31:Tae7,Many of the fancy Machine Learning algorithms you've already learned in other classes work in such a way that the classification decisions (binary predictions) that they arrive at, for a given observation with feature vector ${tex`\mathbf{x}_i`}, are either **explicitly** or **implicitly** based on the following two-step process: 1. Learn a single **real-valued "risk score"** ${tex`r(\mathbf{x}_i)`} (as some combination of the available **features** for each observation), then 2. Apply a **threshold** ${tex`t`} to this risk score to determine the final 0/1 classification, such that ${tex.block` \hat{y} = \begin{cases}0 &\text{if }r(\mathbf{x}_i) < t, \\ 1 &\text{if }r(\mathbf{x}_i) \geq t \end{cases} `} **Support Vector Machines**, for example, have an "implicit" risk-scoring function and threshold value which you can derive mathematically, but **Logistic Regression** is the most straightforward case, since it computes this score **ex**plicitly: you can directly ask e.g. `scikit-learn` for a trained model's pre-binary-prediction "score" ${tex.block` \Pr(Y = 1 \mid \mathbf{x}_i) = \frac{\exp[{\boldsymbol\beta}^{\top}\mathbf{x}_i]}{1 + \exp[\boldsymbol\beta^{\top}\mathbf{x}_i]}, `} from which you can then derive an actual **binary prediction** based on whether this value is above or below some threshold ${tex`t`}. A person's [**credit score**](https://consumer.ftc.gov/articles/free-credit-reports) in the US is intended to work in a similar way: there are three major "credit bureaus" (an odd alternative name for these *profit-maximizing, publicly-traded corporations*) — Equifax, Experian, and TransUnion — who crunch a bunch of **features** together via some process that results in a **score between 300 and 850** (a score which magically goes up if you [provide them with more data](https://www.experian.com/credit/score-boost/) that they then sell, or... sometimes they just [leak it](https://www.ftc.gov/enforcement/refunds/equifax-data-breach-settlement), whoopsies). Banks then base their loan decisions on these credit scores via the same kind of "thresholding rule": people whose credit scores are **below** some threshold ${tex`t`} are rejected when they apply for a loan. In this problem you'll explore: 1. How any US bank's profit-maximizing decision "may be" (...is literally guaranteed to be) discriminatory, given existing racial and gendered gaps in credit scores, and then 2. How three of the most popular "fairness" measures **constrain** this profit-maximizing decision in different ways to try and ameliorate these credit score gaps... ***(Your job is then to think, after the midterm and on your own terms*** 😉 ***about the extent to which these measures may succeed or fail to achieve this goal in practice!)***32:T448,## Question 4.1: Is a "Race Blind" Threshold Profit Maximizing? Like we did at the beginning of our fairness-measures journey (in HW1), let's start with the notion of **"fairness through unawareness":** can we achieve fairness by simply restricting the bank from **"explicitly"** utilizing a **race** feature as a direct determinant of their loan decisions? For the midterm itself, we've set the parameters of this simplified model such that: * If the loan is a **true positive** (where an individual is approved, then pays it back with a pre-specified amount of interest), the bank **makes $300** * If the loan is a **false positive** (an individual is approved but does not end up paying back the loan), the bank **loses $700** *(Feel free to change these values after the midterm, to explore whether different choices might affect what you find here!)* Based on this setup, use the **slider** immediately above the stacked dot plot to find the **threshold score which maximizes profits** in this "race blind" setup, then record your answer in the **Colab notebook cell for Question 4.1**.33:Tb46,Now, the "hidden" element here is that, each of the individuals in this simulated dataset **also** have an (employer-observable) **race** variable. So, this is where HW1 comes in: **if** the algorithm is able to use a bunch of other variables to "recover" race with close-to-perfect accuracy, can the company make a greater profit than the amount you found in Q4.1? Note, by looking at the two stacked-dot histograms (or you can dig into the code and find the parameters if you'd prefer!), that the data here (which is just the data from above re-grouped by race) has some surprising properties, in terms of... where exactly the "unfairness" comes from: * Both white and black applicants are modeled as having the ***same* mean credit score, ${tex`\mu_0 = \mu_1 = 575`}**. So the "unfairness" isn't emerging from differences in mean credit scores. * The mean credit scores for the **subtypes within both races** (defaulters vs. payers) are also **symmetric** about the overall