85 citations · 207 across the 20 of their papers we have counts for
25 papers
Iterating Consistency Models: Stability, Error Bounds and Noise Schedules
Alessio Spagnoletti, Abdul-Lateef Haji-Ali, Andrés Almansa +3
Consistency models (CMs) have become a leading approach for generating high-quality samples in few steps. However, adding steps can improve or degrade sample quality in ways that a…
An Adaptive Sampling Algorithm for Level-set Approximation
Matteo Croci, Abdul-Lateef Haji-Ali, Ian C. J. Powell
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive…
The multi-index Monte Carlo method for semilinear stochastic partial differential equations
Abdul-Lateef Haji-Ali, Håkon Hoel, Andreas Petersson
Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical…
Forward Propagation of Low Discrepancy Through McKean-Vlasov Dynamics: From QMC to MLQMC
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Raúl Tempone +1
This work develops a particle system addressing the approximation of McKean-Vlasov stochastic differential equations (SDEs). The novelty of the approach lies in involving low discr…
Bayesian computation with generative diffusion models by Multilevel Monte Carlo
Abdul-Lateef Haji-Ali, Marcelo Pereyra, Luke Shaw +1
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a…
Nested Multilevel Monte Carlo with Biased and Antithetic Sampling
Abdul-Lateef Haji-Ali, Jonathan Spence
We consider the problem of estimating a nested structure of two expectations taking the form , where . Terms of this form arise…
Multi-index importance sampling for McKean--Vlasov stochastic differential equations
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This work addresses the estimation of rare-event quantities expressed as expectations of smooth observables of solutions to a broad class of McKean--Vlasov stochastic differential…
Efficient Risk Estimation for the Credit Valuation Adjustment
Michael B. Giles, Abdul-Lateef Haji-Ali, Jonathan Spence
The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk…
Multilevel Path Branching for Digital Options
Michael B. Giles, Abdul-Lateef Haji-Ali
We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path split…
Multilevel Importance Sampling for Rare Events Associated With the McKean--Vlasov Equation
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This work combines multilevel Monte Carlo (MLMC) with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of th…
Double-Loop Importance Sampling for McKean--Vlasov Stochastic Differential Equation
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Shyam Mohan Subbiah Pillai +1
This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with solutions to the -dimensional McKean-Vlasov stochastic differential equ…
State-dependent Importance Sampling for Estimating Expectations of Functionals of Sums of Independent Random Variables
Eya Ben Amar, Nadhir Ben Rached, Abdul-Lateef Haji-Ali +1
Estimating the expectations of functionals applied to sums of random variables (RVs) is a well-known problem encountered in many challenging applications. Generally, closed-form ex…
Adaptive Multilevel Monte Carlo for Probabilities
Abdul-Lateef Haji-Ali, Jonathan Spence, Aretha Teckentrup
We consider the numerical approximation of where the -dimensional random variable cannot be sampled directly, but there is a hierarchy of increasingly a…
Efficient Importance Sampling for Large Sums of Independent and Identically Distributed Random Variables
Nadhir Ben Rached, Abdul-Lateef Haji-Ali, Gerardo Rubino +1
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb{P}(\sum_{i=…
Weak convergence analysis in the particle limit of the McKean--Vlasov equations using stochastic flows of particle systems
Abdul-Lateef Haji-Ali, Håkon Hoel, Raúl Tempone
We present a proof showing that the weak error of a system of interacting stochastic particles approximating the solution of the McKean-Vlasov equation is .…
Sub-sampling and other considerations for efficient risk estimation in large portfolios
Michael B. Giles, Abdul-Lateef Haji-Ali
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evalua…
Multilevel nested simulation for efficient risk estimation
Michael B. Giles, Abdul-Lateef Haji-Ali
We investigate the problem of computing a nested expectation of the form where is t…
Multilevel weighted least squares polynomial approximation
Abdul-Lateef Haji-Ali, Fabio Nobile, Raúl Tempone +1
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distr…
Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation
Abdul-Lateef Haji-Ali, Raul Tempone
We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of pa…
Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity
Abdul-Lateef Haji-Ali, Fabio Nobile, Lorenzo Tamellini +1
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDEs) with random data, where th…
Novel results for the anisotropic sparse grid quadrature
Abdul-Lateef Haji-Ali, Helmut Harbrecht, Michael Peters +1
This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account t…
Multi-Index Stochastic Collocation for random PDEs
Abdul-Lateef Haji-Ali, Fabio Nobile, Lorenzo Tamellini +1
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique b…
Multi-Index Monte Carlo: When Sparsity Meets Sampling
Abdul-Lateef Haji-Ali, Fabio Nobile, Raul Tempone
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven…
Optimization of mesh hierarchies in Multilevel Monte Carlo samplers
Abdul Lateef Haji Ali, Fabio Nobile, Erik von Schwerin +1
We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation…