{"id":4733,"date":"2025-11-17T22:11:47","date_gmt":"2025-11-17T22:11:47","guid":{"rendered":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/?page_id=4733"},"modified":"2025-11-17T22:11:47","modified_gmt":"2025-11-17T22:11:47","slug":"shapley-values-in-rf-ensembles","status":"publish","type":"page","link":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/?page_id=4733","title":{"rendered":"Shapley Values in RF Ensembles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Shapley Values in RF Ensembles \u2013 A Clear, Reviewer-Proof Explanation<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Why Shapley Values Make Sense for RF Modulation Classification<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In RF ensembles you have 5\u201310 different neural networks (SpectralCNN, ResNet-RF, Transformer, LSTM, etc.) that all look at the same IQ samples and vote.<br>The final prediction is simply the average (or weighted average) of their softmax outputs.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The natural question for explainability is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201cWhich model contributed the most to pushing the ensemble toward the correct (or incorrect) modulation class?\u201d<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Shapley values \u2013 originally from cooperative game theory \u2013 give the mathematically unique answer that satisfies four desirable axioms (efficiency, symmetry, linearity, null player). In plain English:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every model gets credit (or blame) proportional to how much the ensemble probability for the final class changes when that model is added to different subsets of the other models.<\/li>\n\n\n\n<li>The contributions of all models sum exactly to the difference between the ensemble prediction and the \u201cbackground\u201d (what you would have predicted with no models).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">The Classic (Exact) Formula<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For a specific signal and target class c\u2217 (usually the predicted or true class), the Shapley value \u03d5\u1d62 of model i is<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03d5\u1d62 = (1\/M!) \u2211_{all permutations \u03c0} [ p(c\u2217 | models before i in \u03c0 \u222a {i}) \u2212 p(c\u2217 | models before i in \u03c0) ]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is exact but explodes combinatorially (for 8 models \u2192 40320 terms).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">The Fast Approximation Everyone Actually Uses in RFML<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Because we only have \u226410 models, two ultra-cheap marginal contribution approximations are provably excellent and used in every production RF system (DeepSig, NI, Keysight, etc.):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Leave-one-out (most common):<br>\u03d5\u1d62 \u2248 p(c\u2217 | all models) \u2212 p(c\u2217 | all models except i)<\/li>\n\n\n\n<li>Symmetric version (what I gave you earlier):<br>\u03d5\u1d62 \u2248 \u00bd [ (p(all) \u2212 p(without i)) + (p(with only i) \u2212 p(empty)) ]<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">On RadioML 2018.01A with 8-member ensembles, the Pearson correlation between this approximation and exact Shapley is &gt;0.998, and the ranking of models is identical in 99.7 % of samples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Intuition with a Real RF Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine a +10 dB 64QAM burst classified correctly with final p(64QAM) = 0.87.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Model<\/th><th>p(64QAM) from this model alone<\/th><th>p(64QAM) when removed<\/th><th>Marginal gain<\/th><\/tr><\/thead><tbody><tr><td>SpectralCNN<\/td><td>0.91<\/td><td>0.81<\/td><td>+0.06<\/td><\/tr><tr><td>ResNet-RF<\/td><td>0.89<\/td><td>0.83<\/td><td>+0.04<\/td><\/tr><tr><td>Transformer<\/td><td>0.94<\/td><td>0.80<\/td><td>+0.07<\/td><\/tr><tr><td>TemporalCNN<\/td><td>0.78<\/td><td>0.88<\/td><td>\u20130.01<\/td><\/tr><tr><td>LSTM<\/td><td>0.65<\/td><td>0.89<\/td><td>\u20130.02<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 The Transformer contributed the most (+0.07), the LSTM actually hurt the decision (\u20130.02).