race-specific mean value (the white-defaulter mean is the same distance from the overall white mean as the white-payer mean, and the black-defaulter mean is the same distance from the overall black mean as the black-payer mean). This means that, the "unfairness" also isn't coming from e.g. black defaulters being modeled as "worse" than white defaulters, credit-score-wise. * *(In fact, the same result here holds even if the **standard deviation** of all four distributions is set to a single constant: after the midterm you can dig into the code and change all these values to to ${tex`\sigma_{00} = \sigma_{01} = \sigma_{10} = \sigma_{11}`} to see this; it just becomes harder to visually "intuit" the result from the histograms in that case!)* Thus, if profit maximization in this scenario *does* give rise to a discriminatory outcome, it is **not** due to higher/lower mean credit scores, nor due to differently "skewed" distributions. This illustrates how even just having **worse predictions** of credit-worthiness between races (which could arise, for example, from simply having fewer observations ${tex`n_1 < n_0`}, due to less entry into the credit market relative to whites) is sufficient for this discrimination to arise, even i of the "true" expected Use the **two** sliders in this case – one for black applicants and one for white applicants – to check: find the greatest profit level attainable by the company **if** they're able to use a collection of non-racial characteristics to **infer** an applicant's race, then record what you find in the **Colab notebook cell for Question 4.2**. *Remember that, if they **are** able to increase profits relative to Q4.1 in this case, some constraint that is **more strict than "dropping" race** will be necessary (if we indeed want to prevent the discrimination which comes automatically with profit-maximization plus unequal-base-rates)*34:T12aa,viewof raceBlindHist = Plot.plot({ width: 580, height: 580 * (50 / 100), marginTop: 54, // marginLeft: 55, // marginRight: 55, x: { label: "Credit Score", domain: [300, 850], }, y: { // axis: false, grid: true, label: null, // domain: [0, 10], // interval: 1, }, color: { legend: true, type: "categorical", domain: [0,1], tickFormat: (d) => d == 1 ? "Future Repayer" : "Future Defaulter", // range: ['x','y'], // title: "Would Pay Back", }, marks: [ Plot.dot( distExamplesCombined.items, Plot.stackY2( Plot.binX( { y: 'count', // filter: null, // filter: null, // title: (d)=>d fillOpacity: (d,e) => e.x1 >= trb ? 1.0 : 0.3, }, { x: { value: d => d.score, // interval: 10, // thresholds: 50, thresholds: d3.range(300, 850, 10), }, z: (_, i) => i, // z: "value", // y: (d) => d.value === 1 ? 1 : -1, // stroke: 'value', fill: "value", // fillOpacity: (d) => (d < trb) ? 0.9 : 0.1, stroke: 'grey', strokeOpacity: 0.9, // inset: 5, }, // End binX 2nd arg ), // End binX() ), // End stackY2() ), // End Plot.dot() Plot.ruleY([0]), Plot.rectX( distExamplesCombined.items, Plot.pointerX( Plot.binX( { }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, fill: 'grey', fillOpacity: 0.5, insetTop: -5, } ), // end binX ), // end pointer ), // end ruleX Plot.textX( distExamplesCombined.items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -15, dx: 6, text: (d) => `${d.filter(d=>d.value==1).length}`, fill: '#e69f00', fontSize: 11, fontWeight: 600, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distExamplesCombined.items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -15, dx: -6, text: (d) => `${d.filter(d=>d.value==0).length}`, fill: '#56b4e9', fontSize: 11, fontWeight: 600, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distExamplesCombined.items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -30, text: (d) => `${d.length}`, fill: 'black', textDecoration: "underline", fontVariant: "underline", fontStyle: "bold", fontWeight: 800, fontSize: 15, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distExamplesCombined.items, Plot.pointerX( Plot.binX( { // filter: null, // This is... amazing lol. For future use... // text: d => `${d.map(d2=>d2.value)}`, text: (d,e) => `[${e.x1}-${e.x2}]`, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -45, // text: (d) => `${d.x}`, fill: 'black', textDecoration: "underline", fontVariant: "underline", fontStyle: "bold", // fontWeight: 800, fontSize: 11, } ), // end binX ), // end pointerX ), // end textX Plot.ruleX([trb], { strokeWidth: 2, clip: false, insetTop: -5, }), ] })35:T12a4,viewof a0Hist = Plot.plot({ width: 550, height: 550 * (35 / 100), marginTop: 54, marginLeft: 55, // marginRight: 55, x: { label: "Credit Score", domain: [300, 850], }, y: { axis: true, grid: true, domain: [0, 15], label: null, // interval: 1, }, color: { legend: true, type: "categorical", domain: [0,1], tickFormat: (d) => d == 1 ? "White Repayer" : "White Defaulter", // range: ['x','y'], // title: "Would Pay Back", }, marks: [ Plot.dot( distributionExamples[0].items, Plot.stackY2( Plot.binX( { y: 'count', // filter: null, // filter: null, // title: (d)=>d fillOpacity: (d,e) => e.x1 >= ta0 ? 