# Shapley attribution model

1

### This, in turn, powers futile optimizations with no realized performance lift. Back to Shapley. 2 = . My data set contains 2 columns (path and nb_of_conversions): path=c ('Paid Search > Direct > Paid Search','Organic Search > Display (impression) > Display (impression Jul 09, 2021 · An outline of the Shapley Value Model for Data Driven Attribution. SHAP specifies the explanation as: \[g(z')=\phi_0+\sum_{j=1}^M\phi_jz_j'\] where g is the explanation model, \(z'\in\{0,1\}^M\) is the coalition The algorithm used for attribution is based on the Harsanyi Dividend from cooperative game theory. Shapley Value Attribution Feb 12, 2020 · If it wasn't clear already, we're going to use Shapely values as our feature attribution method, which is known as SHapely Additive exPlanations (SHAP). Along the way, we establish new results on sensitivity analysis of the Eisenberg-Noe network model of contagion, featuring a Markov-chain interpretation. , model A and B minus model B). Here we explored using simple two-feature binary classifiers on how the importance of a feature can be decomposed into its main and interaction effects as well as its marginal contributions. , 2017] which deÞne attribution as the Feature Attributions that Use Shapley Values. Sep 16, 2021 · Shapley values are a cornerstone of interpretable machine learning, a way to attribute how much each feature played a role in a model's prediction. The Shapley model is also the one used by Google for their own data-driven attribution model in Google Analytics 360, however by creating your own model you will have better control over your data and will avoid the biases that Google Analytics might have by giving more credit to Google Search. We consider an investment process that includes a number of features, each of which can be active or inactive. My data set contains 2 columns (path and nb_of_conversions): path=c ('Paid Search > Direct > Paid Search','Organic Search > Display (impression) > Display (impression In SHAP, this explanation model is represented by a linear model — an additive feature attribution method — or just the summation of present features in the coalition game. e. Define a coalition game for each model input x to be explained Players are the features of the input Gain is the model prediction F(x) Feature attributions are the Shapley values of this game We call the coalition game setup for computing Shapley Values as the “Explanation Game” We elaborate on our presentation in §3and show how selected existing node-based attribution approaches are captured by our graphical model framework. Moehle, S. In this way, the marketer can gauge the relative efficiency of each channel in turning opportunities for conversion into actual conversions. Attribution Modeling give us the model generation process, as well as the reasons and justification of the attribution model being derived. Sep 19, 2020 · The Markov chain is a model describing a sequence of possible events in which the probability of each event depends only on the current state. Shapley Value is based on the following idea. Revised version to appear, Journal of Investment Management, 2021. May 11, 2011 · One innovation that SHAP brings to the table is that the Shapley value explanation is represented as an additive feature attribution method, a linear model. ai/ going trough the two different data driven attribution models used in marketing:- Shapley value- Markov modelHere removal effect) or Shapley value (SV) as a measure for attribution. We can extend the Shapley value method to incorporate the ordering effect of the channels. Shapley computes feature contributions for single predictions with the Shapley value, an approach from cooperative game theory. What is the Markov chain? The Markov chain is a model describing a sequence of possible events in which the probability of each event depends only on the current state. Model Interpretability for PyTorch. SHAP also offers alternatives to estimating Shapley Values. One of the simplest model types is standard linear regression, and so below we train a linear regression model on the classic boston housing dataset. The glove game is a coalitional game where the players have left and right hand gloves and the goal is to form pairs. You can use Shapley values to determine the contribution that each feature made to model predictions. , 2020). Define a coalition game for each model input x to be explained Players are the features of the input Gain is the model prediction F(x) Feature attributions are the Shapley values of this game We call the coalition game setup for computing Shapley Values as the “Explanation Game” How to calculate in R attribution of conversions using Shapley value? - Cross Validated. As you can see, all of the different touchpoints have been given different percentages of credit for the conversion. Manuscript. Recursive Shapley Value (RSV) 10 0 X1 X2 X3 = 5X1 X3 X4 X4 = X2 X5 X5 = X2 Y Y = X1+ X3+ 2X4+ 2X5 6 4 attributions via the decomposition of individual predictions (local attribution) and importance scores for the model as a whole (global attribution). " May 19, 2019 · Shapley Value vs. The obvious main advantage of game theory Niklas Kolster from https://www. Note: The Shapley value model can only be used with cm_dt_* and dv360_dt uence attribution is inspired by the concept of Shapley value, which was introduced by Lloyd Shapley in 1953 [22]. 