import * as math from 'mathjs' import { USER_ID, SN_ADMIN_IDS } from '@/lib/constants' export async function trust ({ boss, models }) { try { console.time('trust') console.timeLog('trust', 'getting graph') const graph = await getGraph(models) console.timeLog('trust', 'computing trust') const [vGlobal, mPersonal] = await trustGivenGraph(graph) console.timeLog('trust', 'storing trust') await storeTrust(models, graph, vGlobal, mPersonal) } finally { console.timeEnd('trust') } } const MAX_DEPTH = 10 const MAX_TRUST = 1 const MIN_SUCCESS = 1 // increasing disgree_mult increases distrust when there's disagreement // ... this cancels DISAGREE_MULT number of "successes" for every disagreement const DISAGREE_MULT = 10 // https://en.wikipedia.org/wiki/Normal_distribution#Quantile_function const Z_CONFIDENCE = 6.109410204869 // 99.9999999% confidence const GLOBAL_ROOT = 616 const SEED_WEIGHT = 0.25 const AGAINST_MSAT_MIN = 1000 const MSAT_MIN = 1000 const SIG_DIFF = 0.1 // need to differ by at least 10 percent /* Given a graph and start this function returns an object where the keys are the node id and their value is the trust of that node */ function trustGivenGraph (graph) { // empty matrix of proper size nstackers x nstackers let mat = math.zeros(graph.length, graph.length, 'sparse') // create a map of user id to position in matrix const posByUserId = {} for (const [idx, val] of graph.entries()) { posByUserId[val.id] = idx } // iterate over graph, inserting edges into matrix for (const [idx, val] of graph.entries()) { for (const { node, trust } of val.hops) { try { mat.set([idx, posByUserId[node]], Number(trust)) } catch (e) { console.log('error:', idx, node, posByUserId[node], trust) throw e } } } // perform random walk over trust matrix // the resulting matrix columns represent the trust a user (col) has for each other user (rows) // XXX this scales N^3 and mathjs is slow let matT = math.transpose(mat) const original = matT.clone() for (let i = 0; i < MAX_DEPTH; i++) { console.timeLog('trust', `matrix multiply ${i}`) matT = math.multiply(original, matT) matT = math.add(math.multiply(1 - SEED_WEIGHT, matT), math.multiply(SEED_WEIGHT, original)) } console.timeLog('trust', 'transforming result') const seedIdxs = SN_ADMIN_IDS.map(id => posByUserId[id]) const isOutlier = (fromIdx, idx) => [...seedIdxs, fromIdx].includes(idx) const sqapply = (mat, fn) => { let idx = 0 return math.squeeze(math.apply(mat, 1, d => { const filtered = math.filter(d, (val, fidx) => { return val !== 0 && !isOutlier(idx, fidx[0]) }) idx++ if (filtered.length === 0) return 0 return fn(filtered) })) } console.timeLog('trust', 'normalizing') console.timeLog('trust', 'stats') mat = math.transpose(matT) const std = sqapply(mat, math.std) // math.squeeze(math.std(mat, 1)) const mean = sqapply(mat, math.mean) // math.squeeze(math.mean(mat, 1)) const zscore = math.map(mat, (val, idx) => { const zstd = math.subset(std, math.index(idx[0])) const zmean = math.subset(mean, math.index(idx[0])) return zstd ? (val - zmean) / zstd : 0 }) console.timeLog('trust', 'minmax') const min = sqapply(zscore, math.min) // math.squeeze(math.min(zscore, 1)) const max = sqapply(zscore, math.max) // math.squeeze(math.max(zscore, 1)) const mPersonal = math.map(zscore, (val, idx) => { const zmin = math.subset(min, math.index(idx[0])) const zmax = math.subset(max, math.index(idx[0])) const zrange = zmax - zmin if (val > zmax) return MAX_TRUST return zrange ? (val - zmin) / zrange : 0 }) const vGlobal = math.squeeze(math.row(mPersonal, posByUserId[GLOBAL_ROOT])) return [vGlobal, mPersonal] } /* graph is returned as json in adjacency list where edges are the trust value 0-1 graph = [ { id: node1, hops: [{node : node2, trust: trust12}, {node: node3, trust: trust13}] }, ... ] */ async function getGraph (models) { return await models.