Cumulative accuracy profile: Difference between revisions
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A '''cumulative accuracy profile''' (CAP) is a concept utilized in [[data science]] to visualize [[discrimination power]]. The CAP of a model represents the cumulative number of positive outcomes along the ''y''-axis versus the corresponding cumulative number of a classifying parameter along the ''x''-axis. The output is called a CAP curve.<ref>{{Cite web|title=CUMULATIVE ACCURACY PROFILE AND ITS APPLICATION IN CREDIT RISK|url=https://www.linkedin.com/pulse/cumulative-accuracy-profile-its-application-credit-frm-prm-cma-acma|access-date=2020-12-11|website=www.linkedin.com|language=en}}</ref> The CAP is distinct from the [[receiver operating characteristic]] (ROC) curve, which plots the [[true-positive rate]] against the [[false-positive rate]]. |
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CAPs are used in robustness evaluations of classification models. |
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==Example== |
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Imagine you are a saleswoman or a salesman at a store selling clothes. The store has a total of 100,000 customers, which we place on the horizontal axis. Based on your observations, every time you offer your customers a deal, almost only 10% of them respond and buy the product, which means that 10% of the total (10,000) is placed on the vertical axis. Now we've got a proposal that we want to offer, and we want to see how many customers are going to purchase our product by drawing a line that will represent the random selection. The slope of the line equal to the 10% that we know responds on average to an offer as if we just send them out like that. Now the questions are, can we somehow improve this experience? Can we get more customers to respond to offers? Can we somehow target our customers more appropriately to get a better response rate? How about instead of sending out these offers randomly, to say a random sample of 20000 customers, how could we pick and choose the customer we send these offers to? How do we pick and choose? To start with, we will build a model. A customer segmentation model demographic segmentation model but which wants to predict whether or not they will leave the company will predict whether or not they will purchase the product. It's a very simple process. It's the same thing because purchased is also a binary variable yes or no. And we can also run the same experiment and we can take a group of customers before we send out the offer and then look back and see who purchased whether male or female, Which country were they in what age predominately were they browsing on mobile were they browsing via a computer and all of these factors we can take them into account them put them into a logistic regression and get a model which will help us assess the likelihood of certain types of customers purchasing based of their characteristics or the general demographic status and other characteristics. |
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[[File:Cap curve.png|thumb|The CAP Curve for the perfect, good and random model predicting the buying customers from a pool of 100000 individuals.]] |
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Once we have built this model we apply it to a select customer and send the offer to a female customer of a bank whose favorite color is red. They're most likely to leave the bag and we will have a similar result. Say perhaps a male customer in this certain age group who is most likely to purchase a mobile or something else if it will tell us something or it will actually rank our Customers. We 'll give them probability of purchasing and we use the portability to contact your customer, of course, we contact we get zero response, then if we contact 20000 we'll probably get a much higher response rate than just 2000 because we're contacted 2000. Our response rate will be higher than 4000 which we get in this random scenario. If our model is good, by the time we're at around 60 thousand or more we are really getting to that 10000 mark so we get 10000 people. So now this draws a line through these crosses. So what you see here is called the cumulative accuracy profile of your model. |
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==Analyzing a CAP== |
==Analyzing a CAP== |
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A cumulative accuracy profile can be used to evaluate a model by comparing the current curve to both the 'perfect' and a randomized curve. A good model will have a CAP between the perfect and random curves; the closer a model is to the perfect CAP, the better it is. |
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The accuracy ratio (AR) is defined as the ratio of the area between the model CAP and |
The accuracy ratio (AR) is defined as the ratio of the area between the model CAP and random CAP, and the area between the perfect CAP and random CAP.<ref>{{Citation |
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| first = Raffaella |
| first = Raffaella |
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| last = Calabrese |
| last = Calabrese |
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| year = 2009 |
| year = 2009 |
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| place = Geneva, Switzerland |
| place = Geneva, Switzerland |
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| url = http://www.statoo.ch/jss09/presentations/Calabrese.pdf }}</ref> |
| url = http://www.statoo.ch/jss09/presentations/Calabrese.pdf }}</ref> In a successful model, the AR has values between zero and one, and the higher the value is, the stronger the model. |
