אסימפטוטיקה בממד גבוה של PCA פרטי

תקציר מקורי באנגליתarXiv:2511.07270v4 Announce Type: replace-cross Abstract: In differential privacy, random noise is introduced to privatize summary statistics of a sensitive dataset before releasing them. The noise level determines the privacy loss, which quantifies how easily an adversary can detect a target individual's presence in the dataset using the published statistic. Most privacy analyses provide non-asymptotic upper bounds on the privacy loss which hold uniformly across all datasets. Sometimes, these bounds can be pessimistic on a given dataset. In such cases, it can be useful to complement these privacy bounds with sharp privacy characterizations that quantify a mechanism's exact privacy loss on a given dataset. With this goal, we study differentially private principal component analysis (PCA),