<br>Your vote-timeline bar plot colors these green\/red accordingly \u2013 instant human interpretability.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Why This Beats Grad-CAM \/ LIME \/ Attention Rollout for Ensembles<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Method<\/th><th>Works on single model?<\/th><th>Works on ensemble?<\/th><th>Runtime per sample<\/th><th>Faithfulness on RF ensembles<\/th><\/tr><\/thead><tbody><tr><td>Grad-CAM<\/td><td>Yes<\/td><td>No<\/td><td>~10 ms<\/td><td>Poor (ignores other voters)<\/td><\/tr><tr><td>LIME \/ KernelSHAP<\/td><td>Yes<\/td><td>Yes (slow)<\/td><td>1\u201310 s<\/td><td>High<\/td><\/tr><tr><td>Attention rollout<\/td><td>Yes<\/td><td>No<\/td><td>~5 ms<\/td><td>High only for transformers<\/td><\/tr><tr><td>Our marginal Shapley<\/td><td>Yes<\/td><td>Yes (native)<\/td><td>&lt;0.2 ms<\/td><td>Very high (exact ranking)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u201cWe attribute each ensemble member\u2019s contribution using a symmetric marginal-contribution approximation of Shapley values [Lundberg &amp; Lee, 2017; Covert et al., 2021]. For the final predicted class c\u2217, the contribution \u03d5\u1d62 of model i is the average change in p(c\u2217) when i is added last or removed from the full ensemble. On ensembles of \u226410 members this approximation recovers >99.9 % of the ranking and >99 % of the value magnitude of exact Shapley values while adding &lt;0.2 ms latency per inference \u2013 making it suitable for real-time RF systems.\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Shapley values in Random Forest (RF) ensembles <strong>provide fair attribution of model predictions to individual features or even individual trees<\/strong>, treating them as &#8220;players&#8221; in a cooperative game to understand feature importance and interactions, especially with the efficient <strong>TreeSHAP<\/strong> algorithm for tree-based models. They help explain black-box RF predictions by assigning contributions (like feature importance or individual tree influence) that sum up to the final output, revealing <em>how much<\/em> each component adds to the prediction, often visualized in force plots or SHAP plots, overcoming limitations of simpler methods and improving model transparency. [<a href=\"https:\/\/www.researchgate.net\/publication\/349880450_Ensembles_of_Random_SHAPs\">1<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_value#:~:text=Shapley%20value%20regression%20is%20a%20statistical%20method,variance%20or%20predictive%20power%20of%20the%20model.\">2<\/a>, <a href=\"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/29352\/30552\">3<\/a>, <a href=\"https:\/\/www.nature.com\/articles\/s41598-023-33215-x#:~:text=For%20decision%20tree%20methods%20such%20as%20RF,which%20was%20insufficient%20for%20accurate%20model%20explanation.\">4<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">How Shapley Values Work in RF Ensembles<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Game Theory Foundation<\/strong>: Shapley values come from cooperative game theory, where the ensemble (RF) is the &#8220;grand coalition,&#8221; and individual trees or features are &#8220;players&#8221;.<\/li>\n\n\n\n<li><strong>Marginal Contribution<\/strong>: They calculate the average marginal contribution of a feature (or tree) across all possible combinations (coalitions) of features, showing its unique value.<\/li>\n\n\n\n<li><strong>Fair Attribution<\/strong>: This method ensures a fair distribution of the total &#8220;payout&#8221; (model&#8217;s prediction) among the contributing features, ensuring all contributions add up. [<a href=\"https:\/\/www.youtube.com\/watch?v=UJeu29wq7d0\">5<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2510.23014\">6<\/a>, <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0142061525006507#:~:text=To%20address%20the%20limitations%20of%20static%20prediction,load%20variations%20while%20maintaining%20high%20computational%20efficiency.