sensor-placement

Information-theoretic sensor placement [1] implemented in Python, Cython, JAX, and Julia.

[1] A. Krause, A. Singh, and C. Guestrin, "Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies," J. Mach. Learn. Res., vol. 9, pp. 235–284, Jun. 2008.

Installation

Python

The Python dependencies are installed with Nix.

Navigate to the python directory and run

nix develop

Cython

The Cython implementation relies on Intel's oneMKL library which is unfree.

Navigate to the python directory and uncomment pkgs.mkl in flake.nix. Run

NIXPKGS_ALLOW_UNFREE=1 nix develop --impure
python setup.py build_ext --inplace

to compile the Cython extensions.

JAX

JAX on CPU is automatically installed with the Python dependencies.

For GPU support, create a Conda environment with micromamba from the explicitly pinned dependencies with

micromamba create -y --prefix ./.venv -f linux-64-spec-list.txt
eval "$(micromamba shell hook)"
micromamba activate ./.venv
pip install --requirement requirements.txt

from the python directory. Note that this requires a x86-64 Linux system.

Alternatively, create from the environment specification with

micromamba create --prefix ./.venv -f environment.yml
eval "$(micromamba shell hook)"
micromamba activate ./.venv

This is up-to-date and works on more platforms but the resolved dependencies may not work as expected.

Julia

Installation is done using the standard Pkg interface.

Navigate to the Sensors.jl/examples directory and run

julia --project="@."

(examples) pkg> instantiate

Running

Python, Cython, and JAX

Navigate to the python directory and run

python main.py

Julia

Navigate to the Sensors.jl/examples directory and run

julia --project="@." main.jl

Benchmarks

All experiments are done with a Matérn kernel with smoothness 5 / 2 and length scale 1. Points are uniformly drawn from the unit hypercube with spacial dimension d = 3. n denotes the number of points and s the number of points selected. entropy refers to greedily selecting the points with maximum conditional entropy and mi to maximizing the conditional mutual information with unselected points.

CPU experiments were run on a laptop. The GPU used was an A100 with 12 GB of memory.

entropy (n = 1000, s = 100)

method	time (seconds)
entropy naive	2.884e-02 (1.000)
python prec	9.967e-03 (2.893)
python prechol	1.234e-02 (2.337)
python chol	7.763e-03 (3.714)
cython chol	1.481e-03 (19.473)
julia	1.419e-03 (20.324) (5 allocations: 798.047 KiB)
jax (cpu)	1.875e-02 (1.538)
jax (gpu)	4.372e-03 ( 6.596)

mi (n = 100, s = 10)

method	time (seconds)
mi naive	2.970e-03 (1.000)
python prec	1.420e-03 (2.091)
python chol	3.988e-03 (0.745)
julia	7.320e-04 (4.057) (1.22 k allocations: 1.416 MiB)
jax (cpu)	6.456e-04 (4.600)
jax (gpu)	1.675e-03 (4.400)

entropy (n = 10_000, s = 200)

method	time (seconds)
entropy naive	2.075e+00 (1.000)
python prec	2.203e-01 (9.416)
python prechol	2.219e-01 (9.352)
python chol	1.925e-01 (10.779)
cython chol	7.852e-02 (26.423)
julia	8.293e-02 (25.021) (7 allocations: 15.413 MiB)
jax (cpu)	5.322e-01 (3.899)
jax (gpu)	1.309e-02 (158.517)

mi (n = 1000, s = 100)

method	time (seconds)
mi naive	2.929e+00 (1.000)
python prec	8.127e-01 (3.604)
python chol	1.329e+00 (2.203)
julia	5.660e-01 (5.175) (92.78 k allocations: 729.614 MiB, 2.48% gc time)
jax (cpu)	2.934e-01 (9.983)
jax (gpu)	2.364e-02 (123.900)