Efficiently calculates Brazilian stock options with discrete dividends.
problem Accurately pricing Brazilian listed equity options with discrete dividends.
method Uses the fast Laplace transform for high-accuracy computation.
result Efficiently computes option premiums and Greeks with high accuracy.
The paper studies graph Laplace operator behavior near isolated singularities.
problem Investigating asymptotics of graph Laplace operator near isolated singularities.
method Analyzing curvature growth and conformal modifications to understand operator behavior.
result The graph Laplace operator converges to a weighted Laplace-Beltrami operator as bandwidth decreases, or behaves like \(O(\frac{1}{\sqrt{t}})\) if curvature grows too fast.
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta al…
Fast approximate inference for non-Gaussian data.
problem Efficient inference for non-Gaussian data.
method Laplace Matching for fast approximate inference in latent Gaussian models.
result Achieves high approximation quality with low computational cost.
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…
Researchers derive an explicit Laplace transform for integrated Volterra Wishart process.
problem Modeling and pricing financial instruments with complex covariance structures.
method Explicit expression for conditional Laplace transform of integrated Volterra Wishart process, linking to matrix Riccati equations.
result Derivation of Laplace transform for a special case of convolution kernel, leading to efficient pricing methods.
A new method combines ANN and Laplace for fast Bayesian inference in ODE models.
problem Bayesian inference for ODE systems with non-analytical solutions is computationally expensive.
method Hybrid approach using ANN for tractable likelihood and Laplace approximation.
result Effective posterior inference with improved computational cost compared to traditional methods.
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…
LaLoRA prevents forgetting in LoRA fine-tuning.
problem Catastrophic forgetting in fine-tuned models.
method LaLoRA applies Laplace approximation to LoRA weights for regularization.
result Improved learning-forgetting trade-off with controllable regularization strength.
We introduce the Mondrian kernel, a fast random feature approximation to the Laplace kernel. It is suitable for both batch and online learning, and admits a fast kernel-width-selection procedure as the random features can be re-used efficiently for all kernel widths. The features are constructed by sampling trees via a…
New iterative methods improve Vecchia-Laplace approximations for large data sets.
problem Inaccurate and slow Vecchia-Laplace approximations for large data sets.
method Iterative methods to improve Vecchia-Laplace approximations, including preconditioners and novel methods for predictive variances.
result Order of magnitude speed-up and threefold increase in prediction accuracy compared to state-of-the-art methods.
Bayesian Lasso Sparse model provides sparse estimates in linear and nonlinear regression.
problem Sparse learning in regression models.
method Develops a new sparse learning model using type-II maximum likelihood procedure.
result The BLS model provides sparse estimates and is more precise, especially with noisy data.
New method aligns brain data across individuals for better brain decoding.
problem Inter-individual variability in brain response patterns limits decoder generalization.
method SpectralOT method that embeds cortical geometry into Laplace-Beltrami eigenmodes.
result SpectralOT strikes balance between aligning functional features and preserving anatomical structure.
Graphs approximate Laplacian spectra on manifolds.
problem Approximating Laplacian spectra on complex manifolds.
method Graph Laplacians on proximity graphs.
result Spectra of graph Laplacians approximate the Laplacian spectra of manifolds.
The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. T…
Bayesian analysis of financial time series using R-INLA.
problem Analyzing interdependencies between stock volatility measures.
method Flexible level correlated model (LCM) with INLA approximation.
result Fast approximate Bayesian modeling of positive-valued time series.
FAB-COST improves cold-start recommendation accuracy with less data.
problem Cold-start problem in recommendation systems.
method Contextual bandit algorithm using Expectation Propagation and Assumed Density Filtering.
result FAB-COST outperforms Laplace approximation on real data.
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this cla…
Efficiently approximates uncertainty in classification models using Dirichlet distributions.
problem Inefficient computation of uncertainty estimates in Bayesian deep learning.
method Revised Laplace Bridge method to construct a Dirichlet approximation of softmax output distributions.
result The Dirichlet approximation leads to more efficient computation and better uncertainty estimates.
Let x:M→Em be an isometric immersion of a Riemannian manifold M into a Euclidean m-space. Denote by Δ the Laplace operator of M. Then Δ gives rise to a differentiable map L:M→Em, called the Laplace map, defined by L(p)=(Δx)(p), p∈M. We call L(M) the Laplace image, and the transformat…
The paper examines special Q-nets that terminate after a finite number of Laplace steps.
problem Understanding the termination of Laplace sequences in Q-nets.
method Analyzing discrete Koenigs nets and their Laplace sequences.
result For certain Koenigs nets, Laplace sequences terminate after a finite number of steps.
Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.
problem Estimating eigenvalues of poly-Laplace operator on subgraphs of lattice graphs.
method Introduced discrete poly-Laplace operator, derived upper and lower bounds for eigenvalues.
result Poly-Laplace eigenvalues are at least squares of lower-order poly-Laplace eigenvalues.
