40:null 41:["$","title",null,{"children":"Overlapping Data | Sakura Gavin | Observable"}] 47:[] 45:{"id":"bc9977a7ca94531f","slug":null,"title":"Overlapping Data","thumbnail":"90016ce5b821ddd5c9437a018c80540296e15a9463442bb5264693060a81ed69","access_level":"public","create_time":"$D2023-10-03T12:58:13.261Z","update_time":"$D2023-10-05T13:07:13.427Z","view_time":null,"first_public_time":"$D2023-10-03T12:58:13.261Z","has_unpublished_edits":null,"fork":{"id":"b54a365a6af95da2","slug":null,"title":"Logistic Regression","owner":{"id":"e6e35eaca7d80d81","login":"sgavin93","name":"Sakura Gavin"}},"stars":0,"starred":false,"owner":{"type":"team","id":"e6e35eaca7d80d81","login":"sgavin93","name":"Sakura Gavin","avatar_url":null,"tier":"starter_2024","bio":"","following":false},"version":142,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"eab589938d94f1ab","login":"sgavin93","name":"Sakura Gavin","avatar_url":null,"tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"eab589938d94f1ab","login":"sgavin93","name":"Sakura Gavin","avatar_url":null,"tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Overlapping Data","cells":[{"id":0,"value":"# Overlapping Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":32,"value":"viewof threshold = Inputs.range([0,10],{step:.1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"html`\n\n \n \n \n\n \n \n \n\n \n \n \n

	Predicted Negative	Predicted Positive
Actual Positive	${falseNegatives}	${truePositives}
Actual Negative	${trueNegatives}	${falsePositives}

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"Plot.plot({\n x:{domain:[0,10]},\n y:{domain:[0,1]},\n marks:[\n Plot.ruleX([0]),\n Plot.ruleY([0]),\n Plot.dot(Xblue, {x:Xblue,y:0,fill:\"blue\",r:5}),\n Plot.dot(Xred, {x:Xred,y:Yred,fill:\"red\",r:5}),\n Plot.line([[threshold,0],[threshold,1]],{strokeDasharray:\"5,5\"}),\n Plot.line(x,{x:x,y:y,stroke:\"red\"}),\n Plot.line([[0,0.5],[10,0.5]],{strokeDasharray:\"5,5\"}),\n Plot.dot(X,{x:X,y:Yhat,fill:\"green\",r:5})\n \n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":78,"value":"### Sigmoid","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":82,"value":"f = (x,a,b) => Math.exp(a*x + b)/(1+Math.exp(a*x + b))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"x = {\n const x = []\n for(let i = 0; i <=10; i=i+.1){\n x.push(i)\n }\n return x\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"y = x.map(x => f(x,0.79000056, -4.18321431))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"### The Loss","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":103,"value":"Yhat = X.map(X => f(X,0.79000056,-4.18321431))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"penalties = X.map((X,i) =>\n\n Y[i]*Math.log(Yhat[i])\n +\n (1-Y[i])*Math.log(1-Yhat[i])\n )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":139,"value":"d3.mean(penalties)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"tex`\\text{probabilities of being positive (green points)} \\\\\nYln(Yhat) + (1-y)ln(1-Yhat) \\\\\n\\text{log - loss}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"### Positives and Negatives","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":40,"value":"trueNegatives = Xblue.filter(x => x <= threshold).length","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":55,"value":"falseNegatives = Xred.filter(x => x <= threshold).length","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"truePositives = Xred.filter(x => x >= threshold).length","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"falsePositives = Xblue.filter(x => x >= threshold).length","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"### Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":15,"value":"Xblue = [0.23172273283556077, 6.261636528327473, 4.6010247891667335, 1.660132912093145, 1.2024450601909025, 4.746559515821619, 4.9280744954032425, 5.250737883974269, 1.7705201542833398, 5.349311712251664]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"Xred = [4.557295223920891, 6.8297789235508315, 4.413710405238934, 7.690735156159806, 7.343854883275675, 8.804357813742223, 9.431131316191179, 4.968596810930029, 9.914854428874769, 5.195561411674539]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"Yblue = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"Yred = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"X = [0.23172273, 6.26163653, 4.60102479, 1.66013291, 1.20244506,\n 4.74655952, 4.9280745 , 5.25073788, 1.77052015, 5.34931171,\n 4.55729522, 6.82977892, 4.41371041, 7.69073516, 7.34385488,\n 8.80435781, 9.43113132, 4.96859681, 9.91485443, 5.19556141]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":97,"value":"Y = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W47","stdlib":"1"}} 46:"$45:body"