class: center, middle, inverse, title-slide .title[ #
Comparing Classifier Performance with Baselines
] .author[ ### Ying-Ju Tessa Chen, PhD
Scholar
|
@ying-ju
|
ychen4@udayton.edu
Joint work with:
Fadel Megahed, PhD
Miami University
Allison Jones-Farmer, PhD
Miami University
Steven E. Rigdon, PhD
Saint Louis University
Martin Krzywinski, PhD
Canada's Michael Smith Genome Sciences Centre
Naomi Altman, PhD
The Pennsylvania State University
] .date[ ### April 11, 2024 | Pi Mu Epsilon Banquet | Dayton OH ] --- ## Outline - Introduction - Understand Baselines - Performance Metrics - Analyzing the Distribution of Baselines - Showcase: Beyond the Basics --- ## Introduction - `Brief overview:` Explore the pivotal role of baselines in machine learning by comparing classifier performance, highlighting the path to more accurate, sensitive, and specific model evaluations. - `Objective:` By the end of this talk, you will: - Be familiar with some commonly used baselines for classification problems. - Understand the key performance metrics used in classifier evaluation. - Learn how these concepts aid in comprehensive model evaluations. --- ## Understand Baselines Baselines are typically generated independently for each dataset using very simple models. - `Goal:` Set the minimum level of acceptable performance and help with comparing relative improvements in performance of other models. **Regression** - `Baseline:` mean of the response variable `\(Y\)` to estimate the response of all observations. - `Performance Metric:` `\(R^2\)` is interpreted as the fraction of observed variance relative to this baseline that is explained by the regression model using at least one predictor. **Classification** - `Uniform Random Predictions:` Sampled with equal probability for each class. - `Proportional Random Predictions:` Sampled with probabilities matching the distribution of class labels in the training dataset. - `Most Frequent Predictions:` Always predict the most frequently observed class in the training dataset. --- ### Example of Commonly Used Baseline Classifiers Three baseline classifiers applied to an imbalanced dataset with 10 diseased and 30 normal cells. <img src="PME2024_files/figure-html/unnamed-chunk-1-1.png" style="display: block; margin: auto;" /> --- ## Performance Metrics <table class="table table-striped table-hover table-condensed table-responsive" style="font-size: 18px; color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th> <th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-size: 18px;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Predicted Condition</div></th> </tr> <tr> <th style="text-align:left;font-weight: bold;font-style: italic;"> </th> <th style="text-align:left;font-weight: bold;font-style: italic;"> Predicted Positive (PP) </th> <th style="text-align:left;font-weight: bold;font-style: italic;"> Predicted Negative (PN) </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Actual Positive (P) </td> <td style="text-align:left;"> True Positive (TP) </td> <td style="text-align:left;"> False Negative (FN) </td> </tr> <tr> <td style="text-align:left;"> Actual Negative (N) </td> <td style="text-align:left;"> False Positive (FP) </td> <td style="text-align:left;"> True Negative (TN) </td> </tr> </tbody> </table> <br> <table class="table table-striped table-hover table-condensed table-responsive" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> Metric </th> <th style="text-align:left;"> Description </th> <th style="text-align:left;"> Formula </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;font-weight: bold;"> Accuracy </td> <td style="text-align:left;width: 45%; "> Overall correctness of the model </td> <td style="text-align:left;width: 35%; "> TP+TN / (TP+TN+FP+FN) </td> </tr> <tr> <td style="text-align:left;font-weight: bold;"> Precision </td> <td style="text-align:left;width: 45%; "> Correctly predicted positive observations to the total predicted positives </td> <td style="text-align:left;width: 35%; "> TP / (TP+FP) </td> </tr> <tr> <td style="text-align:left;font-weight: bold;"> Sensitivity (Recall) </td> <td style="text-align:left;width: 45%; "> Correctly predicted positive observations to all observations in actual positive class </td> <td style="text-align:left;width: 35%; "> TP / (TP+FN) </td> </tr> <tr> <td style="text-align:left;font-weight: bold;"> Specificity </td> <td style="text-align:left;width: 45%; "> Correctly predicted negative observations to all observations in actual negative class </td> <td style="text-align:left;width: 35%; "> TN / (TN+FP) </td> </tr> <tr> <td style="text-align:left;font-weight: bold;"> F1 Score </td> <td style="text-align:left;width: 45%; "> Weighted average of Precision and Recall </td> <td style="text-align:left;width: 35%; "> 2 * (Recall * Precision) / (Recall + Precision) </td> </tr> </tbody> </table> --- ### Comparing Performance Metrics: Balanced vs. Imbalanced Data Performance metrics of various baselines. a, A balanced dataset (50 normal and 50 diseased cells). b, An imbalanced dataset (90 normal and 10 diseased cells). <img src="PME2024_files/figure-html/unnamed-chunk-4-1.png" style="display: block; margin: auto;" /> --- ## Distribution of Baselines <img src="PME2024_files/figure-html/unnamed-chunk-5-1.png" style="display: block; margin: auto;" /> .footnote[Distribution of uniform and proportional baseline performance metrics for an imbalanced dataset. Based on 10,000 iterations of a dataset with 100 observations (90 normal and 10 diseased cells). Vertical lines show medians. The distribution for some metrics can be enumerated and/or