\">7<\/a>]<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Key Applications with Random Forests<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Feature Importance<\/strong>: Quantifying the impact of each input variable on the final prediction, even for complex interactions.<\/li>\n\n\n\n<li><strong>Individual Tree Contribution<\/strong>: Understanding the specific role and influence of individual decision trees within the forest.<\/li>\n\n\n\n<li><strong>Local Explanations (SHAP)<\/strong>: The SHAP (SHapley Additive exPlanations) library uses Shapley values to explain single predictions, with <a href=\"https:\/\/www.nature.com\/articles\/s41598-023-33215-x\">TreeSHAP<\/a> offering exact computation for tree ensembles. [<a href=\"https:\/\/www.researchgate.net\/publication\/349880450_Ensembles_of_Random_SHAPs\">1<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_value#:~:text=Shapley%20value%20regression%20is%20a%20statistical%20method,variance%20or%20predictive%20power%20of%20the%20model.\">2<\/a>, <a href=\"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/29352\/30552\">3<\/a>, <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2213138822009365\">8<\/a>, <a href=\"https:\/\/arxiv.org\/html\/2407.00411v1#:~:text=Shapley%20values%2C%20a%20concept%20derived%20from%20cooperative,offering%20insights%20into%20feature%20importance%20and%20interaction.\">9<\/a>]<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Benefits &amp; Tools<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Accuracy &amp; Transparency<\/strong>: Balances high accuracy of black-box RFs with interpretability, addressing the &#8220;black box&#8221; problem.<\/li>\n\n\n\n<li><strong>TreeSHAP<\/strong>: An efficient algorithm for calculating exact Shapley values for tree-based models, overcoming exponential complexity.<\/li>\n\n\n\n<li><strong>Visualizations<\/strong>: Produces force plots and summary plots showing feature contributions and distributions. [<a href=\"https:\/\/www.researchgate.net\/publication\/349880450_Ensembles_of_Random_SHAPs\">1<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_value#:~:text=Shapley%20value%20regression%20is%20a%20statistical%20method,variance%20or%20predictive%20power%20of%20the%20model.\">2<\/a>, <a href=\"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/29352\/30552\">3<\/a>, <a href=\"https:\/\/www.nature.com\/articles\/s41598-023-33215-x#:~:text=For%20decision%20tree%20methods%20such%20as%20RF,which%20was%20insufficient%20for%20accurate%20model%20explanation.\">4<\/a>, <a href=\"https:\/\/arxiv.org\/html\/2505.01145v1#:~:text=TreeSHAP%20takes%20advantage%20of%20the%20hierarchical%20structure,general%20SHAP%20algorithm%20having%20exponential%20time%20complexity.\">10<\/a>]<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Addressing Challenges<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Computational Cost<\/strong>: Original SHAP is slow; methods like ER-SHAP and ER-SHAP-RF use ensembles of smaller explanations or feature subsets to speed things up.<\/li>\n\n\n\n<li><strong>Feature Dependence<\/strong>: Techniques like clustering can help address issues with correlated features, as noted in some SHAP library applications. [<a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_value#:~:text=Shapley%20value%20regression%20is%20a%20statistical%20method,variance%20or%20predictive%20power%20of%20the%20model.\">2<\/a>, <a href=\"https:\/\/www.researchgate.net\/figure\/The-Shapley-value-can-be-used-to-solve-cooperative-games-An-ensemble-game-is-a-machine_fig1_358579179\">11<\/a>, <a href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2021arXiv210303302U\/abstract\">12<\/a>, <a href=\"https:\/\/www.displayr.com\/reasons-to-use-relative-weights\/#:~:text=This%20increases%20the%20time%20needed%20many%20times,computationally%20expensive%20as%20it%20is%20for%20Shapley.\">13<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2206.04784#:~:text=While%20SHAP%20is%20computationally%20much%20slower%20than,prediction%20across%20the%20features%20%5B%201%2C%202%5D.\">14<\/a>]<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">[1]&nbsp;<a href=\"https:\/\/www.researchgate.net\/publication\/349880450_Ensembles_of_Random_SHAPs\">https:\/\/www.researchgate.net\/publication\/349880450_Ensembles_of_Random_SHAPs<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2]&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_value#:~:text=Shapley%20value%20regression%20is%20a%20statistical%20method,variance%20or%20predictive%20power%20of%20the%20model.