2), and (3) asymmetric Shapley value (§A. It can be shown that the division made Feb 08, 2018 · In particular, we consider a Markovian model for the user journey through the conversion funnel, in which ad actions may have disparate impacts at different stages. The Shapley value approach for online marketing attribution in these articles seems to be as follows: This runs into issues in certain cases though, due to a large number of possible coalitions - which is why it was reformulated for online marketing specifically in 2. Game theory is when two or more players Sep 17, 2021 · Shapley values are a cornerstone of interpretable machine learning, a way to attribute how much each feature played a role in a model’s prediction. While I may talk about Shapley values in the context of interpretable ML in the future, this post is about Shapley values in its original context: cooperative game theory. com Abstract Many existing approaches for estimating fea-ture importance are problematic because Oct 26, 2020 · There is a mathematically correct way to solve this attribution cake-cutting problem, discovered by mathematician and economist Lloyd Shapley in 1953. Known as “The Shapley value,” it is a solution concept in cooperative game theory, developed when Shapley was working on the problem of apportioning credit in cooperative games to distribute Apr 28, 2017 · In more detail, the Shapley value Cooperative Game algorithm is used in my custom data driven attribution model, which I developed using the open-source software R (See link). Another common model is a Markov Chain model. They are be good approximations for Shapley values under some assumptions of data distributions. May 22, 2021 · Then, the researchers propose a new metric for attribution in the Markovian model of user behavior, called counterfactual adjusted Shapley value. Relationships¶. This is the most common metric for attribution [2–5, 15, 27, 29, 30]. The Shapley value is a commonly used method to attribute a model's prediction to its base features. Nov 16, 2016 · Game theory attribution uses algorithms and the Shapley value to identify the impact of each touchpoint and then fairly distribute credit to each touchpoint in a conversion path. Let’s find out together! A Python implementation of "Shapley Value Methods for Attribution Modeling in Online Advertising" by Zhao, et al. , Organic Search , Display , and Email ) as “team members Oct 14, 2020 · A different technique, for diagnosing model misspecification, is to calculate the Shapley decomposition of the estimated strength of dependence between Y ˆ and X, so that each feature v receives attribution ϕ v C ˆ y ˆ. 2 when added to B (i. This is also an assumption made by attribution methods based on Shapley values such as Integrated Gradient [Sun-dararajan et al. 4 - . Shapley sampling values are meant to explain any model by: (1) applying sampling approximations to Equation 4, and (2) approximating the effect of removing a variable from the model by integrating Attribution modeling is about the process where attribution model is generated. 4. N. attr. These attributions can be provided for specific predictions and at a global level for the model as a whole. SHAP (SHapley Additive exPlanations) is a game theoretic approach to explain the output of any machine learning model. We propose a novel attribution metric, that we refer to as counterfactual adjusted Shapley value, which inherits the desirable properties of the traditional Shapley value while Jun 11, 2021 · A very broad brush explanation of a typical Shapley approach is to find an average incremental value for a particular channel touchpoint by looking at all conversion paths that exist. In the last 70 years, SV gained enormous popularity, was adapted to different contexts, and applied in many industries. The attribution is dominated by the linear term. Use Python and SQL to crack the Multi-Touch Attribution Model using the Shapley value approach. Oct 26, 2020 · Nowadays, there are data-driven solutions, such as Markov chain attribution (analysing how the removal of a given touchpoint from the customer journey affects the likelihood of conversion) or the Shapley Value (calculating the average value of each channel’s marginal contribution given all possible channel combinations). Jul 06, 2020 · In this post, we will only go over the game theory model and the Shapley value. For each predictor we compute the average improvement that is created when adding that variable to a model. IVH. Our goal is to attribute or decompose an Jun 02, 2021 · There are many use cases for within-model Shapley values, such as providing transparency to model predictions, e. Each color represents a different channel in the conversion path. See original paper for more details. The Shapley Value was also applied as an approach to the Google Analytics Data-Driven Attribution model. Shapley Value Attribution Abstract. A well-motivated local decomposition is provided by model Shapley values (Strumbelj and Kononenko (2010); Lundberg and Lee Aug 23, 2021 · Shapley: this approach takes into account each customer’s journey as well but disregards the sequence in which interactions take place. To understand exactly how this attribution model works, let’s consider the following example: suppose we know the conversion rate for the three marketing channels organic search, paid search and display: organic search – 20% Feb 08, 2018 · In particular, we consider a Markovian model for the user journey through the conversion funnel, in which ad actions may have disparate impacts at different stages. 5 Beyond Feature Attribution: Concept Based Explanations Nov 16, 2018 · In more detail, the Shapley value Cooperative Game algorithm is used in my custom data driven attribution model, which I developed using the open-source software R (See link). SV would be a robust and reliable model in all these cases. . The Shapley Value-based attribution model The Shapley Value methodology was developed in a cooperative game setting, and has been applied from measuring systemic risk in a macroeconomic environment to inequality indices (Osborne and Rubinstein, 1994). The Shapley value is a way to assign credit among a group of “players” who cooperate for a certain end. There are two possible pairs that we can form and in both of them, Player 1 needs to be involved. It is not difficult to come up with an attribution model, in fact, we can make up one in seconds. 3. The Shapley value is the only attribution method that satisfies the properties Efficiency, Symmetry, Dummy and Additivity, which together can be considered a definition of a fair payout. 马尔科夫链. We propose a novel attribution metric, that we refer to as counterfactual adjusted Shapley value, which inherits the desirable properties of the traditional Shapley value. Approaches using Shapley values [30, 31] satisfy intuitively expected axiomatic properties over attributions [32]. Thus, the proposed combined model is a useful profit allocation mechanism for the fourth party logistics supply chain coalition that the contribution and risks are fully considered. My data set contains 2 columns (path and nb_of_conversions): path=c ('Paid Search > Direct > Paid Search','Organic Search > Display (impression) > Display (impression 8 Shapley Additive Explanations (SHAP) for Average Attributions. Raghav SingalFlow-based Attribution in Graphical Models 1/6. 4 when added to C Oct 09, 2013 · Finally, the numerical study shows that the profit allocation method improved weighted Shapley value model is relatively rational and practical. Aug 11, 2021 · Portfolio Performance Attribution via Shapley Value. lundberg@microsoft. By combining the flexibility of R, over 1000 lines of manually written code, and raw data of the business, it is possible to create a custom data driven attribution model Jun 08, 2020 · A limitation of Shapley value is the need to define a baseline (aka reference point) representing the missingness of a feature. This metric inherits the benefits of the classical Shapley value (SV), such as efficiency, symmetry, and linearity, but in contrast to the classical SV, can be easily computed. This previous post describes Shapley values as conceived in the context of game theory; in this post we will explain how Shapley values can apply in the context of interpretable ML. The biggest drawback is that the order in which channel appears in the journey has no bearing on the attribution value that it gets, but we know that a channel serves different purpose at different stage of user journey. We show how to do systemic risk attribution in a network model of contagion with interlock-ing balance sheets, using the Shapley and Aumann-Shapley values. We develop a model- Feb 24, 2019 · Ordered Shapley Value Method. By combining the flexibility of R, over 1000 lines of manually written code, and raw data of the business, it is possible to create a custom data driven attribution model A data-driven attribution model is based on the solution concept in cooperative game theory, called the Shapley value. 