<invoke name="tool_call"> <parameter name="reasoning">No evidence exists yet, so I need to compute association between the columns. Computing pairwise mutual information and normalized MI in one SQL query over categorical columns, with the amount log-bucketed and year taken from the date.</parameter> <parameter name="tool">query_sql</parameter> <parameter name="args">{"purpose":"Rank column pairs by mutual information and normalized MI","source":"raw","sql":"WITH base AS (SELECT row_number() OVER () AS rid, regexp_extract(\"Date dd/mm/yyyy\", '(\\d{4})', 1) AS yr, coalesce(\"Industry Vertical\",'NA') AS vert, coalesce(SubVertical,'NA') AS subv, coalesce(\"City Location\",'NA') AS city, coalesce(InvestmentnType,'NA') AS itype, coalesce(Remarks,'NA') AS rem, CASE WHEN try_cast(replace(\"Amount in USD\",',','') AS DOUBLE) > 0 THEN cast(floor(log10(try_cast(replace(\"Amount in USD\",',','') AS DOUBLE))) AS VARCHAR) ELSE 'NA' END AS amt FROM raw.startup_funding), l AS (SELECT rid, 'year' AS c, yr AS v FROM base UNION ALL SELECT rid, 'industry_vertical', vert FROM base UNION ALL SELECT rid, 'subvertical', subv FROM base UNION ALL SELECT rid, 'city', city FROM base UNION ALL SELECT rid, 'investment_type', itype FROM base UNION ALL SELECT rid, 'remarks', rem FROM base UNION ALL SELECT rid, 'amount_log10_bucket', amt FROM base), nn AS (SELECT count(*)::DOUBLE AS n FROM base), j AS (SELECT x.c AS c1, y.c AS c2, x.v AS v1, y.v AS v2, count(*) AS k FROM l x JOIN l y ON x.rid = y.rid AND x.c < y.c GROUP BY ALL), m AS (SELECT c, v, count(*) AS k FROM l GROUP BY ALL), h AS (SELECT m.c, -sum(m.k/nn.n*ln(m.k/nn.n)) AS ent, count(*) AS distinct_vals FROM m, nn GROUP BY m.c), mi AS (SELECT j.c1, j.c2, sum(j.k/nn.n*ln(j.k*nn.n/(m1.k*m2.k))) AS mi FROM j JOIN m m1 ON m1.c=j.c1 AND m1.v=j.v1 JOIN m m2 ON m2.c=j.c2 AND m2.v=j.v2, nn GROUP BY j.c1, j.c2) SELECT mi.c1, mi.c2, round(mi.mi,3) AS mi_nats, round(mi.mi/sqrt(h1.ent*h2.ent),3) AS nmi, h1.distinct_vals AS distinct_1, h2.distinct_vals AS distinct_2 FROM mi JOIN h h1 ON h1.c=mi.c1 JOIN h h2 ON h2.c=mi.c2 ORDER BY nmi DESC"}</parameter> </invoke>