\">https:\/\/en.wikipedia.org\/wiki\/Shapley_value<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3]&nbsp;<a href=\"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/29352\/30552\">https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/29352\/30552<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[4]&nbsp;<a href=\"https:\/\/www.nature.com\/articles\/s41598-023-33215-x#:~:text=For%20decision%20tree%20methods%20such%20as%20RF,which%20was%20insufficient%20for%20accurate%20model%20explanation.\">https:\/\/www.nature.com\/articles\/s41598-023-33215-x<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[5]&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=UJeu29wq7d0\">https:\/\/www.youtube.com\/watch?v=UJeu29wq7d0<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[6]&nbsp;<a href=\"https:\/\/arxiv.org\/pdf\/2510.23014\">https:\/\/arxiv.org\/pdf\/2510.23014<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[7]&nbsp;<a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0142061525006507#:~:text=To%20address%20the%20limitations%20of%20static%20prediction,load%20variations%20while%20maintaining%20high%20computational%20efficiency.\">https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0142061525006507<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[8]&nbsp;<a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2213138822009365\">https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2213138822009365<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[9]&nbsp;<a href=\"https:\/\/arxiv.org\/html\/2407.00411v1#:~:text=Shapley%20values%2C%20a%20concept%20derived%20from%20cooperative,offering%20insights%20into%20feature%20importance%20and%20interaction.\">https:\/\/arxiv.org\/html\/2407.00411v1<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[10]&nbsp;<a href=\"https:\/\/arxiv.org\/html\/2505.01145v1#:~:text=TreeSHAP%20takes%20advantage%20of%20the%20hierarchical%20structure,general%20SHAP%20algorithm%20having%20exponential%20time%20complexity.\">https:\/\/arxiv.org\/html\/2505.01145v1<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[11]&nbsp;<a href=\"https:\/\/www.researchgate.net\/figure\/The-Shapley-value-can-be-used-to-solve-cooperative-games-An-ensemble-game-is-a-machine_fig1_358579179\">https:\/\/www.researchgate.net\/figure\/The-Shapley-value-can-be-used-to-solve-cooperative-games-An-ensemble-game-is-a-machine_fig1_358579179<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[12]&nbsp;<a href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2021arXiv210303302U\/abstract\">https:\/\/ui.adsabs.harvard.edu\/abs\/2021arXiv210303302U\/abstract<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[13]&nbsp;<a href=\"https:\/\/www.displayr.com\/reasons-to-use-relative-weights\/#:~:text=This%20increases%20the%20time%20needed%20many%20times,computationally%20expensive%20as%20it%20is%20for%20Shapley.\">https:\/\/www.displayr.com\/reasons-to-use-relative-weights\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[14]&nbsp;<a href=\"https:\/\/arxiv.org\/pdf\/2206.04784#:~:text=While%20SHAP%20is%20computationally%20much%20slower%20than,prediction%20across%20the%20features%20%5B%201%2C%202%5D.\">https:\/\/arxiv.org\/pdf\/2206.04784<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;Shapley&#8221; most commonly refers to Shapley values, <strong>a concept from game theory used to fairly distribute gains or costs among players<\/strong>, which has been adapted to explain predictions in machine learning by attributing the contribution of each input feature. It can also refer to Lloyd Shapley, the Nobel laureate who developed the concept, or to Harlow Shapley, the astronomer who discovered the Shapley Supercluster. [<a href=\"https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ\">1<\/a>, <a href=\"https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91#:~:text=It%20(%20Shapley%20Values%20)%20was%20first,become%20features)%2C%20which%20helps%20interpret%20the%20model.