0.95 : 0.3, }, { x: { value: d => d.score, // interval: 10, // thresholds: 50, thresholds: d3.range(300, 850, 10), }, z: (_, i) => i, // z: "value", // y: (d) => d.value === 1 ? 1 : -1, // stroke: 'value', fill: "value", // fillOpacity: (d) => (d < trb) ? 0.9 : 0.1, stroke: 'grey', strokeOpacity: 0.9, // inset: 5, }, // End binX 2nd arg ), // End binX() ), // End stackY2() ), // End Plot.dot() Plot.ruleY([0]), Plot.rectX( distributionExamples[0].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 9.55, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, fill: 'grey', fillOpacity: 0.5, } ), // end binX ), // end pointer ), // end ruleX Plot.textX( distributionExamples[0].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -12, dx: 6, text: (d) => `${d.filter(d=>d.value==1).length}`, fill: '#e69f00', fontSize: 11, fontWeight: 600, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distributionExamples[0].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -12, dx: -6, text: (d) => `${d.filter(d=>d.value==0).length}`, fill: '#56b4e9', fontSize: 11, fontWeight: 600, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distributionExamples[0].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -27, text: (d) => `${d.length}`, fill: 'black', textDecoration: "underline", fontVariant: "underline", fontStyle: "bold", fontWeight: 800, fontSize: 15, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distributionExamples[0].items, Plot.pointerX( Plot.binX( { // filter: null, // This is... amazing lol. For future use... // text: d => `${d.map(d2=>d2.value)}`, text: (d,e) => `[${e.x1}-${e.x2}]`, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -41, // text: (d) => `${d.x}`, fill: 'black', textDecoration: "underline", fontVariant: "underline", fontStyle: "bold", // fontWeight: 800, fontSize: 11, } ), // end binX ), // end pointerX ), // end textX Plot.ruleX([ta0], { strokeWidth: 2, }), ] })36:T12a4,viewof a1Hist = Plot.plot({ width: 550, height: 550 * (35 / 100), marginTop: 54, marginLeft: 55, // marginRight: 55, x: { label: "Credit Score", domain: [300, 850], }, y: { axis: true, grid: true, domain: [0, 15], label: null, // interval: 1, }, color: { legend: true, type: "categorical", domain: [0,1], tickFormat: (d) => d == 1 ? "Black Repayer" : "Black Defaulter", // range: ['x','y'], // title: "Would Pay Back", }, marks: [ Plot.dot( distributionExamples[1].items, Plot.stackY2( Plot.binX( { y: 'count', // filter: null, // filter: null, // title: (d)=>d fillOpacity: (d,e) => e.x1 >= ta1 ? 0.95 : 0.3, }, { x: { value: d => d.score, // interval: 10, // thresholds: 50, thresholds: d3.range(300, 850, 10), }, z: (_, i) => i, // z: "value", // y: (d) => d.value === 1 ? 1 : -1, // stroke: 'value', fill: "value", // fillOpacity: (d) => (d < trb) ? 0.9 : 0.1, stroke: 'grey', strokeOpacity: 0.9, // inset: 5, }, // End binX 2nd arg ), // End binX() ), // End stackY2() ), // End Plot.dot() Plot.ruleY([0]), Plot.rectX( distributionExamples[1].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 9.55, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, fill: 'grey', fillOpacity: 0.5, } ), // end binX ), // end pointer ), // end ruleX Plot.textX( distributionExamples[1].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -12, dx: 6, text: (d) => `${d.filter(d=>d.value==1).length}`, fill: '#e69f00', fontSize: 11, fontWeight: 600, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distributionExamples[1].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -12, dx: -6, text: (d) => `${d.filter(d=>d.value==0).length}`, fill: '#56b4e9', fontSize: 11, fontWeight: 600, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distributionExamples[1].items, Plot.pointerX( Plot.binX( { // y1: () => 0, // y2: () => 10, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -27, text: (d) => `${d.length}`, fill: 'black', textDecoration: "underline", fontVariant: "underline", fontStyle: "bold", fontWeight: 800, fontSize: 15, // z: (_, i) => i, // tip: true, // anchor: "bottom", // frameAnchor: 'bottom', } ), ), ), Plot.textX( distributionExamples[1].items, Plot.pointerX( Plot.binX( { // filter: null, // This is... amazing lol. For future use... // text: d => `${d.map(d2=>d2.value)}`, text: (d,e) => `[${e.x1}-${e.x2}]`, }, { x: {value: d => d.score, thresholds: d3.range(300, 850, 10)}, // fill: 'value', frameAnchor: "top", dy: -41, // text: (d) => `${d.x}`, fill: 'black', textDecoration: "underline", fontVariant: "underline", fontStyle: "bold", // fontWeight: 800, fontSize: 11, } ), // end binX ), // end pointerX ), // end textX Plot.ruleX([ta1], { strokeWidth: 2, }), ] })37:T465,columns = (args) => { const form = html`` form.value = {} let cols = 0 for (const key in args) { let cur_child = args[key]; console.log(Object.keys(args).length); if (Object.keys(args).length > 1) { cur_child.style = `padding: 5px; margin-top: 5px; margin-bottom: 5px;` } else { cur_child.style = `padding: 5px;` + ` grid-column:1/span 2;` + ` width:96%;` + ` justify-content:center;` + ` align-text: center;` + ` max-width: 100%;` // + ` display: flex;` } form.appendChild(cur_child); cols++ } form.style = `display: grid; grid-gap: 10px 15px; grid-template-columns: repeat(${cols}, auto); grid-auto-flow: dense; width:100%` // form.style = `display: grid; grid-gap: 5px 5px; grid-template-columns: repeat(${cols}, 48%); grid-auto-flow: dense; width:100%; height:100%; padding:5px;` form.oninput = () => { form.value = Object.keys(args).reduce((result, key) => { result[key] = args[key].value return result }, Array.isArray(args) ? [] : {}) } form.oninput() return form }38:T48c,function genInputGrid(views, names, args) { const spaceOnLeft = "margin-left: 12px;"; // const spaceOnRight = "margin-right: 20px;"; const cellPadding = "padding-left: 1px; padding-right: 1px;"; const cellBorder = false; const borderStyle = "border: 2px solid darkgrey;"; const widthSettings = `min-width: ${globs.gridCellWidth}; max-width: ${globs.gridCellWidth};`; const form = html`

${views.map( (row, rowIndex) => html`

${row.map( (input, inputIndex) => html`

${input}

` )}

`; form.oninput = () => { const values = views.map(row => row.map(input => input.value)); form.value = values; if (args && args.objOnly) form.value = {}; if (names) { names.forEach((row, i) => row.forEach( (c, j) => values[i][j] != null && (form.value[c] = values[i][j]) ) ); } }; form.oninput(); return form; }39:[] 2f:{"title":"Midterm Part 4: \"Fair\" Threshold Classifiers and Social Welfare","cells":[{"id":0,"value":"# Midterm Part 4: \"Fair\" Threshold Classifiers and Social Welfare\n\n## *DSAN 5450: Data Ethics and Policy, Spring 2026*","pinned":false,"hidden":false,"mode":"md"},{"id":879,"value":"***(Now that midterm is over(!), source for this data/approach is [this visualization](https://research.google.com/bigpicture/attacking-discrimination-in-ml/ ) of the \"Equality of Opportunity\" paper we discussed in class)***","pinned":false,"hidden":false,"mode":"md"},{"id":43,"value":"$31","pinned":false,"hidden":false,"mode":"md"},{"id":85,"value":"$32","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"unawarenessPanel = Inputs.form({\n row0: simpleTwoCol(\n Inputs.form({\n r0c0slider: viewof trb, // divCombine(viewof trb, viewof rbResetButton),\n // r0space: md``,\n r0c0eqn: viewof profitRBEqn,\n // r0c0space: md` `,\n r0c0reset: viewof rbResetButton,\n }),\n viewof rbCMPlot\n ),\n viz: columns({\n vc0: Inputs.form({\n vc00: centerCell(md`**Race-Blind Threshold**`),\n vc01: viewof raceBlindHist,\n }),\n vc1: Inputs.form({\n vc10: centerCell(md`**Race-Blind Profits**`),\n vc11: viewof rbProfitPlot,\n }),\n }),\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":452,"value":"## Question 4.2: Unconstrained Profit Maximization","pinned":false,"hidden":false,"mode":"md"},{"id":662,"value":"$33","pinned":false,"hidden":false,"mode":"md"},{"id":671,"value":"profitDashboard = Inputs.form({\n profitHeader: centerCell(viewof profitEqn),\n r0: simpleTwoCol(\n Inputs.form({\n a0header: simpleTwoCol(\n Inputs.form({\n a0label: centerCell(md`**White Threshold**`),\n a0slider: viewof ta0,\n }),\n viewof a0CMPlot,\n ),\n a0plot: viewof a0Hist,\n }),\n Inputs.form({\n a1header: simpleTwoCol(\n Inputs.form({\n a1label: centerCell(md`**Black Threshold**`),\n a1slider: viewof ta1,\n }),\n viewof a1CMPlot,\n ),\n a1plot: viewof a1Hist,\n }),\n ),\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":862,"value":"## Question 4.3: Demographic Parity","pinned":false,"hidden":false,"mode":"md"},{"id":867,"value":"As mentioned at the end of the previous question, it seems that a **stronger constraint** may therefore be necessary if we want a \"fair\" outcome wherein the \"fairness\" matches with some of our intuitions.\n\nAs a first candidate for one such stronger constraint: in class we briefly discussed **Demographic Parity**, which simplifies to just, the constraint that the **proportion of black applicants approved for loans is *equal to* the proportion of white applicants approved for loans**. (Here, since the number of applicants is equal between the two races, ${tex`n_0 = n_1 = 298`}, this is equivalent to equalizing the **number** approved between races).