The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.
problem Understanding Stein-Weiss operators on symmetric tensors of arbitrary rank.
method Analyzing the decomposition of tensor spaces into irreducible components and computing Weitzenbock formulas.
result Unified framework for second-order Stein-Weiss operators and tools for geometric analysis.
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…
In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…
The square root of Fredholm determinants causes numerical instabilities in option pricing models.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
Researchers derived formulas for joint moments of elliptical distributions.
problem Calculating joint moments of elliptical distributions.
method Used Stein's lemma and two different methods to derive expressions.
result New formulae for expectations of product of normally distributed random variables and simplified expressions for other distributions.
Unified model for financial derivatives pricing with stochastic interest rates.
problem Pricing and hedging financial derivatives with stochastic interest rates.
method Volterra Stein-Stein model with correlated Gaussian Volterra processes.
result Explicit formulas for bond and cap/floor pricing, and characteristic function for log-forward index.
Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.
problem Computing Greeks under rough Volterra stochastic volatility models.
method Malliavin calculus techniques, extending integration by parts to non-square integrable functionals.
result Formulas for computing Greeks (Delta, Gamma, Rho, Vega) under various rough Volterra SV models.
The notion of topological degree is studied for mappings from the boundary of a relatively compact strictly pseudo-convex domain in a Stein manifold into a manifold in terms of index theory of Toeplitz operators on the Hardy space. The index formalism of non-commutative geometry is used to derive analytic integral form…
New formulae identify discrete probability laws without needing normalization constants.
problem Characterizing non-normalized discrete probability distributions.
method Derive explicit formulae for mass functions using Stein's method.
result Developed tools for solving statistical problems without normalization constants.
SDG uses optimal control to improve classifier guidance in low-density regions.
problem Inefficient guidance in low-density regions of posterior distributions.
method Integrates stochastic optimal control with Stein variational inference to compute the steepest descent direction.
result SDG improves guidance in low-density regions, outperforming standard methods.
The aim of this paper is to use mapping class group relations to approach the `geography' problem for Stein fillings of a contact 3-manifold. In particular, we adapt a formula of Endo and Nagami so as to calculate the signature of such fillings as a sum of the signatures of basic relations in the monodromy of a related…
Using theorems of Eliashberg and McDuff, Etnyre [Et] proved that the intersection form of a symplectic filling of a contact 3-manifold supported by planar open book is negative definite. In this paper, we prove a signature formula for allowable Lefschetz fibrations over D2 with planar fiber by computing Maslov index…
Study on convex ordering in stochastic control for swing contracts, proving value function convexity.
problem Pricing of swing contracts under stochastic dynamics.
method Discrete-time stochastic optimal control problem, convexity propagation, Brownian diffusion model, Stein's formula.
result Value function is convex in underlying asset price, relaxation of convexity assumption for semi-convexity.
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
Legendrian surgery describes canonical contact structures and calculates Gompf's θ-invariant.
problem Understanding canonical contact structures and their properties.
method Legendrian surgery and explicit formulas for Gompf's θ-invariant.
result Explicit description and closed-form formula for Gompf's θ-invariant.
Researchers derive an analytic expression for Gaussian stochastic volatility models.
problem Analyzing rich autocorrelation structures and persistence in financial markets.
method Two different analytic derivations of the joint characteristic function.
result First analytic formulae for option pricing in rough volatility models.
Stein's method improves probabilistic inference and learning.
problem Improving probabilistic inference and learning methods.
method Constructing Stein discrepancies from Stein operators and Stein sets, discussing their properties.
result Connection between Stein operators and Stein variational gradient descent.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined L-plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L-plurisubharmonic exhaustion functions and GH embeddings. Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected a…
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Develops Stein's method for Riemannian manifolds using diffusion.
problem Bounding integral metrics on probability measures on Riemannian manifolds.
method Exploits the relationship between diffusion generators and Stein operators to derive Stein factors.
result Derives curvature-dependent Stein factors that generalize existing results for Euclidean spaces.
It is shown that every subcritical Stein manifold is deformation equivalent to the product of a Stein manifold with $\C$.
Regularized Stein thinning improves MCMC output approximations.
problem Pathologies in Stein thinning leading to poor approximations.
method Theoretical analysis and regularization to improve KSD.
result Regularized Stein thinning alleviates pathologies and improves efficiency.
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either required strong technical assumptions or were limited to Gaussian distributions with …
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).
In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most results pertain to proper maps into Stein manifolds. We include a new result saying that every continuous map X→Y between Stein manifolds is homotopic to a proper holomorphic em…
Counterexample found for Stein property of certain solvable Lie groups.
problem Stein property of simply connected unimodular solvable Lie groups with left-invariant complex structures.
method Constructing a solvable Lie group with specific properties.
result A simply connected solvable Lie group with a left-invariant complex structure whose universal cover is not Stein.
Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ∂~-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner,…
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we …
This paper selects features in deep neural networks with theoretical guarantees.
problem Feature selection in deep neural networks with unknown nonlinear functions.
method Reformulate neural networks as index models, estimate feature sets using Stein's formula, and apply screening-and-selection mechanism.
result Consistent feature selection with theoretical guarantees, even in high-dimensional settings.
Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…
2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.
problem Characterizing submanifolds with constant curvature in space forms.
method Analyzing submanifolds with flat normal connection or codimension 2.
result 2-stein submanifolds have constant curvature under specified conditions.
We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic Stein 4-manifo…
Paper proves robust M-estimators' coordinates' normality in high dimensions.
problem High-dimensional robust M-estimators' asymptotic normality.
method Develops Stein formulae for high-dimensional random vectors on the sphere.
result Asymptotic normality holds for most coordinates of robust M-estimators with convex penalty.
We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
For any integer n≥2, we construct an infinite family of Stein fillable contact (4n−1)-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.
Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.
problem Classify Stein fillings of planar contact 3-manifolds under constraints on their relative trisections.
method Partial classification of diffeomorphism types of fillings with relative trisections of genus at most 2.
result Partially classify the diffeomorphism types of Stein fillings with relative trisections of genus at most 2.
Study continuity and Hölder estimates for solutions on Stein spaces.
problem Continuity and Hölder estimates for solutions to degenerate complex Monge-Ampère equations.
method Prove continuity up to the boundary and local Hölder estimates on the regular locus.
result Local Hölder estimates on the regular locus for solutions to degenerate complex Monge-Ampère equations.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…
Paper proves existence of compatible Lefschetz fibrations on 6-ball and Stein domains.
problem Existence of compatible Lefschetz fibrations on Stein domains.
method Topological proof for 6-ball fibrations, construction of relative Stein pairs.
result Existence of compatible Lefschetz fibrations on Stein domains of dimension six.
New Stein operator improves robustness in model inference.
problem Improving robustness in inference for unnormalized models.
method Density-power weighted Stein operator (γ-Stein operator). result Robust methods for goodness-of-fit testing and posterior approximation.
Characterizes Stein surfaces with finite homotopy rank-sum.
problem Finite homotopy rank-sum in Stein spaces.
method Rational homotopy theory, classification of Stein surfaces.
result Affine Stein surfaces with finite fundamental group are either simply connected or of order 2.
A new method reduces complexity and uncertainty in neural networks.
problem Uncertainty quantification in complex neural networks.
method Condensed Stein Variational Gradient Descent (cSVGD) method.
result Condensed SVGD provides uncertainty quantification on parameters.