2. IVH computes the change in the eventual conversion1 prob-ability of a user when a specific ad is removed from her path. From Theorem 1, we know that Shapely values provide the only unique solution to Properties 1-3 for an additive feature attribution model. 1. g. – and a theoretical framework for understanding them using the 3x3 matrix of the mutual intersections of their component point sets 3: the DE-9IM. , a local linear approximation D(z) = a 0 + Nov 09, 2020 · The Shapley Value algorithm is a way to gain insights into how much each predictor value contributes to a machine learning model. We extend the notion of attribution to also apply to feature interactions. , a local linear approximation D(z) = a 0 + May 22, 2021 · Then, the researchers propose a new metric for attribution in the Markovian model of user behavior, called counterfactual adjusted Shapley value. SageMaker Clarify provides feature attributions based on the concept of Shapley value. As a credit allocation solution in cooperative game theory, Shapley value May 15, 2021 · We study the attribution problem in a graphical model, wherein the objective is to quantify how the effect of changes at the source nodes propagates through the graph. Feb 14, 2019 · The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. Suppose you want to predict the political leaning (conservative, moderate, liberal) from four predictors: sex, age, income, number of children. A. Let us review a few interesting ways to use SV in marketing and market research. The Shapley value fairly distributes the difference of the instance's prediction and the datasets average prediction among the features. However, most prior work has focused on post-hoc Shapley explanations, which can be computationally demanding due to its exponential time complexity and preclude model regularization based on Shapley explanations during training. Cooperative Sep 14, 2020 · Shapley Value Attribution is also the approached used by Google Analytics Data-Driven Attribution model. To understand exactly how this attribution model works, let’s consider the following example: suppose we know the conversion rate for the three marketing channels organic search, paid search and display: organic search – 20% Shapley Value. 1), (2) conditional Shapley value (§A. Sep 17, 2021 · Shapley values are a cornerstone of interpretable machine learning, a way to attribute how much each feature played a role in a model’s prediction. 5 - . In the case of MCF Data-Driven Attribution, the “team” being analyzed has marketing touchpoints (e. This paper re-examines the Shapley value methods for attribution analysis in the area of online advertising. " Flow-based Attribution in Graphical Models: A Recursive Shapley Approach Raghav Singal 1George Michailidis1 2 Hoiyi Ng Abstract We study the attribution problem in a graphical model, wherein the objective is to quantify how the effect of changes at the source nodes prop-agates through the graph. In particular, we discuss three existing approaches: (1) independent Shapley value (§A. In Chapter 6, we introduced break-down (BD) plots, a procedure for calculation of attribution of an explanatory variable for a model’s prediction. How to calculate in R attribution of conversions using Shapley value? - Cross Validated. 2. In particular, we consider a Markovian model for the user journey through the conversion funnel, in which ad actions may have disparate impacts at different stages. Working paper, February 2021. In a typical Shapley Value cooperative Dec 01, 2018 · A misattributing attribution model, such as last touch, allows publishers to ride freely on others' efforts. Efficiency The feature contributions must add up to the difference of prediction for x and the average. Feb 12, 2020 · If it wasn't clear already, we're going to use Shapely values as our feature attribution method, which is known as SHapely Additive exPlanations (SHAP). The computational complexity of L-Shapley is only exponential to k, while the computational complexity of C-Shapley is further reduced to polynomial. 