\n\nIs this constraint satisfiable given the setup here? Re-visit the above cell, using the sliders to see if it is, then answer Question 4.3 in the **Colab notebook**","pinned":false,"hidden":false,"mode":"md"},{"id":864,"value":"## Question 4.4: (Non-Roemerian) Equality of Opportunity","pinned":false,"hidden":false,"mode":"md"},{"id":873,"value":"The final \"fairness\" measure we'll look at is called [\"Equality of Opportunity\"](https://arxiv.org/abs/1610.02413), which was defined in a paper that was brought up in the recorded lecture video, but boils down to be very similar to **demographic parity** except that it demands only that the **true positive rates across races** are equalized. Once more, use the sliders above to see if this constraint is satisfiable, then answer the final piece of Part 4 in your **Colab notebook!**","pinned":false,"hidden":false,"mode":"md"},{"id":11,"value":"## JS Pieces","pinned":false,"hidden":false,"mode":"md"},{"id":154,"value":"### New","pinned":false,"hidden":false,"mode":"md"},{"id":543,"value":"*Race-Blind Histogram Code*","pinned":false,"hidden":false,"mode":"md"},{"id":107,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":540,"value":"*Race-Blind Profit Plot Code*","pinned":false,"hidden":false,"mode":"md"},{"id":350,"value":"viewof rbProfitPlot = Plot.plot({\n width: 580,\n height: 580 * (50/100),\n marginLeft: 80,\n x: {\n domain: [300, 850],\n label: \"Threshold\",\n },\n y: {\n domain: [-120000, 70000],\n label: \"Profit\",\n tickFormat: (value) =>\n value.toLocaleString({\n style: \"currency\",\n currency: \"USD\"\n }),\n },\n color: {\n legend: true,\n domain: [\"Loss\", \"Profit\"],\n range: [negRed, posGreen],\n },\n marks: [\n Plot.line(trbHist, {\n x: 'trbVal',\n y: 'profitVal',\n stroke: 'profitLabel',\n z: null,\n }),\n Plot.dot(trbHist, {\n x: trb,\n y: profitRB,\n fill: 'black',\n r: 5,\n }),\n Plot.dot(trbHist, {\n x: 'trbVal',\n y: 'profitVal',\n fill: 'profitLabel',\n }),\n Plot.ruleY([0], {\n // strokeWidth: 1.5,\n // strokeDasharray: [5],\n }),\n ],\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":545,"value":"*Race-Blind Confusion Matrix Code*","pinned":false,"hidden":false,"mode":"md"},{"id":549,"value":"viewof rbCMPlot = plotConfusionMatrix(rbCM)","pinned":false,"hidden":false,"mode":"ojs"},{"id":675,"value":"*${tex`A=0`} Histogram*","pinned":false,"hidden":false,"mode":"md"},{"id":236,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":727,"value":"*${tex`A = 0`} Confusion Matrix Code*","pinned":false,"hidden":false,"mode":"md"},{"id":725,"value":"viewof a0CMPlot = plotConfusionMatrix(aCM[0])","pinned":false,"hidden":false,"mode":"ojs"},{"id":677,"value":"*${tex`A = 1`} Histogram*","pinned":false,"hidden":false,"mode":"md"},{"id":239,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":733,"value":"*${tex`A = 1`} Confusion Matrix Code*","pinned":false,"hidden":false,"mode":"md"},{"id":735,"value":"viewof a1CMPlot = plotConfusionMatrix(aCM[1])","pinned":false,"hidden":false,"mode":"ojs"},{"id":470,"value":"### Race-Blind Computations","pinned":false,"hidden":false,"mode":"md"},{"id":212,"value":"viewof profitRBEqn = tex`\\pi_{\\text{RB}} = \\$300 \\times (${rbTPCount}\\text{ TP}) - \\$700 \\times (${rbFPCount}\\text{ FP}) = \\boxed{\\color{${profitRBColor}}\\mathbf{${profitRBUnits}${Math.abs(profitRB)}}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":159,"value":"viewof trb = genSlider(tex`\\Large{t_{\\text{RB}}} =`, [300, 850], globs.default_trb);","pinned":false,"hidden":false,"mode":"ojs"},{"id":311,"value":"rbApproved = distExamplesCombined.items.filter(d => d.score > trb)","pinned":false,"hidden":false,"mode":"ojs"},{"id":314,"value":"rbApprovedRepaid = rbApproved.filter(d => d.value == 1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":316,"value":"rbApprovedDefaulted = rbApproved.filter(d => d.value == 0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":525,"value":"rbDenied = distExamplesCombined.items.filter(d => d.score <= trb)","pinned":false,"hidden":false,"mode":"ojs"},{"id":523,"value":"rbDeniedRepayer = rbDenied.filter(d => d.value == 1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":528,"value":"rbDeniedDefaulter = rbDenied.filter(d => d.value == 0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":318,"value":"rbTPCount = rbApprovedRepaid.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":320,"value":"rbFPCount = rbApprovedDefaulted.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":530,"value":"rbTNCount = rbDeniedDefaulter.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":532,"value":"rbFNCount = rbDeniedRepayer.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":535,"value":"rbCM = [\n {'y': 1, 'yhat': 1, 'count': rbTPCount, 'prop': rbTPCount / rbTotal},\n {'y': 0, 'yhat': 1, 'count': rbFPCount, 'prop': rbFPCount / rbTotal},\n {'y': 0, 'yhat': 0, 'count': rbTNCount, 'prop': rbTNCount / rbTotal},\n {'y': 1, 'yhat': 0, 'count': rbFNCount, 'prop': rbFNCount / rbTotal},\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":332,"value":"profitRB = globs.TPProfit * rbTPCount + globs.FPProfit * rbFPCount","pinned":false,"hidden":false,"mode":"ojs"},{"id":340,"value":"profitRBUnits = profitRB < 0 ? `-\\\\$` : `\\\\$`","pinned":false,"hidden":false,"mode":"ojs"},{"id":346,"value":"profitRBColor = profitRB < 0 ? \"red\" : \"black\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":294,"value":"rbTotal = distExamplesCombined.items.