mmrc.py

import numpy as np


def mmrc_encoder(seed, x, number_candidates, c1, c2, gamma):
  """This is the encoder used by the mmrc algorithm.
  Args:
    seed: The random seed to be used by the encoder.
    x: The 1-dimensional input data.
    number_candidates: The number of candidates to be sampled.
    c1: The larger constant that the privunit density is proportional to.
    c2: The smaller constant that the privunit density is proportional to.
    gamma: The gamma parameter of privunit.
  Returns:
    k: The index sampled by the encoder.
    z: The set of candidates sampled at the encoder.
    pi: The distribution over the candidates for the given input data x.
  """
  if x.ndim > 1:
    raise ValueError(f"x must be a vector, got shape {x.shape}.")
  d = x.shape[0]

  rs = np.random.RandomState(seed)
  # The proposal distribution is chosen to be uniform on surface of the sphere.
  z = rs.normal(0, 1, (d, number_candidates))
  z /= np.linalg.norm(z, axis=0)

  pi = np.where(np.dot(x, z) >= gamma, c1, c2)
  pi /= np.sum(pi)
  k = np.random.choice(number_candidates, 1, p=pi)[0]
  return k, z, pi


def mmrc_decoder(seed, k, d, number_candidates):
  """This is the decoder used by the mmrc algorithm.
  Args:
    seed: The random seed to be used by the decoder (this seed should be the
      same as the one used by the encoder).
    k: The index transmitted by the encoder.
    d: The dimension of the data.
    number_candidates: The number of candidates to be sampled.
  Returns:
    z_k: The candidate corresponding to the index k (This is the candidate that
    is distributed according to the conditional distribution of privunit).
  """
  rs = np.random.RandomState(seed)
  # The proposal distribution should be the same as the one used by the encoder.
  z = rs.normal(0, 1, (d, number_candidates))
  z /= np.linalg.norm(z, axis=0)
  z_k = z[:, k]
  return z_k