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Another indication of a model's strength is given by the cumulative number of positive outcomes at 50% of the classifying parameter. For a successful model, this value should lie between 50% and 100% of the maximum, with a higher percentage for stronger models. |
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The cumulative number of positive outcomes indicates a model's strength. For a successful model, this value should lie between 50% and 100% of the maximum, with a higher percentage for stronger models. In sporadic cases, the accuracy ratio can be negative. In this case, the model is performing worse than the random CAP. |
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==Applications== |
==Applications== |
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The cumulative accuracy profile (CAP) and ROC curve are both commonly used by banks and regulators to analyze the discriminatory ability of rating systems that evaluate credit risks.<ref>{{Citation |
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| last1 =Engelmann |
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| first1 =Bernd |
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| last2 =Hayden |
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| first2 =Evelyn |
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| journal =Discussion Paper |
| journal =Discussion Paper |
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| volume =Series 2: Banking and Financial Supervision |
| volume =Series 2: Banking and Financial Supervision |
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| issue = |
| issue = 1 |
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| date =2003}}</ref> |
| date =2003}}</ref><ref>{{Citation |
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| last1 =Sobehart |
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<ref>{{Citation |
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| first1 =Jorge |
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| first =Jorge |
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| last2 =Keenan |
| last2 =Keenan |
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| journal =Moody's Risk Management Services |
| journal =Moody's Risk Management Services |
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| date =2000-05-15 |
| date =2000-05-15 |
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| url = http://www.rogermstein.com/wp-content/uploads/SobehartKeenanStein2000.pdf }}</ref> |
| url = http://www.rogermstein.com/wp-content/uploads/SobehartKeenanStein2000.pdf }}</ref> The CAP is also used by instructional design engineers to assess, retrain and rebuild instructional design models used in constructing courses, and by professors and school authorities for improved decision-making and managing educational resources more efficiently. |
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== References == |
== References == |
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Latest revision as of 13:43, 28 March 2024
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A cumulative accuracy profile (CAP) is a concept utilized in data science to visualize discrimination power. The CAP of a model represents the cumulative number of positive outcomes along the y-axis versus the corresponding cumulative number of a classifying parameter along the x-axis. The output is called a CAP curve.[1] The CAP is distinct from the receiver operating characteristic (ROC) curve, which plots the true-positive rate against the false-positive rate.
CAPs are used in robustness evaluations of classification models.
Analyzing a CAP
[edit]A cumulative accuracy profile can be used to evaluate a model by comparing the current curve to both the 'perfect' and a randomized curve. A good model will have a CAP between the perfect and random curves; the closer a model is to the perfect CAP, the better it is.
The accuracy ratio (AR) is defined as the ratio of the area between the model CAP and random CAP, and the area between the perfect CAP and random CAP.[2] In a successful model, the AR has values between zero and one, and the higher the value is, the stronger the model.
The cumulative number of positive outcomes indicates a model's strength. For a successful model, this value should lie between 50% and 100% of the maximum, with a higher percentage for stronger models. In sporadic cases, the accuracy ratio can be negative. In this case, the model is performing worse than the random CAP.
Applications
[edit]The cumulative accuracy profile (CAP) and ROC curve are both commonly used by banks and regulators to analyze the discriminatory ability of rating systems that evaluate credit risks.[3][4] The CAP is also used by instructional design engineers to assess, retrain and rebuild instructional design models used in constructing courses, and by professors and school authorities for improved decision-making and managing educational resources more efficiently.
References
[edit]- ^ "CUMULATIVE ACCURACY PROFILE AND ITS APPLICATION IN CREDIT RISK". www.linkedin.com. Retrieved 2020-12-11.
- ^ Calabrese, Raffaella (2009), The validation of Credit Rating and Scoring Models (PDF), Swiss Statistics Meeting, Geneva, Switzerland
{{citation}}: CS1 maint: location missing publisher (link) - ^ Engelmann, Bernd; Hayden, Evelyn; Tasche, Dirk (2003), "Measuring the Discriminative Power of Rating Systems", Discussion Paper, Series 2: Banking and Financial Supervision (1)
- ^ Sobehart, Jorge; Keenan, Sean; Stein, Roger (2000-05-15), "Validation methodologies for default risk models" (PDF), Moody's Risk Management Services