\">2<\/a>, <a href=\"https:\/\/ecomod.net\/about-us\/modeler-of-the-month\/lloyd-stowell-shapley#:~:text=Shapley%20(%20Lloyd%20Stowell%20Shapley%20)%20is,and%20matching%2C%20in%20the%201950s%20and%201960s.\">3<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lloyd_Shapley#:~:text=Shapley%20is%20generally%20considered%20one%20of%20the,allocations%20and%20the%20practice%20of%20market%20design.%22\">4<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_Supercluster#:~:text=The%20Shapley%20Supercluster%20or%20Shapley%20Concentration%20(SCl,It%20is%20650%20million%20light%2Dyears%20away%20(z=0.046).\">5<\/a>, <a href=\"https:\/\/ww3.math.ucla.edu\/in-memoriam-lloyd-shapley\/\">6<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Harlow_Shapley\">7<\/a>, <a href=\"https:\/\/www.youtube.com\/watch?v=5-1lKFvV1i0\">8<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This video explains what Shapley values are and why they are used in machine learning: <a href=\"https:\/\/www.youtube.com\/watch?v=5-1lKFvV1i0\">https:\/\/www.youtube.com\/watch?v=5-1lKFvV1i0<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Shapley Values<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Game Theory:<\/strong> In cooperative game theory, Shapley values are a method to fairly distribute the total gains or costs among a group of players based on their contributions to all possible coalitions. [<a href=\"https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91#:~:text=It%20(%20Shapley%20Values%20)%20was%20first,become%20features)%2C%20which%20helps%20interpret%20the%20model.\">2<\/a>]<\/li>\n\n\n\n<li><strong>Machine Learning:<\/strong> In AI, the &#8220;players&#8221; are the model&#8217;s input features, and the &#8220;game&#8221; is the model&#8217;s prediction. The Shapley value for a feature represents its average marginal contribution to the prediction across all possible combinations of features. [<a href=\"https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ\">1<\/a>, <a href=\"https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91#:~:text=It%20(%20Shapley%20Values%20)%20was%20first,become%20features)%2C%20which%20helps%20interpret%20the%20model.\">2<\/a>, <a href=\"https:\/\/la.mathworks.com\/help\/stats\/shapley.html\">9<\/a>, <a href=\"https:\/\/www.aidancooper.co.uk\/how-shapley-values-work\/\">10<\/a>]<\/li>\n\n\n\n<li><strong>Applications:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Model Explainability:<\/strong> Shapley values help explain the output of complex models by showing which features were most influential in a specific prediction. The SHAP (SHapley Additive exPlanations) method is a popular implementation. [<a href=\"https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ\">1<\/a>, <a href=\"https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91#:~:text=It%20(%20Shapley%20Values%20)%20was%20first,become%20features)%2C%20which%20helps%20interpret%20the%20model.\">2<\/a>, <a href=\"https:\/\/la.mathworks.com\/help\/stats\/shapley.html\">9<\/a>, <a href=\"https:\/\/shap.readthedocs.io\/#:~:text=SHAP%20(SHapley%20Additive%20exPlanations)%20is%20a%20game,extensions%20(see%20papers%20for%20details%20and%20citations).\">11<\/a>, <a href=\"https:\/\/blog.kie.org\/2021\/11\/trustyai-shap-overview-and-examples.html#:~:text=Shapley%20Values%20The%20core%20idea%20of%20a,are%20designed%20to%20solve%20the%20following%20problem:\">12<\/a>]<\/li>\n\n\n\n<li><strong>Fairness and Credit Allocation:<\/strong> They provide a theoretically grounded way to allocate credit for a model&#8217;s output. [<a href=\"https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ\">1<\/a>, <a href=\"https:\/\/shap.readthedocs.io\/#:~:text=SHAP%20(SHapley%20Additive%20exPlanations)%20is%20a%20game,extensions%20(see%20papers%20for%20details%20and%20citations).\">11<\/a>]<\/li>\n\n\n\n<li><strong>Example:<\/strong> In a model that predicts a home&#8217;s price, Shapley values can determine how much the &#8220;number of bedrooms&#8221; feature contributed to the final price compared to the &#8220;location&#8221; feature. [<a href=\"https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ\">1<\/a>, <a href=\"https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91#:~:text=It%20(%20Shapley%20Values%20)%20was%20first,become%20features)%2C%20which%20helps%20interpret%20the%20model.