We say that a function $f\colon \Sigma^n \to \{0, 1\}$ is $\epsilon$-fooled by $k$-wise indistinguishability if $f$ cannot distinguish with advantage $\epsilon$ between any two distributions $\mu$ and $\nu$ over $\Sigma^n$ whose projections to any $k$ symbols are identical. We study the class of functions $f$ that are fooled by ... more >>>

Prediction algorithms assign numbers to individuals that are popularly understood as individual ``probabilities''---what is the probability of 5-year survival after cancer diagnosis?---and which increasingly form the basis for life-altering decisions. Drawing on an understanding of computational indistinguishability developed in complexity theory and cryptography, we introduce Outcome Indistinguishability. Predictors that are ... more >>>

A pair of sources $\mathbf{X},\mathbf{Y}$ over $\{0,1\}^n$ are $k$-indistinguishable if their projections to any $k$ coordinates are identically distributed. Can some $\mathit{AC^0}$ function distinguish between two such sources when $k$ is big, say $k=n^{0.1}$? Braverman's theorem (Commun. ACM 2011) implies a negative answer when $\mathbf{X}$ is uniform, whereas Bogdanov et ... more >>>