4 when added on its own (i. Oct 23, 2017 · Data-driven attribution then applies to this probabilistic data set an algorithm based on a concept from cooperative game theory called the Shapley Value. I want to compare attribution results made by Markov Chain and Shapley Value. Shapley Value Sampling¶ class captum. Aug 05, 2016 · Data-Driven Attribution uses an algorithm based on a concept from cooperative game theory called the Shapley Value. In this paper, we present a method to choose a baseline based on a neutrality value: a parameter defined by decision makers at which their choices are determined by the returned value of the model being either below or . The features values of an instance cooperate to achieve the prediction. ShapleyValueSampling (forward_func) [source] ¶. Sep 30, 2019 · This table shows how the Shapley model works, with percentage values representing the conversion rate for each channel: To help you compare each attribution model we’ve discussed so far, take a look at this chart: Which attribution model will work best? There is no universal attribution model applicable for all campaigns. Shapley values have become one of the most popular feature attribution explanation methods. 3). uence attribution is inspired by the concept of Shapley value, which was introduced by Lloyd Shapley in 1953 [22]. Sep 14, 2020 · Shapley Value Attribution is also the approached used by Google Analytics Data-Driven Attribution model. Each blue dot is a row (a day in this case). However, most prior work has focused on post-hoc Shapley explanations, which can be computationally Feature Attributions that Use Shapley Values. We also indicated that, in the presence of interactions, the computed value of the attribution depends on the order of explanatory SV would be a robust and reliable model in all these cases. Axiom 3 (Nullity) guarantees that if a feature is completely disconnected from the model’s output, it receives zero Shapley value. Shapley value and logistic regression stand out as reliable attribution models with a reputation across-industry verticals. Boyd, and A. Axiom 4 (Symmetry) requires attribution to DNN model and the attributions, which reßect the fact that the model is well-trained and the attribution method is well-founded: 1. To realize the full value of multi-touch attribution, it’s critical that the output is used to guide how marketing spend is allocated on an ongoing basis. It connects optimal credit allocation with local explanations using the classic Shapley values from game theory and their related extensions (see papers for details and citations). Applied to marketing attribution, it attempts to fairly model how much each A data-driven attribution model is based on the solution concept in cooperative game theory, called the Shapley value. The Shapley Value was developed by the economics Nobel Laureate Lloyd S. COOPERATIVE GAME THEORY “Non-Cooperative Games covers competitive social interactions where there will be some winners & some losers, and in Cooperative Games, every player agreed to work together a common goal. The Shapley value is a game-theoretic concept devised for fair division of gains obtained by co-operation of nplayers, namely in a setting very similar to the one we consider in this paper. In SHAP, this explanation model is represented by a linear model — an additive feature attribution method — or just the summation of present features in the coalition game. Complex attribution problem The number of channels are large You also want to model the order of the touchpoints You want to take continuous variables into account → Computationally heavy, exact shapley values cannot be computed and needs to be approximated in some way Background Given a model C : Rd 7!R, additive feature-attribution methods form a linear approximation of the function over simpliﬁed binary inputs, z 2f0;1g d , indicating the “presence” and “absence”, respectively: i. The use of the Shapley value is justified by citing [16] showing that it is the \\emph{unique} method that satisfies certain good properties (\\emph{axioms}). Explaining a linear regression model Before using Shapley values to explain complicated models, it is helpful to understand how they work for simple models. Introduction. , the A-only model minus the No Predictors model). This dataset consists of 506 Jun 29, 2021 · The dashboard also displays each channel’s percentage of total impressions and its ratio of impressions to conversions, according to the Shapley attribution model. The model worked well but had one gap : the fact that the data we were using was mainly click data . Complex attribution problem The number of channels are large You also want to model the order of the touchpoints You want to take continuous variables into account → Computationally heavy, exact shapley values cannot be computed and needs to be approximated in some way Shapley Flow: A Graph-based Approach to Interpreting Model Predictions Jiaxuan Wang Jenna Wiens Scott Lundberg University of Michigan jiaxuan@umich. The Harsanyi dividend is a generalization of the Shapley value solution (named after Lloyd Shapley, a Nobel