How to print the decision path / rules used to predict sample of a specific row in PySpark?

I changed your dataframe just slightly so that we could ensure we could see different features in the explanations
I changed the Assembler to use a feature_list, so we have easy access to that later
changes below:

#change1: ball goes from [0,1,2,3] ->[0,1,1,3] so we can see other features in explanations
#change2: added in multiple paths to the same prediction
#change3: added in a categorical variable
#change3: feature_list so we can re-use those indicies easily later
data = pd.DataFrame({
    'ball': [0, 1, 1, 3, 1, 0, 1, 3],
    'keep': [4, 5, 6, 7, 7, 4, 6, 7],
    'hall': [8, 9, 10, 11, 2, 6, 10, 11],
    'fall': [12, 13, 14, 15, 15, 12, 14, 15],
    'mall': [16, 17, 18, 10, 10, 16, 18, 10],
    'wall': ['a','a','a','a','a','a','c','e'],
    'label': [21, 31, 41, 51, 51, 51, 21, 31]
})

df = spark.createDataFrame(data)

df = df.withColumn("mono_ID", monotonically_increasing_id())
w = Window().orderBy("mono_ID")
df = df.select(row_number().over(w).alias("tagvalue"), col("*"))

indexer = StringIndexer(inputCol='wall', outputCol='wallIndex')
encoder = OneHotEncoder(inputCol='wallIndex', outputCol='wallVec')

#i added this line so feature replacement later is easy because of the indices
features = ['ball','keep','wallVec','hall','fall']
assembler = VectorAssembler(
    inputCols=features, outputCol='features')
dtc = DecisionTreeClassifier(featuresCol='features', labelCol='label')

pipeline = Pipeline(stages=[indexer, encoder, assembler, dtc]).fit(df)
transformed_pipeline = pipeline.transform(df)

Below is a method I've found to be able to work with the decision tree itself:

#get the pipeline back out, as you've done earlier, this changed to [3] because of the categorical encoders
ml_pipeline = pipeline.stages[3]

#saves the model so we can get at the internals that the scala code keeps private
ml_pipeline.save("mymodel_test")

#read back in the model parameters
modeldf = spark.read.parquet("mymodel_test/data/*")

import networkx as nx


#select only the columns that we NEED and collect into a list
noderows = modeldf.select("id","prediction","leftChild","rightChild","split").collect()


#create a graph for the decision tree; you Could use a simpler tree structure here if you wanted instead of a 'graph'
G = nx.Graph()

#first pass to add the nodes
for rw in noderows:
    if rw['leftChild'] < 0 and rw['rightChild'] < 0:
        G.add_node(rw['id'], cat="Prediction", predval=rw['prediction'])
    else: 
        G.add_node(rw['id'], cat="splitter", featureIndex=rw['split']['featureIndex'], thresh=rw['split']['leftCategoriesOrThreshold'], leftChild=rw['leftChild'], rightChild=rw['rightChild'], numCat=rw['split']['numCategories'])

#second pass to add the relationships, now with additional information
for rw in modeldf.where("leftChild > 0 and rightChild > 0").collect():
    tempnode = G.nodes()[rw['id']]
    G.add_edge(rw['id'], rw['leftChild'], reason="{0} less than {1}".format(features[tempnode['featureIndex']],tempnode['thresh']))
    G.add_edge(rw['id'], rw['rightChild'], reason="{0} greater than {1}".format(features[tempnode['featureIndex']],tempnode['thresh']))

Now let's build a function to work with the all this stuff
Note: this could be written more cleanly

