters and a novel variational algorithm.
Recent studies identified that sequential Recommendation is improved by the attention mechanism. By following this development, we propose Relation-Aware Kernelized Self-Attention (RKSA) adopting a self-attention mechanism of the Transformer with augmentation of a probabilistic model. The original self-attention of Tra…
A new approach for pricing FX options that uses a single model for all markets.
problem Consistent pricing of FX options across different markets.
method Intermediate currency approach, calibrating to domestic market volatility smile.
result Model automatically reproduces correct foreign market volatility smiles.
Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood estimator and standard Bayesian procedures do not admit the root-n parametric rate…
Unified Skew-Gaussian process framework for various regression and classification tasks.
problem Handling multiple types of regression and classification problems.
method Generalization of Skew-Gaussian processes to handle various types of data and likelihoods.
result Closed-form posterior distributions for multiple tasks.
Face recall is a basic human cognitive process performed routinely, e.g., when meeting someone and determining if we have met that person before. Assisting a subject during face recall by suggesting candidate faces can be challenging. One of the reasons is that the search space - the face space - is quite large and lac…
Skew Gaussian Processes improve classification performance by allowing asymmetry.
problem Limited use of Gaussian processes in applications requiring asymmetry.
method Propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions, extending the multivariate Unified Skew-Normal distribution to stochastic processes.
result SkewGPs provide better performance than symmetric Gaussian processes in classification tasks.
Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification and clustering. For continuous data which we consider here in the context of regression and cluster analysis, MoE usually use normal experts, that is, expert components following the Gaussian distribution. …
Bayesian framework predicts post-disruption travel times in metro networks.
problem Uncertainty in post-disruption travel times in metro networks.
method Bayesian spatiotemporal modeling framework capturing train interactions and non-Gaussian distributional characteristics.
result The proposed models consistently outperform baseline specifications in point prediction and uncertainty quantification.
The Mean-Variance Criterion is equivalent to Second-order Stochastic Dominance under symmetric Elliptical distributions.
problem Determining the equivalence of Mean-Variance Criterion and Stochastic Dominance Criteria.
method Analyzing under symmetric and Skew-Elliptical distributions using Monte Carlo simulations.
result The Mean-Variance Criterion does not coincide with Second-order Stochastic Dominance for some types of risk-averse investors.
Constructs families of Toeplitz operators for symplectic fibrations.
problem Quantization of symplectic fibrations.
method Smooth families of Szegö projections and Toeplitz operators.
result Deformation quantization of prequantizable symplectic fibrations.
In the paper we formulate and derive the family blowup formula of family Seiberg-Witten invariants. The formula has been used in the enumerative application of counting singular curves on algebraic surfaces. We first give a topological derivation of the formula by using family index theorem. Then we define the algebrai…
Proves an equivariant version of index theorem for geometric families.
problem Index theorem for geometric families with group action.
method Apply equivariance --> families principle to Clifford module bundles.
result Equivariant version of Bismut's families index theorem.
Squared families are a new model class derived from linear transformations, offering convenient properties and universal approximation.
problem Developing a new class of probability models that are easier to handle and have useful properties.
method Introducing squared families as families of probability densities obtained by squaring a linear transformation of a statistic, and showing their properties and applications.
result Squared families have convenient properties and can approximate target densities well.
Smooth families of biholomorphisms between strongly pseudoconvex domains are shown to be smooth.
problem Smoothness of families of biholomorphisms between strongly pseudoconvex domains.
method Riemannian geometry of Bergman metrics and smoothness of families of isometries.
result Smoothness of families of biholomorphisms between strongly pseudoconvex domains.
Computes Seiberg-Witten invariants for Kähler families of 4-manifolds.
problem Computing invariants for families of Kähler 4-manifolds.
method Generalized Seiberg-Witten invariants for smooth families of 4-manifolds with Kähler structures.
result Computed invariants for specific Kähler families in terms of characteristic classes.
We investigate families of Legendrian submanifolds of 1-jet spaces by developing and applying a theory of families of generating family homologies. This theory allows us to detect an infinite family of loops of Legendrian n-spheres embedded in the standard contact (2n+1)-space (for n>1) that are contractible in the smo…
Study families of flat connections with nilpotent Higgs fields, showing similar monodromy to regular Higgs bundles.
problem Investigate Cimes-families of flat connections with nilpotent Higgs fields. method Analyze families of flat connections including real twistor lines and conformal limits, deducing monodromy similarities.
result Traces of holonomies are asymptotically exponential in rational powers of the parameter of the family.
Tangential families are 1-parameter families of rays emanating tangentially from smooth curves. We classify tangential family germs up to Left-Right equivalence: we prove that there are two infinite series and four sporadic simple singularities of tangential family germs (in addition to two stable singularities). We gi…
Study families of Morse functions for manifolds with boundary.
problem Characterize degeneracies in 1-parameter families of Morse functions.
method List all possible degeneracies in generic 1-parameter families.
result Identified all degeneracies in generic 1-parameter families.
We consider the local analytic behavior for a family of holomorphic differentials on a family of degenerating annuli. Three results and discussion are presented. The first is the normal families Lemma 1. The second is an isomorphism of sheaves, formula (3), giving a direct description of families of regular k-differe…
Extends width estimates to family case using index theory.
problem Sharp width estimates for Riemannian bands with positive scalar curvature.
method Dirac operators and family index theory.
result Proves width estimate for fiber bundles with infinite A-hat area.
Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the second. Typically, an i-dimensional family and a j-dimensional family will produce …
Paper introduces kernel deformed exponential families for sparse continuous attention.
problem Creating efficient attention mechanisms for sparse data.
method Developed kernel deformed exponential families, theoretically and experimentally.
result Kernel deformed exponential families can attend to multiple compact regions of data.
After defining reduced minimum braid word and criteria for a braid family representative, different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established.
We show how the families Seiberg-Witten invariants of a family of smooth 4-manifolds can be recovered from the families Bauer-Furuta invariant via a cohomological formula. We use this formula to deduce several properties of the families Seiberg-Witten invariants. We give a formula for the Steenrod squares of the fami…
Study algebraic relations of Vassiliev invariants for families of knots.
problem Understanding algebraic structure of Vassiliev invariants for knot families.
method Analyzing algebraic relations and generating sets of Vassiliev invariants in 3D Chern-Simons theory.
result For 1-parametric knot families, Vassiliev invariants are finitely generated. For more parameters, there can be an infinite number of generators.
Constructs non-abelian G2-instantons on ALC members of B7 family.
problem Constructing non-abelian G2-instantons on ALC members of B7 family.
method Using co-homogeneity one symmetries, classify and describe the solutions as perturbations of abelian instantons.
result Find a one-parameter family of instantons with polynomial decay.
The paper introduces structured variational families to improve scalability in black-box variational inference.
problem Scalability issues in black-box variational inference, especially for large datasets and hierarchical models.
method Developed structured variational families that achieve better iteration complexity of O(N) compared to full-rank families.
result Structured variational families can achieve better scaling with respect to dataset size N, improving iteration complexity from O(N^2) to O(N).