From b2d707b651a549d4c10358f3f735f46a0136a350 Mon Sep 17 00:00:00 2001 From: Bas Nijholt <basnijholt@gmail.com> Date: Wed, 21 Aug 2019 18:30:27 +0200 Subject: [PATCH] add periods --- paper.md | 46 +++++++++++++++++++++++----------------------- 1 file changed, 23 insertions(+), 23 deletions(-) diff --git a/paper.md b/paper.md index 1142fb8..3686431 100755 --- a/paper.md +++ b/paper.md @@ -16,84 +16,84 @@ contribution: | # Introduction -#### Simulations are costly and often require sampling a region in parameter space +#### Simulations are costly and often require sampling a region in parameter space. -#### Chosing new points based on existing data improves the simulation efficiency +#### Chosing new points based on existing data improves the simulation efficiency. <!-- examples here --> -#### We describe a class of algorithms replying on local criteria for sampling which allow for easy parallelization and have a low overhead +#### We describe a class of algorithms replying on local criteria for sampling which allow for easy parallelization and have a low overhead. <!-- This is useful for intermediary cost simulations. --> -#### We provide a reference implementation, the Adaptive package, and demonstrate its performance +#### We provide a reference implementation, the Adaptive package, and demonstrate its performance. # Review of adaptive sampling -#### Experiment design uses Bayesian sampling because the computational costs are not a limitation +#### Experiment design uses Bayesian sampling because the computational costs are not a limitation. <!-- high dimensional functions --> -#### Plotting and low dimensional integration uses local sampling +#### Plotting and low dimensional integration uses local sampling. <!-- can refer to Mathematica's implementation --> -#### PDE solvers and computer graphics use adaptive meshing +#### PDE solvers and computer graphics use adaptive meshing. <!-- hydrodynamics anisotropic meshing paper ref --> # Design constraints and the general algorithm -#### We aim to sample low dimensional low to intermediate cost functions in parallel +#### We aim to sample low dimensional low to intermediate cost functions in parallel. <!-- because of curse of dimensionality --> <!-- fast functions don't require adaptive --> <!-- When your function evaluation is very expensive, full-scale Bayesian sampling will perform better, however, there is a broad class of simulations that are in the right regime for Adaptive to be beneficial. --> -#### We propose to use a local loss function as a criterion for chosing the next point +#### We propose to use a local loss function as a criterion for chosing the next point. -#### As an example interpoint distance is a good loss function in one dimension +#### As an example interpoint distance is a good loss function in one dimension. <!-- Plot here --> -#### In general local loss functions only have a logarithmic overhead +#### In general local loss functions only have a logarithmic overhead. -#### With many points, due to the loss being local, parallel sampling incurs no additional cost +#### With many points, due to the loss being local, parallel sampling incurs no additional cost. # Loss function design -#### A failure mode of such algorithms is sampling only a small neighborhood of one point +#### A failure mode of such algorithms is sampling only a small neighborhood of one point. <!-- example of distance loss on singularities --> -#### A solution is to regularize the loss such that this would avoided +#### A solution is to regularize the loss such that this would avoided. <!-- like resolution loss which limits the size of an interval --> -#### Adding loss functions allows for balancing between multiple priorities +#### Adding loss functions allows for balancing between multiple priorities. <!-- i.e. area + line simplification --> -#### A desireble property is that eventually all points should be sampled +#### A desireble property is that eventually all points should be sampled. <!-- exploration vs. explotation --> # Examples ## Line simplification loss -#### The line simplification loss is based on an inverse Visvalingam’s algorithm +#### The line simplification loss is based on an inverse Visvalingam’s algorithm. <!-- https://bost.ocks.org/mike/simplify/ --> ## A parallelizable adaptive integration algorithm based on cquad -#### The `cquad` algorithm belongs to a class that is parallelizable +#### The `cquad` algorithm belongs to a class that is parallelizable. ## isosurface sampling # Implementation and benchmarks <!-- API description --> -#### The learner abstracts a loss based priority queue +#### The learner abstracts a loss based priority queue. -#### The runner orchestrates the function evaluation +#### The runner orchestrates the function evaluation. # Possible extensions -#### Anisotropic triangulation would improve the algorithm +#### Anisotropic triangulation would improve the algorithm. -#### Learning stochastic functions is promising direction +#### Learning stochastic functions is promising direction. -#### Experimental control needs to deal with noise, hysteresis, and the cost for changing parameters +#### Experimental control needs to deal with noise, hysteresis, and the cost for changing parameters. <!-- We can include things like: -- GitLab