40:null 41:["$","title",null,{"children":"Logistic Regression | Gwennyth Melvin's Workspace | Observable"}] 47:[] 45:{"id":"fcca06abb5fd27db","slug":null,"title":"Logistic Regression","thumbnail":"e36efe567f84080085facb32ae6b38ac0d6b92376e2e7454292e66418fa06f59","access_level":"public","create_time":"$D2023-10-03T12:08:41.415Z","update_time":"$D2023-10-24T12:38:35.632Z","view_time":null,"first_public_time":"$D2023-10-03T12:08:41.415Z","has_unpublished_edits":null,"fork":{"id":"f5958ccb5dee020e","slug":null,"title":"Logistic Regression","owner":{"id":"66151b62b45d9fca","login":"credmond","name":"Charles Redmond"}},"stars":0,"starred":false,"owner":{"type":"team","id":"0a54ca9c65d05895","login":"gwennyth-melvin-ws","name":"Gwennyth Melvin's Workspace","avatar_url":"https://avatars-next.observableusercontent.com/056cc5c99803c028db2d3ce53e3250fe6d931299c17df2f8bd1d67cbeee185d5","tier":"starter_2024","bio":"","following":false},"version":205,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"63807ceead5e218f","login":"gwennyth-melvin","name":"Gwennyth Melvin","avatar_url":"https://avatars-next.observableusercontent.com/8249abe263fde5ff1d00d97b572238491626d5e13f6c2a567ba2d9fe0f1a1a4f","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"63807ceead5e218f","login":"gwennyth-melvin","name":"Gwennyth Melvin","avatar_url":"https://avatars-next.observableusercontent.com/8249abe263fde5ff1d00d97b572238491626d5e13f6c2a567ba2d9fe0f1a1a4f","tier":null,"role":"editor"},{"type":"team","id":"0a54ca9c65d05895","login":"gwennyth-melvin-ws","name":"Gwennyth Melvin's Workspace","avatar_url":"https://avatars-next.observableusercontent.com/056cc5c99803c028db2d3ce53e3250fe6d931299c17df2f8bd1d67cbeee185d5","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Logistic Regression","cells":[{"id":0,"value":"# Logistic Regression","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":136,"value":"viewof threshold = Inputs.range([0,10],{step:.1})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"### Confusion matrix ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":160,"value":"html`\n\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\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"Plot.plot({\n x:{domain:[0,10]},\n y:{domain:[0,1]},\n marks:[\n Plot.ruleX([0]),\n Plot.ruleY([0]),\n Plot.dot(Xblue,{x:Xblue,y:Yblue,fill:\"blue\",r:5}), //ln(1-Yhat) blue (for blue points, y=0) - loss. do this to each\n Plot.dot(Xred,{x:Xred,y:Yred,fill:\"red\",r:5}), //ln(Yhat) red (for red points, y=1) point & avg to get loss\n Plot.line([[threshold,0],[threshold,1]],{strokeDasharray:\"5,5\"}), //log-loss\n Plot.line(x,{x:x,y:y,stroke:\"red\"}),\n Plot.line([[0,.5],[10,.5]],{strokeDasharray:\"5,5\"}),\n Plot.dot(X,{x:X,y:Yhat,fill:\"green\",r:5}) // loss - probabilities of being positive (green points) \n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"### Sigmoid","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":170,"value":"x = {\n const x = []\n for(let i = 0; i <= 10; i+=.1){\n x.push(i)\n }\n return x\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"f = (x,a,b) => Math.exp(a*x + b)/(1+Math.exp(a*x + b))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":174,"value":"y = x.map(x => f(x,0.79000056,-4.18321431))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":183,"value":"### The Loss","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":192,"value":"Yhat = X.map(X => f(X,0.79000056,-4.18321431))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"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 \n \n ) // -'s needed added to make sure the loss (below) was positive. otherwise it should be negative","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":200,"value":"d3.mean(penalties) ","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":143,"value":"### Positives and Negatives","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":145,"value":"trueNegatives = Xblue.filter(x => x <= threshold).length // lists how many points are left of the line; true negatives","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"falsePositives = Xblue.filter(x => x > threshold).length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":154,"value":"falseNegatives = Xred.filter(x => x <= threshold).length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"truePositives = Xred.filter(x => x > threshold).length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"### Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":124,"value":"Xblue = [0.23172273283556077, 6.261636528327473, 4.6010247891667335, 1.660132912093145, 1.2024450601909025, 4.746559515821619, 4.9280744954032425, 5.250737883974269, 1.7705201542833398, 5.349311712251664]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"Xred = [4.557295223920891, 6.8297789235508315, 4.413710405238934, 7.690735156159806, 7.343854883275675, 8.804357813742223, 9.431131316191179, 4.968596810930029, 9.914854428874769, 5.195561411674539]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"Yblue = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"Yred = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":187,"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":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":188,"value":"Y = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] // this x and y are the red and blues combined, used only for finding the loss. 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