{
  "annotation_id": "8640d98c-4c01-4409-b942-bbb3b5359b54",
  "date_created": "2026-02-17T05:53:12.601000Z",
  "date_modified": "2026-02-17T05:53:12.601000Z",
  "file_hash": "4ef2936b06a81c59e5b1e727c43f2a9b08c9688427cd77a9e979b2be38f4d5c4",
  "private": false,
  "record": {
    "abstract": "We study an information-theoretic privacy mechanism design problem, where an agent observes useful data $Y$ that is arbitrarily correlated with sensitive data $X$, and design disclosed data $U$ generated from $Y$ (the agent has no direct access to $X$). We introduce \\emph{sparse point-wise privacy leakage}, a worst-case privacy criterion that enforces two simultaneous constraints for every disclosed symbol $u\\in\\mathcal{U}$: (i) $u$ may be correlated with at most $N$ realizations of $X$, and (ii) the total leakage toward those realizations is bounded. In the high-privacy regime, we use concepts from information geometry to obtain a local quadratic approximation of mutual information which measures utility between $U$ and $Y$. When the leakage matrix $P_{X|Y}$ is invertible, this approximation reduces the design problem to a sparse quadratic maximization, known as the Rayleigh-quotient problem, with an $\\ell_0$ constraint. We further show that, for the approximated problem, one can without loss of optimality restrict attention to a binary released variable $U$ with a uniform distribution. For small alphabet sizes, the exact sparsity-constrained optimum can be computed via combinatorial support enumeration, which quickly becomes intractable as the dimension grows. For general dimensions, the resulting sparse Rayleigh-quotient maximization is NP-hard and closely related to sparse principal component analysis (PCA). We propose a convex semidefinite programming (SDP) relaxation that is solvable in polynomial time and provides a tractable surrogate for the NP-hard design, together with a simple rounding procedure to recover a feasible leakage direction. We also identify a sparsity threshold beyond which the sparse optimum saturates at the unconstrained spectral value and the SDP relaxation becomes tight.",
    "arxiv_id": "2601.07523",
    "authors": [
      "Amirreza Zamani",
      "Sajad Daei",
      "Parastoo Sadeghi",
      "Mikael Skoglund"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Sparse Point-wise Privacy Leakage: Mechanism Design and Fundamental Limits",
    "url": "https://arxiv.org/abs/2601.07523",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f4ed98b7-1bed-4a6f-bd49-89ff083702c4",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}