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":301,"value":"rbPos = distExamplesCombined.items.filter(d => d.value == 0).length;","pinned":false,"hidden":false,"mode":"ojs"},{"id":304,"value":"rbNeg = rbTotal - rbPos","pinned":false,"hidden":false,"mode":"ojs"},{"id":356,"value":"// trbHist = {\n// return (this || new Set()).concat({trbVal: trb, profitVal: profitRB}).filter((value, index, self) => {\n// return self.indexOf(value) === index;\n// }).toSorted();\n// }\ntrbHist = {\n let preFilter = (this || []).concat({trbVal: trb, profitVal: profitRB, nonNeg: profitRB >= 0, profitLabel: profitRB >= 0 ? \"Profit\" : \"Loss\"});\n let preFilterSet = new Set(preFilter);\n let sortedPostFilter = Array.from(preFilterSet).sort((a, b) => a.trbVal > b.trbVal);\n return sortedPostFilter;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":486,"value":"resetTrbHist = () => {trbHist.length = 0}","pinned":false,"hidden":false,"mode":"ojs"},{"id":375,"value":"emptySet = new Set()","pinned":false,"hidden":false,"mode":"ojs"},{"id":682,"value":"### Race-Threshold Computations","pinned":false,"hidden":false,"mode":"md"},{"id":853,"value":"*Race-specific threshold profit equation*","pinned":false,"hidden":false,"mode":"md"},{"id":740,"value":"viewof profitEqn = tex`\\pi = \\$300 \\times (${aTPTotal}\\text{ TP}) - \\$700 \\times (${aFPTotal}\\text{ FP}) = \\boxed{\\color{${profitAColor}}\\mathbf{${profitAUnits}${Math.abs(profitA)}}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":684,"value":"viewof ta0 = genSlider(tex`\\Large{t_0} =`, [300, 850], globs.default_t0);","pinned":false,"hidden":false,"mode":"ojs"},{"id":687,"value":"viewof ta1 = genSlider(tex`\\Large{t_1} =`, [300, 850], globs.default_t1);","pinned":false,"hidden":false,"mode":"ojs"},{"id":754,"value":"aApproved = [\n distributionExamples[0].items.filter(d => d.score > ta0),\n distributionExamples[1].items.filter(d => d.score > ta1),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":756,"value":"aApprovedRepaid = [\n aApproved[0].filter(d => d.value == 1),\n aApproved[1].filter(d => d.value == 1),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":760,"value":"aApprovedDefaulted = [\n aApproved[0].filter(d => d.value == 0),\n aApproved[1].filter(d => d.value == 0),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":762,"value":"aDenied = [\n distributionExamples[0].items.filter(d => d.score <= ta0),\n distributionExamples[1].items.filter(d => d.score <= ta1),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":764,"value":"aDeniedRepayer = [\n aDenied[0].filter(d => d.value == 1),\n aDenied[1].filter(d => d.value == 1),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":766,"value":"aDeniedDefaulter = [\n aDenied[0].filter(d => d.value == 0),\n aDenied[1].filter(d => d.value == 0),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":768,"value":"aTPCount = [\n aApprovedRepaid[0].length,\n aApprovedRepaid[1].length,\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":791,"value":"aTPTotal = aTPCount[0] + aTPCount[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":770,"value":"aFPCount = [\n aApprovedDefaulted[0].length,\n aApprovedDefaulted[1].length,\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":793,"value":"aFPTotal = aFPCount[0] + aFPCount[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":774,"value":"aTNCount = [\n aDeniedDefaulter[0].length,\n aDeniedDefaulter[1].length,\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":797,"value":"aTNTotal = aTNCount[0] + aTNCount[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":776,"value":"aFNCount = [\n aDeniedRepayer[0].length,\n aDeniedRepayer[1].length,\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":799,"value":"aFNTotal = aFNCount[0] + aFNCount[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":779,"value":"aCM = [\n [\n {'y': 1, 'yhat': 1, 'count': aTPCount[0], 'prop': aTPCount[0] / aTotal[0]},\n {'y': 0, 'yhat': 1, 'count': aFPCount[0], 'prop': aFPCount[0] / aTotal[0]},\n {'y': 0, 'yhat': 0, 'count': aTNCount[0], 'prop': aTNCount[0] / aTotal[0]},\n {'y': 1, 'yhat': 0, 'count': aFNCount[0], 'prop': aFNCount[0] / aTotal[0]},\n ],\n [\n {'y': 1, 'yhat': 1, 'count': aTPCount[1], 'prop': aTPCount[1] / aTotal[1]},\n {'y': 0, 'yhat': 1, 'count': aFPCount[1], 'prop': aFPCount[1] / aTotal[1]},\n {'y': 0, 'yhat': 0, 'count': aTNCount[1], 'prop': aTNCount[1] / aTotal[1]},\n {'y': 1, 'yhat': 0, 'count': aFNCount[1], 'prop': aFNCount[1] / aTotal[1]},\n ],\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":783,"value":"aTotal = [\n distributionExamples[0].items.length,\n distributionExamples[1].items.length,\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":802,"value":"profitA = globs.TPProfit * aTPTotal + globs.FPProfit * aFPTotal","pinned":false,"hidden":false,"mode":"ojs"},{"id":804,"value":"profitAUnits = profitA < 0 ? `-\\\\$` : `\\\\$`","pinned":false,"hidden":false,"mode":"ojs"},{"id":807,"value":"profitAColor = profitA < 0 ? \"red\" : \"black\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":152,"value":"### Adapted","pinned":false,"hidden":false,"mode":"md"},{"id":27,"value":"// Set values of true positives vs. false positives.