Related papers: Homotopy Sampling, with an Application to Particle…
Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating properties from multiple executions of a system and by giving results within confidence bounds. Rare properties…
In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and…
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during the tracking even though both start and end points are…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
$ \ell_1 $-regularized linear inverse problems are frequently used in signal processing, image analysis, and statistics. The correct choice of the regularization parameter $ t \in \mathbb{R}_{\geq 0} $ is a delicate issue. Instead of…
Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating…
Automated 3D pose estimation of satellites and other known space objects is a critical component of space situational awareness. Ground-based imagery offers a convenient data source for satellite characterization; however, analysis…
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
Copies have been proposed as a viable alternative to endow machine learning models with properties and features that adapt them to changing needs. A fundamental step of the copying process is generating an unlabelled set of points to…
State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in…
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
Hypothesis testing is a statistical method used to draw conclusions about populations from sample data, typically represented in tables. With the prevalence of graph representations in real-life applications, hypothesis testing in graphs is…
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…