Library / Code module

Dithered sign expectation and its inverse

dithered_sign_expectation

Compute the mean of sign(x + noise) for Gaussian or uniform dither, 2 Phi(x/sigma) - 1 or x/a, check it against a seeded Monte Carlo estimate with its standard error, and invert it to recover x from an observed mean of one-bit readings.

Files, names only

ATTRIBUTION.md 3.9 KB
LICENSE 1.0 KB
README.md 2.6 KB
atom_cli.py 3.0 KB
component.json 7.7 KB
dithered_sign_expectation.py 3.8 KB
numerics.py 28.0 KB
schema_lite.py 8.9 KB
test_dithered_sign_expectation.py 2.5 KB
test_package.py 12.0 KB

Full files in your harness.

What it takes and gives

Runs with: Python 3.10 or later
Entry points: sign_expectation, monte_carlo_sign_expectation, recover_offset
Known answers: 10 cases its tests reproduce

Cases it covers

not the undithered sign: Without dither the mean sign is 1 for every positive x and the magnitude is lost.
not the small signal slope: Extrapolating the slope sqrt(2/pi) at zero overstates the mean once x is comparable to sigma.

Limits and scope

Limits: Gaussian and uniform dither only, with a known scale. Inversion of the Gaussian form needs a mean strictly inside (-1, 1) and loses precision near the ends, where the curve is flat. The Monte Carlo check uses a Box-Muller generator on random() and is a consistency check, not a proof.
Guarantees: Gaussian: E[sign(x + sigma Z)] = 2 Phi(x / sigma) - 1, computed as erf(x / (sigma sqrt 2)). Uniform on [-a, a]: x / a inside [-a, a], sign(x) outside. recover_offset inverts sign_expectation; the Monte Carlo standard error is sqrt((1 - m^2) / N).
Assumes: The dither is independent of x and of the other draws, with the stated distribution and scale. sign(0) = 0; with continuous dither this happens with probability 0.

Details

Kind: Code module
Licence: MIT
Declared effects: runs commands
Source: github.com/alisonjieli-png/loop-engine/tools/creative_originals/evaluation_atoms/items/dithered_sign_expectation
Size: 10 files, 73.4 KB
Identity: library.supply.creative_originals.0468786c2ae2e0134b0e3e62.48018416d96a426a
Version: 48018416d96a426a1baa17aae344c6d8ad1ae0dda488095bad5b67eb3d6e4c13

The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.

Where it is shown

Statistics for comparing resultsDeterministic skills

Related components

Something wrong with this item, its rights or its safety? Report it on the support page, or from your harness after a download.