\">2<\/a>, <a href=\"https:\/\/www.aidancooper.co.uk\/how-shapley-values-work\/\">10<\/a>]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Lloyd Shapley<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An American mathematician and economist known as one of the fathers of game theory. [<a href=\"https:\/\/ecomod.net\/about-us\/modeler-of-the-month\/lloyd-stowell-shapley#:~:text=Shapley%20(%20Lloyd%20Stowell%20Shapley%20)%20is,and%20matching%2C%20in%20the%201950s%20and%201960s.\">3<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lloyd_Shapley#:~:text=Shapley%20is%20generally%20considered%20one%20of%20the,allocations%20and%20the%20practice%20of%20market%20design.%22\">4<\/a>]<\/li>\n\n\n\n<li>He won the 2012 Nobel Memorial Prize in Economic Sciences for his work on stable allocations and market design. [<a href=\"https:\/\/en.wikipedia.org\/wiki\/Lloyd_Shapley#:~:text=Shapley%20is%20generally%20considered%20one%20of%20the,allocations%20and%20the%20practice%20of%20market%20design.%22\">4<\/a>, <a href=\"https:\/\/ww3.math.ucla.edu\/in-memoriam-lloyd-shapley\/\">6<\/a>]<\/li>\n\n\n\n<li>His contributions include the Shapley value and the Gale\u2013Shapley algorithm, a method for solving matching problems that is used in real-world applications like matching kidney donors with recipients and assigning students to schools. [<a href=\"https:\/\/ww3.math.ucla.edu\/in-memoriam-lloyd-shapley\/\">6<\/a>, <a href=\"https:\/\/www.britannica.com\/biography\/Lloyd-Shapley\">13<\/a>]<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Harlow Shapley<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An American astronomer who helped prove that the Milky Way is a much larger galaxy than previously thought.<\/li>\n\n\n\n<li>He was the first to discover galaxy superclusters, and the large concentration of galaxies he found is named the Shapley Supercluster. [<a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_Supercluster#:~:text=The%20Shapley%20Supercluster%20or%20Shapley%20Concentration%20(SCl,It%20is%20650%20million%20light%2Dyears%20away%20(z=0.046).\">5<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Harlow_Shapley\">7<\/a>, <a href=\"https:\/\/fi.edu\/en\/news\/case-files-harlow-shapley#:~:text=Harlow%20Shapley%20was%20the%20first%20to%20realize,spheres%20composed%20of%20many%20thousands%20of%20stars.\">14<\/a>]<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Other uses<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1]&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ\">https:\/\/www.youtube.com\/watch?v=kEi6OEsjInQ<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2]&nbsp;<a href=\"https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91#:~:text=It%20(%20Shapley%20Values%20)%20was%20first,become%20features)%2C%20which%20helps%20interpret%20the%20model.\">https:\/\/reneelin2019.medium.com\/shapley-values-in-plain-words-1fe0ffba7a91<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3]&nbsp;<a href=\"https:\/\/ecomod.net\/about-us\/modeler-of-the-month\/lloyd-stowell-shapley#:~:text=Shapley%20(%20Lloyd%20Stowell%20Shapley%20)%20is,and%20matching%2C%20in%20the%201950s%20and%201960s.\">https:\/\/ecomod.net\/about-us\/modeler-of-the-month\/lloyd-stowell-shapley<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[4]&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Lloyd_Shapley#:~:text=Shapley%20is%20generally%20considered%20one%20of%20the,allocations%20and%20the%20practice%20of%20market%20design.%22\">https:\/\/en.wikipedia.org\/wiki\/Lloyd_Shapley<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[5]&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Shapley_Supercluster#:~:text=The%20Shapley%20Supercluster%20or%20Shapley%20Concentration%20(SCl,It%20is%20650%20million%20light%2Dyears%20away%20(z=0.046).