2b:null 2c:["$","title",null,{"children":"Learning curves | Chuncheng | Observable"}] 31:T619,subjects = { const data = [...Array(form.subjects)].map(() => { return {}; }); const totalTime = form.tasks * form.avgTime; let rndTalent = d3.randomUniform(1, 7), rndTime = d3.randomUniform(0, 1), talents = [...Array(form.tasks)], times = [...Array(form.tasks)], sumTimes, oTimes, scores = [...Array(form.tasks)], scores2, oScores; data.map((data, i) => { talents = talents.map(rndTalent); oTimes = optimalTimes(talents, totalTime); times = times.map(rndTime); sumTimes = d3.sum(times); times = times.map((t) => (t / sumTimes) * totalTime); scores = scores.map((_, i) => { let epsilon = talents[i], t = times[i]; return learningCurve1(t, epsilon); }); scores2 = scores.map((_, i) => { let epsilon = talents[i], t = times[i]; return learningCurve1(t / 2, epsilon); }); oScores = scores.map((_, i) => { let epsilon = talents[i], t = oTimes[i]; return learningCurve1(t, epsilon); }); let output = { avgTalent: d3.mean(talents), avgScore: d3.mean(scores), avgScore2: d3.mean(scores2), avgOScore: d3.mean(oScores), stdScore: d3.variance(scores) ** 0.5, stdTalent: d3.variance(talents) ** 0.5, stdTimes: d3.variance(times) ** 0.5, dropScore: -d3.mean(scores) + d3.mean(scores2) }; Object.assign(data, { i, talents, times, scores, oTimes, oScores }); Object.assign(data, output); }); return data; }32:[] 2f:{"id":"c93b136b090f34cf","slug":"learning-curves","title":"Learning curves","thumbnail":"d8d0921b08219d53f4d40ec78b6e9c99268ac964ece79312f041b207d1f4e61c","access_level":"public","create_time":"$D2025-08-20T03:09:31.817Z","update_time":"$D2025-08-21T02:50:20.369Z","view_time":null,"first_public_time":"$D2025-08-20T08:53:20.276Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024"},"version":401,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null}],"members":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null,"role":"editor"},{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Learning curves","cells":[{"id":0,"value":"# Learning curves","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":103,"value":"## Learning curve","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":166,"value":"avgTime = form.avgTime","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":291,"value":"{\n const data = subjects\n .slice(0, 100)\n .toSorted((a, b) => a.stdTimes - b.stdTimes),\n marks = data.map((subject, j) => {\n return Plot.rectY(subject.times, {\n x: (d) => j,\n y: (d) => d,\n fill: (d, i) => i\n });\n });\n\n marks.push(\n Plot.line(data, {\n x: (d, j) => j,\n y: (d) => d.stdTimes * form.tasks,\n strokeWidth: 3\n })\n );\n\n let plt = Plot.plot({\n x: { ticks: [] },\n y: { label: \"times\" },\n color: { legend: true, scheme: \"Category10\", width: 600, columns: 10 },\n marks\n });\n\n return htl.html`\n

Times allocation among tasks

The curve is the std of times allocation, the lower the more unique among tasks

\n${plt}\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"## Output scores with limited time","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":32,"value":"viewof form = Inputs.form({\n tasks: Inputs.range([5, 30], { label: \"tasks\", step: 1, value: 20 }),\n subjects: Inputs.range([1000, 2000], { label: \"subjects\", step: 1 }),\n avgTime: Inputs.range([0.1, 0.9], {\n label: \"avgTime\",\n step: 0.01,\n value: 0.4\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":211,"value":"

\n\n \n

Score1 predicts score2

\n ${plt3}\n

Times & learningCurve (Color refers talent)

\n ${plt0}\n

\n\n

Score vs talent

\n ${plt1}\n

ScoreDrop vs talent (avgTime = ${form.avgTime})

\n ${plt2}\n

\n\n\n

\n","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":15,"value":"plt0 = Plot.plot({\n y: { domain: [0, 1] },\n color: { legend: true, scheme: \"Tableau10\" },\n marks: [\n Plot.dot(data, { x: \"t\", y: \"v\", fill: \"epsilon\" }),\n Plot.link([0], {\n x1: (d) => avgTime,\n y1: (d) => 0,\n x2: (d) => avgTime,\n y2: (d) => 1,\n stroke: \"black\"\n }),\n Plot.link([0], {\n x1: (d) => avgTime / 2,\n y1: (d) => 0,\n x2: (d) => avgTime / 2,\n y2: (d) => 1,\n stroke: \"gray\"\n }),\n Plot.text([0], {\n x: (d) => avgTime,\n y: 0.2,\n text: (d) => \"avgTime\",\n textAnchor: \"middle\",\n dx: 4,\n fontSize: 16\n }),\n Plot.text([0], {\n x: (d) => avgTime / 2,\n y: 0.1,\n text: (d) => \"avgTime(half)\",\n textAnchor: \"middle\",\n dx: 4,\n fontSize: 16,\n fill: \"gray\"\n })\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"plt1 = Plot.plot({\n x: { nice: true },\n y: { nice: true },\n color: {\n legend: true,\n scheme: \"RdBu\",\n type: \"linear\"\n },\n marks: [\n Plot.dot(subjects, {\n x: \"avgTalent\",\n y: \"avgScore\",\n fill: \"stdTimes\"\n }),\n Plot.dot(subjects, {\n x: \"avgTalent\",\n y: \"avgOScore\",\n fill: \"gray\",\n opacity: 0.1\n }),\n Plot.linearRegressionY(subjects, { x: \"avgTalent\", y: \"avgScore\" })\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"plt2 = Plot.plot({\n x: { nice: true },\n y: { nice: true },\n color: { legend: true, scheme: \"RdBu\", type: \"linear\" },\n marks: [\n Plot.dot(subjects, {\n x: \"avgTalent\",\n y: \"dropScore\",\n fill: \"stdTimes\"\n }),\n Plot.linearRegressionY(subjects, {\n x: \"avgTalent\",\n y: \"dropScore\"\n })\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"plt3 = Plot.plot({\n x: { nice: true },\n y: { nice: true },\n color: {\n legend: true,\n scheme: \"RdBu\",\n type: \"linear\"\n // label: \"stdTimes / avgTalent\"\n },\n marks: [\n Plot.dot(subjects, {\n x: \"avgScore\",\n y: \"avgScore2\",\n fill: \"stdTimes\"\n // fill: (d) => d.stdTimes / d.avgTalent\n }),\n Plot.linearRegressionY(subjects, { x: \"avgScore\", y: \"avgScore2\" })\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"$31","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"subjects","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":13,"value":"data = {\n const data = [],\n epsilons = [1, 2, 3, 4, 5, 6, 7];\n\n for (let t = 0; t < 1; t += 0.01) {\n epsilons.map((epsilon) =>\n data.push({ t, epsilon, v: learningCurve1(t, epsilon) })\n );\n }\n\n return data;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":383,"value":"function optimalTimes(mus, T) {\n let a = d3.sum(mus.map((mu) => Math.log(mu) / mu)),\n b = d3.sum(mus.map((mu) => 1 / mu));\n\n return mus.map((mu) => ((T - a) / b + Math.log(mu)) / mu);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"function learningCurve1(t, epsilon) {\n return 1 - Math.exp(-t * epsilon);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":55,"value":"d3 = require(\"d3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 30:"$2f:body"