• AIPressRoom
  • Posts
  • SHAP for Binary and Multiclass Goal Variables | by Conor O’Sullivan | Sep, 2023

SHAP for Binary and Multiclass Goal Variables | by Conor O’Sullivan | Sep, 2023

A information to the code and deciphering SHAP plots when your mannequin predicts a categorical goal variable

SHAP values give the contribution of a mannequin characteristic to a prediction. For binary goal variables, we interpret these values by way of log odds. For multiclass targets, we use softmax. We are going to:

  • Focus on these interpretations in additional depth

  • Give the code for displaying SHAP plots

  • Discover new methods of aggregating SHAP values for multiclass targets

You too can watch this video on the subject:

We proceed on from a earlier SHAP tutorial. It goes into depth on SHAP plots for a steady goal variable. You will notice that these plots and their insights are comparable for categorical goal variables. You too can discover the complete undertaking on GitHub.

To summarise, we used SHAP to elucidate a mannequin constructed utilizing the abalone dataset. This has 4,177 situations and you’ll see examples of the options beneath. We use the 8 options to foretell y — the variety of rings within the abalone’s shell. The rings are associated to the age of the abalone. On this tutorial, we are going to bin y into completely different teams to create binary and multiclass goal variables.

For the continual goal variable, we noticed that every occasion had 8 SHAP values — one for each mannequin characteristic. As seen in Determine 1, if we sum these and the typical prediction E[f(x)] we get the prediction for that occasion f(x). For binary goal variables, we’ve the identical property. The distinction is we interpret the values by way of log odds of a constructive prediction.

To grasp this let’s dive right into a SHAP plot. We begin by making a binary goal variable (line 2). We create two teams primarily based on y:

  • 1 if the abalone has an above-average variety of rings

  • 0 in any other case 

#Binary goal varibale
y_bin = [1 if y_>10 else 0 for y_ in y]

We use this goal variable and the 8 options to coach an XGBoost classifier (strains 2–3). This mannequin had an accuracy of 96.6%.

#Practice mannequin 
model_bin = xgb.XGBClassifier(goal="binary:logistic")
model_bin.match(X, y_bin)

We now calculate the SHAP values (strains 2–3). We output the form of this object (line 5) which provides (4177, 8). So, similar to the continual goal, we’ve one SHAP worth per prediction and have. Later, we are going to see how that is completely different for a multiclass goal. 

#Get shap values
explainer = shap.Explainer(model_bin)
shap_values_bin = explainer(X)
print(shap_values_bin.form) #output: (4177, 8)

We show a waterfall plot for the primary occasion (line 6). We are able to see the end in Determine 2. Discover the code is identical as for the continual variable. Apart from the numbers, the waterfall plot additionally seems to be comparable. 

# waterfall plot for first occasion
shap.plots.waterfall(shap_values_bin[0])

Now E[f(x)] = -0.789 offers the typical predicted log odds throughout all 4,177 abalones. That’s the log odds of a constructive (1) prediction. For this particular abalone, the mannequin predicted a chance of 0.3958 that it had an above-average variety of rings (i.e. P = 0.3958). This offers us a predicted log odds of f(x) = ln(0.3958/(1–0.3958)) = -0.423.

So, the SHAP values give the distinction between the anticipated log odds and the typical predicted log odds. Optimistic SHAP values enhance the log odds. For instance, shucked weight elevated the log odds by 1.32. In different phrases, this characteristic has elevated the chance that the mannequin will predict an above-average variety of rings. Equally, destructive values lower the log odds.

We are able to additionally mixture these values in the identical manner as earlier than. The excellent news is the interpretations of the plots just like the beeswarm or imply SHAP would be the similar. Simply keep in mind that we’re coping with log odds. Now let’s see how this interpretation modifications for multiclass goal variables.

We begin by creating a brand new goal variable (y_cat) with 3 classes — younger (0), medium (1) and previous (2). As earlier than, we prepare an XGBoost classifier to foretell this goal variable (strains 5–6). 

#Categorical goal varibale
y_cat = [2 if y_>12 else 1 if y_>8 else 0 for y_ in y]
#Practice mannequin 
model_cat = xgb.XGBClassifier(goal="binary:logistic")
model_cat.match(X, y_cat)

For this mannequin, we will now not speak about a “constructive prediction”. We are able to see this if we output the anticipated chance for the primary occasion (line 2). This offers us [0.2562, 0.1571, 0.5866]. On this case, the third chance is the very best and so the abalone is predicted to be previous (2). What this implies for SHAP, is we will now not solely take into account values for the constructive class. 

# get chance predictions
model_cat.predict_proba(X)[0]

We are able to see this after we calculate the SHAP values (strains 2–3). The code is identical as for the binary mannequin. But, after we output the form (line 5) we get (4177, 8, 3). We now have one SHAP worth for each occasion, characteristic and class. 

#Get shap values
explainer = shap.Explainer(model_cat)
shap_values_cat= explainer(X)
print(np.form(shap_values_cat))

In consequence, we’ve to show the SHAP values for every class in separate waterfall plots. We do that for the primary occasion within the code beneath. 

# waterfall plot for sophistication 0
shap.plots.waterfall(shap_values_cat[0,:,0])
# waterfall plot for sophistication 1
shap.plots.waterfall(shap_values_cat[0,:,1])


# waterfall plot for sophistication 2
shap.plots.waterfall(shap_values_cat[0,:,2])

Determine 3 offers the waterfall plot for sophistication 0. The values clarify how every characteristic has contributed to the mannequin prediction for this class. That’s in comparison with the typical prediction for this class. We noticed that the chance for this class was comparatively low (i.e. 0.2562). We are able to see that the shucked weight characteristic has made essentially the most important contribution to this low chance.

Determine 4 offers the output for the opposite lessons. You’ll discover that f(x) = 1.211 is the most important for sophistication 2. This is sensible as we noticed the chance for this class was additionally the most important (0.5866). When analysing the SHAP values for this occasion, it could make sense to give attention to this waterfall plot. It’s the class prediction for this abalone.