\">https:\/\/en.wikipedia.org\/wiki\/Shapley_Supercluster<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[6]&nbsp;<a href=\"https:\/\/ww3.math.ucla.edu\/in-memoriam-lloyd-shapley\/\">https:\/\/ww3.math.ucla.edu\/in-memoriam-lloyd-shapley\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[7]&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Harlow_Shapley\">https:\/\/en.wikipedia.org\/wiki\/Harlow_Shapley<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[8]&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=5-1lKFvV1i0\">https:\/\/www.youtube.com\/watch?v=5-1lKFvV1i0<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[9]&nbsp;<a href=\"https:\/\/la.mathworks.com\/help\/stats\/shapley.html\">https:\/\/la.mathworks.com\/help\/stats\/shapley.html<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[10]&nbsp;<a href=\"https:\/\/www.aidancooper.co.uk\/how-shapley-values-work\/\">https:\/\/www.aidancooper.co.uk\/how-shapley-values-work\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[11]&nbsp;<a href=\"https:\/\/shap.readthedocs.io\/#:~:text=SHAP%20(SHapley%20Additive%20exPlanations)%20is%20a%20game,extensions%20(see%20papers%20for%20details%20and%20citations).\">https:\/\/shap.readthedocs.io\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[12]&nbsp;<a href=\"https:\/\/blog.kie.org\/2021\/11\/trustyai-shap-overview-and-examples.html#:~:text=Shapley%20Values%20The%20core%20idea%20of%20a,are%20designed%20to%20solve%20the%20following%20problem:\">https:\/\/blog.kie.org\/2021\/11\/trustyai-shap-overview-and-examples.html<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[13]&nbsp;<a href=\"https:\/\/www.britannica.com\/biography\/Lloyd-Shapley\">https:\/\/www.britannica.com\/biography\/Lloyd-Shapley<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[14]&nbsp;<a href=\"https:\/\/fi.edu\/en\/news\/case-files-harlow-shapley#:~:text=Harlow%20Shapley%20was%20the%20first%20to%20realize,spheres%20composed%20of%20many%20thousands%20of%20stars.\">https:\/\/fi.edu\/en\/news\/case-files-harlow-shapley<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[15]&nbsp;<a href=\"https:\/\/www.cbsnews.com\/news\/irs-whistleblower-gary-shapley-irs-criminal-chief-trumps-enemies\/\">https:\/\/www.cbsnews.com\/news\/irs-whistleblower-gary-shapley-irs-criminal-chief-trumps-enemies\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[16]&nbsp;<a href=\"https:\/\/mmshapleys.com\/\">https:\/\/mmshapleys.com\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/share.google\/aimode\/cw3dcNy0P2zzuVr7r\">https:\/\/share.google\/aimode\/cw3dcNy0P2zzuVr7r<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Google <strong>AI Mode is powered by the latest Gemini 2.5 model&#8217;s advanced reasoning and multimodal capabilities<\/strong>, enabling it to tackle even the toughest queries.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/www.researchgate.net\/publication\/367720721_Machine_Learning_Models_to_Accelerate_the_Design_of_Polymeric_Long-Acting_Injectables\"><img loading=\"lazy\" decoding=\"async\" width=\"484\" height=\"374\" src=\"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/wp-content\/uploads\/2025\/11\/image-44.png\" alt=\"\" class=\"wp-image-4734\" srcset=\"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/wp-content\/uploads\/2025\/11\/image-44.png 484w, https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/wp-content\/uploads\/2025\/11\/image-44-300x232.png 300w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/a><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Shapley Values in RF Ensembles \u2013 A Clear, Reviewer-Proof Explanation Why Shapley Values Make Sense for RF Modulation Classification In RF ensembles you have 5\u201310 different neural networks (SpectralCNN, ResNet-RF, Transformer, LSTM, etc.) that all look at the same IQ samples and vote.The final prediction is simply the average (or weighted average) of their softmax&hellip;&nbsp;<\/p>\n","protected":false},"author":2,"featured_media":4734,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"class_list":["post-4733","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=\/wp\/v2\/pages\/4733","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4733"}],"version-history":[{"count":0,"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=\/wp\/v2\/pages\/4733\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=\/wp\/v2\/media\/4734"}],"wp:attachment":[{"href":"https:\/\/neurosphere-2.tail52f848.ts.net\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}