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Stochastic sampling based trackers have shown good performance for abrupt motion tracking so that they have gained popularity in recent years. However, conventional methods tend to use a two-stage sampling paradigm, in which the search…
This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large…
Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…
We consider an input-to-response (ItR) system characterized by (1) parameterized input with a known probability distribution and (2) stochastic ItR function with heteroscedastic randomness. Our purpose is to efficiently quantify the extreme…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed to calculate steady state probabilities of order…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
Density tempering (also called density annealing) is a sequential Monte Carlo approach to Bayesian inference for general state models; it is an alternative to Markov chain Monte Carlo. When applied to state space models, it moves a…
Stochastic policies (also known as relaxed controls) are widely used in continuous-time reinforcement learning algorithms. However, executing a stochastic policy and evaluating its performance in a continuous-time environment remain open…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
Most state-of-the-art probabilistic time series forecasting models rely on sampling to represent future uncertainty. However, this paradigm suffers from inherent limitations, such as lacking explicit probabilities, inadequate coverage, and…
In non-linear estimations, it is common to assess sampling uncertainty by bootstrap inference. For complex models, this can be computationally intensive. This paper combines optimization with resampling: turning stochastic optimization into…
Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can…
Estimating the probability of failure is a critical step in developing safety-critical autonomous systems. Direct estimation methods such as Monte Carlo sampling are often impractical due to the rarity of failures in these systems. Existing…