Related papers: A mirror descent approach to maximum likelihood es…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…
Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation…
In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
Discrete diffusion models have become highly effective across various domains. However, real-world applications often require the generative process to adhere to certain constraints. To this end, we propose a Sequential Monte Carlo (SMC)…
Sequential Monte Carlo (SMC) is a class of algorithms that approximate high-dimensional expectations of a Markov chain. SMC algorithms typically include a resampling step. There are many possible ways to resample, but the relative…
Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…
Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its…
The advantages of sequential Monte Carlo (SMC) are exploited to develop parameter estimation and model selection methods for GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) style models. It provides an alternative method…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…