#function to parse the path based on the tagvalue and it's corresponding features
def decision_path(tag2search):
    wanted_row = transformed_pipeline.where("tagvalue = "+str(tag2search)).collect()[0]
    wanted_features = wanted_row['features']
    start_node = G.nodes()[0]
    while start_node['cat'] != 'Prediction':
        #do stuff with categorical variables
        if start_node['numCat'] > 0:
            feature_value = wanted_features[start_node['featureIndex']:start_node['featureIndex'] + start_node['numCat']]
            #this assumes that you'll name all your cat variables with the following syntax 'ball' -> 'ballVec' or 'wall' -> 'wallVec'
            feature_column = features[start_node['featureIndex']]
            original_column = feature_column[:-3]
            valToCheck = [x[original_column] for x in transformed_pipeline.select(feature_column, original_column).distinct().collect() if np.all(x[feature_column].toArray()==feature_value)][0]

            if (valToCheck == wanted_row[original_column]) :
                print("'{0}' value of {1} in [{2}]; ".format(original_column, wanted_row[original_column], valToCheck))
                start_node = G.nodes()[start_node['leftChild']]
            else:
                print("'{0}' value of {1} in [{2}]; ".format(original_column, wanted_row[original_column], valToCheck))
                start_node = G.nodes()[start_node['rightChild']]

        #path to do stuff with non-categorical variables
        else:
            feature_value = wanted_features[start_node['featureIndex']]
            if feature_value > start_node['thresh'][0]:
                print("'{0}' value of {1} was greater than {2}; ".format(features[start_node['featureIndex']], feature_value, start_node['thresh'][0]))
                start_node = G.nodes()[start_node['rightChild']]
            else:
                print("'{0}' value of {1} was less than or equal to {2}; ".format(features[start_node['featureIndex']], feature_value, start_node['thresh'][0]))
                start_node = G.nodes()[start_node['leftChild']]

    print("leads to prediction of {0}".format(start_node['predval']))

Results take this form:

[decision_path(X) for X in range(1,8)]
    'fall' value of 8.0 was greater than 6.0; 
    'ball' value of 0.0 was less than or equal to 1.0; 
    'ball' value of 0.0 was less than or equal to 0.0; 
        leads to prediction of 21.0

    'fall' value of 9.0 was greater than 6.0; 
    'ball' value of 1.0 was less than or equal to 1.0; 
    'ball' value of 1.0 was greater than 0.0; 
    'keep' value of 5.0 was less than or equal to 5.0; 
        leads to prediction of 31.0

    'fall' value of 10.0 was greater than 6.0; 
    'ball' value of 1.0 was less than or equal to 1.0; 
    'ball' value of 1.0 was greater than 0.0; 
    'keep' value of 6.0 was greater than 5.0; 
    'wall' value of a in [a]; 
        leads to prediction of 21.0

    'fall' value of 11.0 was greater than 6.0; 
    'ball' value of 3.0 was greater than 1.0; 
    'wall' value of a in [a]; 
        leads to prediction of 31.0

    'fall' value of 2.0 was less than or equal to 6.0; 
        leads to prediction of 51.0

    'fall' value of 6.0 was less than or equal to 6.0; 
        leads to prediction of 51.0

    'fall' value of 10.0 was greater than 6.0; 
    'ball' value of 1.0 was less than or equal to 1.0; 
    'ball' value of 1.0 was greater than 0.0; 
    'keep' value of 6.0 was greater than 5.0; 
    'wall' value of c in [c]; 
        leads to prediction of 21.0

Notes:

• If you want to stay exclusively in Spark-world you could use GraphFrames instead of networkx (I don't have that luxury :( )
• You can modify the phrasing as you wish
• If you need the impurity, impurityStats, or gain, those are all in the model information dataframe that gets saved
• I chose to work with the tree instead of parsing the .toDebugString because having access to the tree sounded more foundationally important (and expandable)
  • On that note, just looking at the .toDebugString AND the sklearn.decision_path outputs, I feel that these are more easily understandable/readable
• if you want to visualize the tree, checkout: https://github.com/tristaneljed/Decision-Tree-Visualization-Spark/blob/master/DT.py
• I had found a pure Scala implementation at some point, but can't find that again right now :(
• I feel like I'm missing a test case with the "Not In" categorical, if someone wants to throw in what that row would look like, I can edit if I have to