Laureate economist) to distributing credit among players in a game with unequal contributions to the outcome. We say that a mechanism is Shapley-fair (or for short, fair) if it pays the agents in the solution that it selects their Shapley payments. Markov Chains are named after the mathematician Andrey Markov, and in essence, enable modelling a sequence of events The Shapley value is a solution concept used in game theory that involves fairly distributing both gains and costs to several actors working in coalition. Nov 06, 2017 · The Shapley value is the solution used by Google Analytics’ Data-Driven Attribution model, and variations on the Shapley value approach are used by most attribution and ad bidding vendors in the market today. for explaining a specific credit decision or detecting algorithmic discrimination (Datta, Sen & Zick, 2016), as well as understanding model structure, measuring interaction effects and detecting concept drift (Lundberg et al. 1. In this approach, one calibrates a model that predicts the conversion prob- Feb 24, 2019 · Ordered Shapley Value Method. Call them A, B, C,… Mar 30, 2021 · Model agnostic approaches, such as Shapley values or SHAP, have improved our understanding of black-box models. It can be shown that the division made the use of Shapley values with roots in cooperative game theory for computing attribution. In the case of predictor A: It adds . Ang. Shapley values for a linear-ensemble model can be computed as linear combinations of Shapley values for its constituent models. Background Given a model C : Rd 7!R, additive feature-attribution methods form a linear approximation of the function over simpliﬁed binary inputs, z 2f0;1g d , indicating the “presence” and “absence”, respectively: i. Markov Model: what are differences between the best models of marketing attributions and how they actually work. We develop a model-agnostic flow-based attribution method, called recursive Shapley value (RSV). Apr 06, 2021 · Shapley values have become one of the most popular feature attribution explanation methods. There are, however, a multiplicity of ways in which the Shapley value is operationalized in the Using the Shapley value method, you can model the contribution that a particular channel has on conversion. edu University of Michigan wiensj@umich. Aug 22, 2019 · The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The spatial data model is accompanied by a group of natural language relationships between geometric objects – contains, intersects, overlaps, touches, etc. A perturbation based approach to compute attribution, based on the concept of Shapley Values from cooperative game theory. - GitHub - ianchute/shapley-attribution-model-zhao-naive: A Python implementation of "Shapley Value Methods for Attribution Modeling in Online Advertising" by Zhao, et al. The Shapely game theory approach considers how to fairly assign credit to individual players based on their real contribution to the overall team goal of winning a game. Our attribution-based conﬁdence metric is theoretically motivated by these axiomatic properties. Jun 10, 2019 · In particular, we consider a Markovian model for the user journey through the conversion funnel, in which ad actions may have disparate impacts at different stages. Define a coalition game for each model input x to be explained Players are the features of the input Gain is the model prediction F(x) Feature attributions are the Shapley values of this game We call the coalition game setup for computing Shapley Values as the “Explanation Game” Shapley regression values match Equation 1 and are hence an additive feature attribution method. Ordered Shapley Value Method. edu Microsoft Research scott. Using multi-touch attribution in production. Jul 06, 2019 · Markov chains, alongside Shapley value, are one of the most common methods used in algorithmic attribution modeling. We propose a generalization of the Shapley value called Shapley-Taylor index that attributes the Aug 05, 2016 · Data-Driven Attribution uses an algorithm based on a concept from cooperative game theory called the Shapley Value. That view connects LIME and Shapley Values. Ads Data Hub uses the "Simplified Shapley Value Method", explained in full detail in the Shapley Value Methods for Attribution Modeling in Online Advertising paper. Shapley as an approach to fairly distributing the output of a team among the constituent team members. of Shapley values, which states that the sum of Shapley values is equal to the value of the solution, this normalizing term for all agents is the budget divided by the value of the solution. 1 = . windsor. Apr 06, 2021 · This model comes out of the box in several attribution platforms including Google Campaign Manager.