14,607 research outputs found
Sequential Design for Optimal Stopping Problems
We propose a new approach to solve optimal stopping problems via simulation.
Working within the backward dynamic programming/Snell envelope framework, we
augment the methodology of Longstaff-Schwartz that focuses on approximating the
stopping strategy. Namely, we introduce adaptive generation of the stochastic
grids anchoring the simulated sample paths of the underlying state process.
This allows for active learning of the classifiers partitioning the state space
into the continuation and stopping regions. To this end, we examine sequential
design schemes that adaptively place new design points close to the stopping
boundaries. We then discuss dynamic regression algorithms that can implement
such recursive estimation and local refinement of the classifiers. The new
algorithm is illustrated with a variety of numerical experiments, showing that
an order of magnitude savings in terms of design size can be achieved. We also
compare with existing benchmarks in the context of pricing multi-dimensional
Bermudan options.Comment: 24 page
Exact approximation of Rao-Blackwellised particle filters
Particle methods are a category of Monte Carlo algorithms that have become popular for performing inference in non-linear non-Gaussian state-space models. The class of 'Rao-Blackwellised' particle filters exploits the analytic marginalisation that is possible for some state-
space models to reduce the variance of the Monte Carlo estimates. Despite being applicable to only a restricted class of state-space models, such as conditionally linear Gaussian models, these algorithms have found numerous applications. In scenarios where no such analytical integration is possible, it has recently been proposed in Chen et al. [2011] to use 'local' particle filters to
carry out this integration numerically. We propose here an alternative approach also relying on \local" particle filters which is more broadly applicable and has attractive theoretical properties. Proof-of-concept simulation results are presented
Particle Gibbs Split-Merge Sampling for Bayesian Inference in Mixture Models
This paper presents a new Markov chain Monte Carlo method to sample from the
posterior distribution of conjugate mixture models. This algorithm relies on a
flexible split-merge procedure built using the particle Gibbs sampler. Contrary
to available split-merge procedures, the resulting so-called Particle Gibbs
Split-Merge sampler does not require the computation of a complex acceptance
ratio, is simple to implement using existing sequential Monte Carlo libraries
and can be parallelized. We investigate its performance experimentally on
synthetic problems as well as on geolocation and cancer genomics data. In all
these examples, the particle Gibbs split-merge sampler outperforms
state-of-the-art split-merge methods by up to an order of magnitude for a fixed
computational complexity
The Iray Light Transport Simulation and Rendering System
While ray tracing has become increasingly common and path tracing is well
understood by now, a major challenge lies in crafting an easy-to-use and
efficient system implementing these technologies. Following a purely
physically-based paradigm while still allowing for artistic workflows, the Iray
light transport simulation and rendering system allows for rendering complex
scenes by the push of a button and thus makes accurate light transport
simulation widely available. In this document we discuss the challenges and
implementation choices that follow from our primary design decisions,
demonstrating that such a rendering system can be made a practical, scalable,
and efficient real-world application that has been adopted by various companies
across many fields and is in use by many industry professionals today
StocHy: automated verification and synthesis of stochastic processes
StocHy is a software tool for the quantitative analysis of discrete-time
stochastic hybrid systems (SHS). StocHy accepts a high-level description of
stochastic models and constructs an equivalent SHS model. The tool allows to
(i) simulate the SHS evolution over a given time horizon; and to automatically
construct formal abstractions of the SHS. Abstractions are then employed for
(ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy
allows for modular modelling, and has separate simulation, verification and
synthesis engines, which are implemented as independent libraries. This allows
for libraries to be easily used and for extensions to be easily built. The tool
is implemented in C++ and employs manipulations based on vector calculus, the
use of sparse matrices, the symbolic construction of probabilistic kernels, and
multi-threading. Experiments show StocHy's markedly improved performance when
compared to existing abstraction-based approaches: in particular, StocHy beats
state-of-the-art tools in terms of precision (abstraction error) and
computational effort, and finally attains scalability to large-sized models (12
continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy
- …