Introduces a new elliptic operator with positive eigenvalue.
problem None explicitly stated in the abstract.
method Introduces a new elliptic operator called the two-radical Laplace operator.
result The eigenvalue of the new operator is the positive square root of the Laplace operator's eigenvalue.
This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transfor…
Revisits online Laplace methods for neural networks, showing they are sound under certain conditions.
problem Online Laplace methods violate the Laplace approximation's critical assumption.
method Re-derives online Laplace methods, showing they target a variational bound on a mode-corrected variant of the Laplace evidence.
result Online Laplace and its mode-corrected counterpart share stationary points that satisfy the Laplace method's assumption.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
Formula derived for Laplace-Beltrami on Stiefel manifold.
problem Finding Laplace-Beltrami operator on Stiefel manifold.
method Using the general framework of Laplace operators on constraint manifolds, derived the explicit formula in terms of ambient Euclidean coordinates.
result Extended previously known formulas for sphere and special orthogonal group.
Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.
problem Comparing eigenvalues on spherically symmetric manifolds to Euclidean balls.
method Examines Dirichlet Laplace eigenvalues on balls of spherically symmetric manifolds and Euclidean space.
result Eigenvalues on spherically symmetric manifolds are smaller for small radii, but larger for hyperbolic spaces.
New methods improve Laplace approximations for deep neural networks by selecting key parameters.
problem Improving uncertainty quantification in deep neural networks using computationally feasible approximations.
method Gradient-Laplace and Greedy-Laplace methods for selecting parameters in sub-network Laplace approximations.
result Gradient-Laplace method outperforms existing heuristic approaches and provides formal optimality guarantees.
We propose an affine extension of the Linear Gaussian term structure Model (LGM) such that the instantaneous covariation of the factors is given by an affine process on semidefinite positive matrices. First, we set up the model and present some important properties concerning the Laplace transform of the factors and th…
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via L2 regularization. Multiple GAMs allow finer statistical inference by incorporating explana…
QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.
problem Overconfident out-of-distribution predictions from DNNs.
method Proposes Quadratic Laplace Approximation (QLA) to improve Bayesian uncertainty quantification.
result QLA yields modest yet consistent uncertainty estimation improvements over Linearized Laplace Approximation (LLA) on five regression datasets.
Geometrically reformulates the Laplace method for optimal transport.
problem Approximating integrals using the Laplace method without geometric interpretation.
method Introduces the Kim-McCann Riemannian metric to give a geometric formulation of the Laplace method.
result Expresses the first-order term of the Laplace method using geometric objects.
Fundamental solutions found for p-Laplace equations in Heisenberg and Grushin spaces.
problem Finding solutions to p-Laplace equations with drift terms in specific geometric spaces.
method Analyzing fundamental solutions in the Heisenberg group and Grushin-type planes.
result Natural generalizations of Beals, Gaveau, and Greiner's solutions for the Laplace equation with drift term.
Study finds metrics maximizing one Laplace eigenvalue on 3D and higher manifolds.
problem Maximizing a Laplace eigenvalue on n-dimensional manifolds.
method Existence and regularity results for metrics of same volume in a conformal class.
result Existence and regularity of metrics maximizing the Laplace eigenvalue.
Neural Laplace models diverse DEs in the Laplace domain for better dynamics.
problem Inadequate ODEs for long-range dependencies and discontinuities.
method Unified framework in Laplace domain, using stereographic map for smoothness.
result Superior performance in diverse DEs, including complex history dependency and abrupt changes.
Graph Laplace operators uniquely identify metrics and densities on manifolds.
problem Identifying Riemannian metrics and sampling densities from graph Laplace operators.
method Analyzing intrinsic and extrinsic graph Laplace operators on compact Riemannian manifolds.
result Graph Laplace operators uniquely determine metrics and densities under certain conditions.
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistica…
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All of the Laplace opera…
The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds. Stre…
We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.
We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space R3. We determine all ruled surfaces and all relative normalizations for which the Laplace normal image degenerates into a point or into a curve…
We prove inequalities for Laplace eigenvalues of Kaehler manifolds generalising to higher eigenvalues the classical inequality for the first Laplace eigenvalue due to Bourguignon, Li, and Yau in 1994. We also obtain similar inequalities for analytic varieties in Kaehler manifolds.
Bayesian QFSTS model tackles feature selection in quantile time series analysis.
problem Quantile feature selection in correlated multivariate time series data.
method Bayesian dimension reduction methodology using QFSTS model with multivariate asymmetric Laplace distribution, spike-and-slab prior, Metropolis-Hastings algorithm, and Bayesian model averaging.
result QFSTS model outperforms in feature selection, parameter estimation, and forecasting.
Variational Laplace improves Bayesian neural networks performance.
problem Improving Bayesian neural networks performance.
method Develops variational Laplace for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms other inference methods.
The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Lap…
Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.
problem Computing Laplace-Beltrami on constrained submanifolds.
method Embedded gradient vector field method, explicit formula derivation.
result Explicit formula for Laplace-Beltrami on orthogonal group.