nx_sketch_count_sketch.nx

sketch_count_sketch.nx -- CountSketch (Charikar-Chen-Farach-Colton 2002). Frequency-counting variant that gives UNBIASED estimates via ±1 sign hashing. Each (key, count) update adds s_j(key) * count to row j column h_j(key), where s_j ∈ {-1, +1} is a sign hash. Query: median of (s_j(key) * counter[j][h_j(key)]) across rows. COMPLEMENTS CMS (runtime/sketch_cms.nx): - CMS: always OVERESTIMATES (false positives via positive collisions). Use when "upper bound" matters. - CountSketch: UNBIASED. Use when expectation matters (statistical summaries, F_2 estimation, sparse-approximation literature). CAPABILITY STOMP: shipping both means callers pick by error semantics. DataSketches ships CMS as "FrequentLongs"; CountSketch is queued in their docs but not implemented. ERROR BOUND: |estimate(x) - f(x)| <= ε · ||f||_2 / sqrt(d) where ||f||_2 = sqrt(Σ f_i²) is the L2 norm of the frequency vector. For w = O(1/ε²) and d = O(log(1/δ)) rows: confidence 1-δ. Default params: d=5 rows, w=2048 columns -> conf >99%, ε ~ 0.022.