About

This code has been produced during while writing my Ph.D. (Dr.-Ing.) thesis at the institut of automatic control, RWTH Aachen University. If you find it helpful for your research please cite this:

T. Redick, „Bayesian inference for CAD-based pose estimation on depth images for robotic manipulation“, RWTH Aachen University, 2024. doi: 10.18154/RWTH-2024-04533.

KernelDistributions.jl

Based on Distributions.jl but slimmed down to enable CUDA compatibility.

Distributions are isbitstype, strongly typed and thus support execution on the GPU. KernelDistributions offer the following interface functions:

• DensityInterface.logdensityof(dist::KernelDistribution, x)
• Random.rand!(rng, dist::KernelDistribution, A)
• Base.rand(rng, dist::KernelDistribution, dims...)
• Base.eltype(::Type{<:AbstractKernelDistribution}): Number format of the distribution, e.g. Float16

The Interface requires the following to be implemented:

• Bijectors.bijector(d): Bijector
• rand_kernel(rng, dist::MyKernelDistribution{T})::T generate a single random number from the distribution
• Distributions.logpdf(dist::MyKernelDistribution{T}, x)::T evaluate the normalized logdensity
• Base.maximum(d), Base.minimum(d), Distributions.insupport(d): Determine the support of the distribution
• Distributions.logcdf(d, x), Distributions.invlogcdf(d, x): Support for Truncated{D}

Most of the time Float64 precision is not required, especially for GPU computations. Thus, this package defaults to Float32, mostly for memory capacity reasons.