# How is Shapley value calculated?

## How is Shapley value calculated?

The Shapley value is computed by taking the average of difference from all combinations. Essentially, the Shapley value is the average marginal contribution of a feature considering all possible combinations.

### What is Shapley method?

Shapely is a Python package for set-theoretic analysis and manipulation of planar features using (via Python’s ctypes module) functions from the well known and widely deployed GEOS library. GEOS, a port of the Java Topology Suite (JTS), is the geometry engine of the PostGIS spatial extension for the PostgreSQL RDBMS.

What is Shapley value Regression?

Shapley Value regression is a technique for working out the relative importance of predictor variables in linear regression. Its principal application is to resolve a weakness of linear regression, which is that it is not reliable when predicted variables are moderately to highly correlated.

Can Shapley values be negative?

Note that a Shapley value can be either positive or negative, as you may infer from the definition.

## Is Shapley value in core?

Every convex game has a nonempty core. In every convex game, the Shapley value is in the core.

### What is a Shapley plot?

SHAP dependence plots are an alternative to partial dependence plots and accumulated local effects. While PDP and ALE plot show average effects, SHAP dependence also shows the variance on the y-axis. Especially in case of interactions, the SHAP dependence plot will be much more dispersed in the y-axis.

What do Shapley values mean?

Essentially, the Shapley value is the average expected marginal contribution of one player after all possible combinations have been considered. Shapley value helps to determine a payoff for all of the players when each player might have contributed more or less than the others.

What are Shapley values in machine learning?

The Shapley value is the (weighted) average of marginal contributions. We replace the feature values of features that are not in a coalition with random feature values from the apartment dataset to get a prediction from the machine learning model.

## What is a convex game?

In game theory, a convex game is one in which the incentives for joining a coalition increase as the coalition grows. This paper shows that the core of such a game — the set of outcomes that cannot be improved on by any coalition of players — is quite large and has an especially regular structure.

### What are Shapley additive exPlanations?

SHAP or SHAPley Additive exPlanations is a visualization tool that can be used for making a machine learning model more explainable by visualizing its output. It can be used for explaining the prediction of any model by computing the contribution of each feature to the prediction.

What is base value in Shap?

SHAP will provide both base value and output value. Base value is the average model output (based on provided training data) while the output value is adjusted (author uses “push” term) by different feature given that feature score is calculated)

What is the difference between Shap and Shapley values?

In the end SHAP values are simply “the Shapley values of a conditional expectation function of the original model” Lundberg and Lee (2017). Basically, the Shapley value is defined for any value function and SHAP is just a special case of the Shapley value by the special definition of the value function!

## Is the Shapley value in the core?

### What is Edgeworth box core?

The core in general equilibrium theory Graphically, and in a two-agent economy (see Edgeworth Box), the core is the set of points on the contract curve (the set of Pareto optimal allocations) lying between each of the agents’ indifference curves defined at the initial endowments.

What is Nash equilibrium example?

Nash Equilibrium Examples The prisoner’s dilemma: In this hypothetical game, two criminals are taken to separate rooms and—without communicating with each other—must make the decision to testify against their partner and convict them or remain silent. If they both betray each other, they each serve two years in prison.

How do you prove a game is convex?

A game with side payments is a generalized convex game if and only if it is a convex game. ≤ v(S ∪ T) + v(S ∪ T ) ≤ v(S ∪ T ∪ T ) + v(S). xi since xS is unblocked by S. Thus (xS,xT ,xT ) ∈ v(S ∪ T ∪ T ).

## How do you read a Shapley plot?

How to interpret the shap summary plot?

1. The y-axis indicates the variable name, in order of importance from top to bottom. The value next to them is the mean SHAP value.
2. On the x-axis is the SHAP value.
3. Gradient color indicates the original value for that variable.
4. Each point represents a row from the original dataset.

### Is Shapley model agnostic?

Shapley values provide a maximally data-agnostic model explanation by uniformly averaging over all orderings in which features can be introduced.

How do you calculate SHAP value?

The SHAP value for each feature in this observation is given by the length of the bar. In the example above, Latitude has a SHAP value of -0.39, AveOccup has a SHAP of +0.37 and so on. The sum of all SHAP values will be equal to E[f(x)] — f(x).

How do you calculate the Shapley value?

The solution, known as the Shapley value, has a nice interpretation in terms of expected marginal contribution. It is calculated by considering all the possible orders of arrival of the players into a room and giving each player his marginal contribution. The following examples illustrate this.

## What is the Shapley value used for?

The Shapley value works for both classification (if we are dealing with probabilities) and regression. We use the Shapley value to analyze the predictions of a random forest model predicting cervical cancer: FIGURE 5.48: Shapley values for a woman in the cervical cancer dataset.

### What is Shapley value in machine learning?

The Shapley value is a solution for computing feature contributions for single predictions for any machine learning model. The Shapley value is defined via a value function val of players in S.

Is there a better alternative to the Shapley value system?

LIME might be the better choice for explanations lay-persons have to deal with. Another solution is SHAP introduced by Lundberg and Lee (2016) 46, which is based on the Shapley value, but can also provide explanations with few features.