23,543 research outputs found
Connecting the Dots: Towards Continuous Time Hamiltonian Monte Carlo
Continuous time Hamiltonian Monte Carlo is introduced, as a powerful
alternative to Markov chain Monte Carlo methods for continuous target
distributions. The method is constructed in two steps: First Hamiltonian
dynamics are chosen as the deterministic dynamics in a continuous time
piecewise deterministic Markov process. Under very mild restrictions, such a
process will have the desired target distribution as an invariant distribution.
Secondly, the numerical implementation of such processes, based on adaptive
numerical integration of second order ordinary differential equations is
considered. The numerical implementation yields an approximate, yet highly
robust algorithm that, unlike conventional Hamiltonian Monte Carlo, enables the
exploitation of the complete Hamiltonian trajectories (hence the title). The
proposed algorithm may yield large speedups and improvements in stability
relative to relevant benchmarks, while incurring numerical errors that are
negligible relative to the overall Monte Carlo errors
Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases
For big data analysis, high computational cost for Bayesian methods often
limits their applications in practice. In recent years, there have been many
attempts to improve computational efficiency of Bayesian inference. Here we
propose an efficient and scalable computational technique for a
state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian
Monte Carlo (HMC). The key idea is to explore and exploit the structure and
regularity in parameter space for the underlying probabilistic model to
construct an effective approximation of its geometric properties. To this end,
we build a surrogate function to approximate the target distribution using
properly chosen random bases and an efficient optimization process. The
resulting method provides a flexible, scalable, and efficient sampling
algorithm, which converges to the correct target distribution. We show that by
choosing the basis functions and optimization process differently, our method
can be related to other approaches for the construction of surrogate functions
such as generalized additive models or Gaussian process models. Experiments
based on simulated and real data show that our approach leads to substantially
more efficient sampling algorithms compared to existing state-of-the art
methods
Increasing pattern recognition accuracy for chemical sensing by evolutionary based drift compensation
Artificial olfaction systems, which mimic human olfaction by using arrays of gas chemical sensors combined with pattern recognition methods, represent a potentially low-cost tool in many areas of industry such as perfumery, food and drink production, clinical diagnosis, health and safety, environmental monitoring and process control. However, successful applications of these systems are still largely limited to specialized laboratories. Sensor drift, i.e., the lack of a sensor's stability over time, still limits real in dustrial setups. This paper presents and discusses an evolutionary based adaptive drift-correction method designed to work with state-of-the-art classification systems. The proposed approach exploits a cutting-edge evolutionary strategy to iteratively tweak the coefficients of a linear transformation which can transparently correct raw sensors' measures thus mitigating the negative effects of the drift. The method learns the optimal correction strategy without the use of models or other hypotheses on the behavior of the physical chemical sensors
Ensemble Transport Adaptive Importance Sampling
Markov chain Monte Carlo methods are a powerful and commonly used family of
numerical methods for sampling from complex probability distributions. As
applications of these methods increase in size and complexity, the need for
efficient methods increases. In this paper, we present a particle ensemble
algorithm. At each iteration, an importance sampling proposal distribution is
formed using an ensemble of particles. A stratified sample is taken from this
distribution and weighted under the posterior, a state-of-the-art ensemble
transport resampling method is then used to create an evenly weighted sample
ready for the next iteration. We demonstrate that this ensemble transport
adaptive importance sampling (ETAIS) method outperforms MCMC methods with
equivalent proposal distributions for low dimensional problems, and in fact
shows better than linear improvements in convergence rates with respect to the
number of ensemble members. We also introduce a new resampling strategy,
multinomial transformation (MT), which while not as accurate as the ensemble
transport resampler, is substantially less costly for large ensemble sizes, and
can then be used in conjunction with ETAIS for complex problems. We also focus
on how algorithmic parameters regarding the mixture proposal can be quickly
tuned to optimise performance. In particular, we demonstrate this methodology's
superior sampling for multimodal problems, such as those arising from inference
for mixture models, and for problems with expensive likelihoods requiring the
solution of a differential equation, for which speed-ups of orders of magnitude
are demonstrated. Likelihood evaluations of the ensemble could be computed in a
distributed manner, suggesting that this methodology is a good candidate for
parallel Bayesian computations
Data-driven Soft Sensors in the Process Industry
In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work
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