\nprVals = ({\n tprValue: 300,\n fprValue: -700,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"distributionExamples = [\n genDistExample(\n 0, 690, 55, 460, 55\n ),\n genDistExample(\n 1, 630, 70, 520, 70\n ),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"function combineDists(d1, d2) {\n let dComb = toGroupModel(\n distributionExamples[0].items.concat(distributionExamples[1].items),\n prVals.tprValue,\n prVals.fprValue\n );\n dComb.items.sort((a,b) => a.value < b.value);\n classifyGroupModel(dComb, 575);\n return dComb;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":221,"value":"distExamplesCombined = combineDists(distributionExamples[0], distributionExamples[1])","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"function genDistExample(cat, mu0, sd0, mu1, sd1) {\n let de = toGroupModel(\n makeNormalItems(cat, 1, 150, mu0, sd0).concat(makeNormalItems(cat, 0, 150, mu1, sd1)),\n prVals.tprValue,\n prVals.fprValue\n );\n classifyGroupModel(de, 575);\n return de;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"function classifyGroupModel(gm, threshold) {\n gm.threshold = threshold;\n\n // Classify and find positive rates.\n var totalGood = 0;\n var totalPredictedGood = 0;\n var totalGoodPredictedGood = 0;\n gm.items.forEach(function(item) {\n item.predicted = item.score >= threshold ? 1 : 0;\n });\n gm.tpr = tpr(gm.items);\n gm.positiveRate = positiveRate(gm.items);\n\n // Find profit.\n gm.profit = profit(gm.items, gm.tprValue, gm.fprValue);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"// A group model defines a group of items, with a threshold\n// for a classifier and associated values for true and\n// false positives. It also can notify listeners that an event\n// has occurred to change the model.\ntoGroupModel = (items, tprValue, fprValue) => {\n // Data defining the model.\n return {\n items: items,\n tprValue: tprValue,\n fprValue: fprValue,\n listeners: [],\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"// Profit of a model, subject to the given values\n// for true and false positives. Note that the simple model\n// in the paper assumes zero value for negatives.\nfunction profit(items, tprValue, fprValue) {\n var sum = 0;\n items.forEach(function(item) {\n if (item.predicted == 1) {\n sum += item.value == 1 ? tprValue : fprValue;\n }\n });\n return sum;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":21,"value":"// Create items whose scores have a\n// \"deterministic normal\" distribution. That is, the items track\n// a Gaussian curve. This not the same as actually choosing scores\n// normally, but for expository purposes it's useful to have\n// deterministic, smooth distributions of values.\nfunction makeNormalItems(category, value, n, mean, std) {\n var items = [];\n var error = 0;\n for (var score = 300; score < 850; score++) {\n var e = error + n * Math.exp(-(score - mean) * (score - mean) / (2 * std * std)) /\n (std * Math.sqrt(2 * Math.PI));\n var m = Math.floor(e);\n error = e - m;\n for (var j = 0; j < m; j++) {\n items.push(toItem(category, value, score));\n }\n }\n return items;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"// An item with an intrinsic value, predicted classification, and\n// a \"score\" for use by a threshold classifier.\n// The going assumption is that the values and predicted values\n// are 0 or 1. Furthermore \"1\" is considered a positive/good value.\ntoItem = (category, value, score) => {\n return {\n category: category,\n value: value,\n predicted: value,\n score: score,\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"// Calculate true positive rate\nfunction tpr(items) {\n var totalGood = 0;\n var totalGoodPredictedGood = 0;\n items.forEach(function(item) {\n totalGood += item.value;\n totalGoodPredictedGood += item.value * item.predicted;\n });\n if (totalGood == 0) {\n return 1;\n }\n return totalGoodPredictedGood / totalGood;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":31,"value":"// Calculate overall positive rate\nfunction positiveRate(items) {\n var totalGood = 0;\n items.forEach(function(item) {\n totalGood += item.predicted;\n });\n return totalGood / items.length;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":148,"value":"### Helper