approximated.] --- ## Showcase: Beyond the Basics - Consider the study where the health of 2,126 fetuses was classified as normal, suspect, or pathological based on several measurable predictor variables. .footnote[Bernardes, J., A. Garrido, and L. Pereira-Leite. "SisPorto 2.0: A program for automated analysis of cardiotocograms." J. Matern. Fetal. Med. 9, no. 5 (2000): 311-318.] - The fetuses' health was predicted using linear discriminant analysis (LDA), while a trained obstetrician determined the ground truth health class. - LDA aims to find a linear combination of features that separates two or more classes of objects or events with the highest possible accuracy. - LDA incorporates the costs of misclassification as well as the prior probabilities of category membership and determines the classification rules to minimize the cost. - `Advantages:` It is relatively simple to understand and implement, performs well even on small datasets, and is particularly effective when the classes exhibit a Gaussian distribution. --- ### Confusion matrix for fetal health classification <table> <thead> <tr> <th colspan="2"></th> <th colspan="3" style="text-align:center;">Predicted with LDA</th> <th></th> </tr> <tr> <td colspan="2"></td> <td>Normal</td> <td>Suspect</td> <td>Pathological</td> <td>Total</td> </tr> </thead> <tbody> <tr> <td rowspan="3" style="vertical-align:middle;"><strong>Ground Truth</strong></td> <td>Normal</td> <td>1,584</td> <td>53</td> <td>18</td> <td>1,655</td> </tr> <tr> <td>Suspect</td> <td>146</td> <td>139</td> <td>10</td> <td>295</td> </tr> <tr> <td>Pathological</td> <td>24</td> <td>53</td> <td>99</td> <td>176</td> </tr> <tr> <td></td> <td>Total</td> <td>1,754</td> <td>245</td> <td>127</td> <td>2,126</td> </tr> </tbody> </table> <br> - Sensitivity: - normal: 1584/1655 = 0.957 - suspect: 139/295 = 0.471 - pathological: 99/176 = 0.562 --- ### Two baselines and LDA sensitivity for each fetal health class .footnote[Vertical lines show medians.] <img src="PME2024_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" /> --- ## Discussion and Concluding Remark **Importance of Correct Baseline:** - Accounts for expected class distribution and sampling variability. - Essential for dealing with class imbalance. **Choosing the Baseline:** - Selection should be judicious, especially in the presence of class imbalance. - The exact baseline value can be derived from a specific percentile of the baseline model's sampling distribution (For example, 95th percentile). --- ### Discussion and Concluding Remark (Continued) **Appropriate Baseline Selection:** - The proportional baseline is most suitable when sample class proportions reflect the population accurately. - For rare diseases, the most frequent baseline may be preferred. - Forgoing testing in cases where disease prevalence is low and testing is costly can act as an implicit most-frequent model application. **Risks of Not Using a Baseline:** - Absence of a baseline, typical fixed reference values (for example, even chance) can easily result in misleading performance assessments (and training), class distribution and sampling variability. --- > `All animals are equal, but some animals are more equal than others. - George Orwell` <br><br> <img src="./figs/animals2.png" width="450px" style="display: block; margin: auto;" /> --- ## References - Megahed, Fadel M., Ying-Ju Chen, L. Allison Jones-Farmer, Steven E. Rigdon, Martin Krzywinski, and Naomi Altman. "Comparing classifier performance with baselines." [Nature Methods](https://www.nature.com/articles/s41592-024-02234-5) (2024). - [App](http://rstudio.fsb.miamioh.edu:3838/megahefm/metric_interpretation/) for the study. - [Supplementary](https://fmegahed.github.io/research/classification/metrics_variability.html) - R package [basemodels](https://cran.r-project.org/web/packages/basemodels/index.html) --- ## Thank You! .pull-left[ <br> <br> - Please do not hesitate to contact me (Tessa Chen) at <a href="mailto:ychen@udayton.edu"><i class="fa fa-paper-plane fa-fw"></i> ychen4@udayton.edu</a> for questions or further discussions. ] .pull-right[ <img src="./figs/Tessa_grey_G.gif" width="60%" style="display: block; margin: auto;" /> ] --- class: center, middle, inverse, title-slide .title[ # <p>Comparing Classifier Performance with Baselines</p> ] .author[ ### Ying-Ju Tessa Chen, PhD <br>[<svg viewBox="0 0 488 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M488 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d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"></path></svg> ychen4@udayton.edu](mailto:ychen4@udayton.edu)</br><br><u><b><font color="white">Joint work with:</b></u><br>Fadel Megahed, PhD [<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"></path></svg> Miami University](https://miamioh.edu/fsb/directory/?up=/directory/megahefm)<br/>Allison Jones-Farmer, PhD [<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"></path></svg> Miami University](https://miamioh.edu/fsb/directory/?up=/directory/farmerl2)<br/>Steven E. Rigdon, PhD [<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"></path></svg> Saint Louis University](https://www.slu.edu/public-health-social-justice/faculty/rigdon-steven.php)<br/>Martin Krzywinski, PhD [<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"></path></svg> Canada's Michael Smith Genome Sciences Centre](https://mk.bcgsc.ca/)<br/>Naomi Altman, PhD [<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"></path></svg> The Pennsylvania State University](https://science.psu.edu/stat/people/nsa1)<br><br/> ] .date[ ### April 11, 2024 | Pi Mu Epsilon Banquet | Dayton OH ]