tsallis-divergence

A Tsallis divergence is a human-made family of statistical divergences between probability distributions P and Q, parameterized by the order q (q ≠ 0, q ≠ 1). It is defined as D_q(P||Q) = (1/(q - 1)) · (1 - Σ_i p_i^q / q_i^(q - 1)) in the discrete case, where p_i = P(i) and q_i = Q(i) are the probability masses (the corresponding integral in the continuous case); the limit q → 1 recovers the Kullback–Leibler divergence. It is non-negative and vanishes iff P = Q (under the support condition), is generally asymmetric, and reduces to the Rényi divergence in the limit q → 1 after appropriate scaling. Parameters: the order q and the distributions P and Q. It persists as a named family in non-extensive statistical mechanics (Tsallis, 1988), information geometry, and machine learning — explicitly named in the accepted definition of statistical-divergence ('Tsallis divergence via q') as a distinct generating functional, taught in information-theory and statistical-mechanics curricula, and used in density-ratio estimation, clustering, and robust statistical inference where the power-law sensitivity of the q-parameter provides tunable robustness to outliers. [formal: divergentia Tsallis | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]