$queryRaw` SELECT id, json_agg(json_build_object( 'node', oid, 'trust', CASE WHEN total_trust > 0 THEN trust / total_trust::float ELSE 0 END)) AS hops FROM ( WITH user_votes AS ( SELECT "ItemAct"."userId" AS user_id, users.name AS name, "ItemAct"."itemId" AS item_id, min("ItemAct".created_at) AS act_at, users.created_at AS user_at, "ItemAct".act = 'DONT_LIKE_THIS' AS against, count(*) OVER (partition by "ItemAct"."userId") AS user_vote_count FROM "ItemAct" JOIN "Item" ON "Item".id = "ItemAct"."itemId" AND "ItemAct".act IN ('FEE', 'TIP', 'DONT_LIKE_THIS') AND "Item"."parentId" IS NULL AND NOT "Item".bio AND "Item"."userId" <> "ItemAct"."userId" JOIN users ON "ItemAct"."userId" = users.id AND users.id <> ${USER_ID.anon} WHERE "ItemAct"."invoiceActionState" IS NULL OR "ItemAct"."invoiceActionState" = 'PAID' GROUP BY user_id, name, item_id, user_at, against HAVING CASE WHEN "ItemAct".act = 'DONT_LIKE_THIS' THEN sum("ItemAct".msats) > ${AGAINST_MSAT_MIN} ELSE sum("ItemAct".msats) > ${MSAT_MIN} END ), user_pair AS ( SELECT a.user_id AS a_id, b.user_id AS b_id, count(*) FILTER(WHERE a.act_at > b.act_at AND a.against = b.against) AS before, count(*) FILTER(WHERE b.act_at > a.act_at AND a.against = b.against) AS after, count(*) FILTER(WHERE a.against <> b.against) * ${DISAGREE_MULT} AS disagree, b.user_vote_count AS b_total, a.user_vote_count AS a_total FROM user_votes a JOIN user_votes b ON a.item_id = b.item_id WHERE a.user_id <> b.user_id GROUP BY a.user_id, a.user_vote_count, b.user_id, b.user_vote_count ), trust_pairs AS ( SELECT a_id AS id, b_id AS oid, CASE WHEN before - disagree >= ${MIN_SUCCESS} AND b_total - after > 0 THEN confidence(before - disagree, b_total - after, ${Z_CONFIDENCE}) ELSE 0 END AS trust FROM user_pair WHERE NOT (b_id = ANY (${SN_ADMIN_IDS})) UNION ALL SELECT a_id AS id, seed_id AS oid, ${MAX_TRUST}::numeric as trust FROM user_pair, unnest(${SN_ADMIN_IDS}::int[]) seed_id GROUP BY a_id, a_total, seed_id UNION ALL SELECT a_id AS id, a_id AS oid, ${MAX_TRUST}::float as trust FROM user_pair ) SELECT id, oid, trust, sum(trust) OVER (PARTITION BY id) AS total_trust FROM trust_pairs ) a GROUP BY a.id ORDER BY id ASC` } async function storeTrust (models, graph, vGlobal, mPersonal) { // convert nodeTrust into table literal string let globalValues = '' let personalValues = '' vGlobal.forEach((val, [idx]) => { if (isNaN(val)) return if (globalValues) globalValues += ',' globalValues += `(${graph[idx].id}, ${val}::FLOAT)` if (personalValues) personalValues += ',' personalValues += `(${GLOBAL_ROOT}, ${graph[idx].id}, ${val}::FLOAT)` }) math.forEach(mPersonal, (val, [fromIdx, toIdx]) => { const globalVal = vGlobal.get([toIdx]) if (isNaN(val) || val - globalVal <= SIG_DIFF) return if (personalValues) personalValues += ',' personalValues += `(${graph[fromIdx].id}, ${graph[toIdx].id}, ${val}::FLOAT)` }) // update the trust of each user in graph await models.$transaction([ models.$executeRaw`UPDATE users SET trust = 0`, models.$executeRawUnsafe( `UPDATE users SET trust = g.trust FROM (values ${globalValues}) g(id, trust) WHERE users.id = g.id`), models.$executeRawUnsafe( `INSERT INTO "Arc" ("fromId", "toId", "zapTrust") SELECT id, oid, trust FROM (values ${personalValues}) g(id, oid, trust) ON CONFLICT ("fromId", "toId") DO UPDATE SET "zapTrust" = EXCLUDED."zapTrust"` ) ]) }