Functions","pinned":false,"hidden":false,"mode":"md"},{"id":163,"value":"globs = ({\n default_trb: 850,\n default_t0: 850,\n default_t1: 850,\n TPProfit: 300,\n FPProfit: -700,\n absXMax: 5,\n gridCellWidth: '300px',\n labelWidth: '60px',\n // inputWidth: '60px',\n sliderWidth: 200,\n figHeight: 310,\n margin: {\n top: 20, right: 40, bottom: 40, left: 40\n }\n});","pinned":false,"hidden":false,"mode":"ojs"},{"id":161,"value":"function genSlider(cname, range, defaultVal) {\n var sliderElt = Inputs.range(range, {\n value: defaultVal,\n label: cname,\n width: globs.sliderWidth,\n // format: x => x.toFixed(2),\n step: 10,\n });\n var styleStr = `--label-width: ${globs.labelWidth};`\n // + `width: 100%;`;\n Object.assign(sliderElt, {style: styleStr});\n return(sliderElt);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":617,"value":"simpleTwoCol = (c1, c2) => {\n return html`

${c1}

${c2}

`\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":103,"value":"$37","pinned":false,"hidden":false,"mode":"ojs"},{"id":115,"value":"function centerCell(orig_cell) {\n // let fw_text = full_width ? \"width: 100%;\" : \"\";\n // let border_text = border ? 'border: 1px solid black; margin-top: 5px;' : '';\n return html`

${orig_cell}

`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":573,"value":"function divCombine(cell1, cell2) {\n // let fw_text = full_width ? \"width: 100%;\" : \"\";\n // let border_text = border ? 'border: 1px solid black; margin-top: 5px;' : '';\n return html`

${cell1}

${cell2}

`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":204,"value":"$38","pinned":false,"hidden":false,"mode":"ojs"},{"id":456,"value":"plotConfusionMatrix = (singleCM) => {\n // tn, fp, fn, tp\n let cm_plot = Plot.plot({\n padding: 0,\n height: 140,\n width: 300,\n grid: true,\n x: {\n axis: \"bottom\",\n label: \"Predicted Value\",\n labelArrow: false,\n interval: 1,\n },\n y: {\n label: \"True Value\",\n interval: 1,\n },\n color: {\n // type: \"linear\",\n scheme: \"viridis\",\n // legend: true,\n // domain: [0.2,0.8],\n },\n marks: [\n Plot.cell(singleCM, {\n x: \"yhat\",\n y: \"y\",\n fill: \"prop\",\n inset: 0.5\n }),\n Plot.text(singleCM, {\n x: \"yhat\",\n y: \"y\",\n text: \"prop\",\n fill: (d) => d.prop > 0.6 ? \"black\" : \"white\",\n // className: \"large-font\",\n fontSize: 15,\n })\n ]\n })\n return cm_plot\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":460,"value":"plotConfusionMatrices = (singleCM) => {\n // tn, fp, fn, tp\n let cm_plot = Plot.plot({\n padding: 0,\n height: 350,\n width: 700,\n grid: true,\n x: {\n axis: \"bottom\",\n label: \"Predicted Value\",\n labelArrow: false,\n interval: 1,\n },\n y: {\n label: \"True Value\",\n interval: 1,\n },\n fx: {\n padding: 0.2,\n },\n color: {\n // type: \"linear\",\n scheme: \"viridis\",\n legend: true,\n domain: [0.2,0.8],\n },\n marks: [\n Plot.cell(singleCM, {\n x: \"yhat\",\n y: \"y\",\n fx: \"race\",\n fill: \"prop\",\n inset: 0.5\n }),\n Plot.text(singleCM, {\n x: \"yhat\",\n y: \"y\",\n fx: \"race\",\n text: \"prop\",\n fill: (d) => d.prop > 0.6 ? \"black\" : \"white\",\n className: \"large-font\",\n })\n ]\n })\n return cm_plot\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":494,"value":"function genButton(bLabel, reduceFn) {\n var buttonElt = Inputs.button(bLabel, {\n reduce: reduceFn,\n width: 50,\n });\n var styleStr = ``\n // + `float: right;`\n // + ` width: 100%;`\n + `--label-width: ${globs.labelWidth};`;\n Object.assign(buttonElt, {style: styleStr});\n return(buttonElt);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":481,"value":"viewof rbResetButton = genButton(\"Reset\", resetRBParams);","pinned":true,"hidden":false,"mode":"ojs"},{"id":483,"value":"resetRBParams = () => {\n resetTrbHist();\n set(viewof trb, globs.default_trb);\n};","pinned":false,"hidden":false,"mode":"ojs"},{"id":489,"value":"function set(input, value) {\n input.value = value;\n input.dispatchEvent(new Event(\"input\"));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":438,"value":"### CSS","pinned":false,"hidden":false,"mode":"md"},{"id":440,"value":"hexIntensity = 8","pinned":true,"hidden":false,"mode":"ojs"},{"id":424,"value":"redHex = [\"#fff5f0\",\"#fee3d6\",\"#fdc9b4\",\"#fcaa8e\",\"#fc8a6b\",\"#f9694c\",\"#ef4533\",\"#d92723\",\"#bb151a\",\"#970b13\",\"#67000d\"]","pinned":true,"hidden":false,"mode":"ojs"},{"id":433,"value":"negRed = redHex[hexIntensity]","pinned":true,"hidden":false,"mode":"ojs"},{"id":426,"value":"greenHex = [\"#f7fcf5\",\"#e8f6e3\",\"#d3eecd\",\"#b7e2b1\",\"#97d494\",\"#73c378\",\"#4daf62\",\"#2f984f\",\"#157f3b\",\"#036429\",\"#00441b\"]","pinned":true,"hidden":false,"mode":"ojs"},{"id":435,"value":"posGreen = greenHex[hexIntensity]","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W39","stdlib":"1","titling":"auto"}