Multi-Touch-Attribution_ShapleyValue

Using the sample marketing dataset from Kaggle, we will be extracting four variables from the dataset: 'user_id', 'date_served', 'marketing_channel', 'converted'. Some pre-processing work is done to drop rows which contain null values, as well as relabel 'converted' into binary.

###  extracting the needed field
columns = ['user_id', 'date_served', 'marketing_channel', 'converted']
data = data_raw[columns].copy()

### dropping null values
data.dropna(axis=0, inplace=True)

### relabel conversion to 1/0
data['converted'] = data['converted'].astype('int') 
### converting date_served into date format
data['date_served'] = pd.to_datetime(data['date_served'], format='%m/%d/%y', errors='coerce')

In the first step of the calculation, we will compute for each channel subset, the sum of conversions generated.

### create a channel mix conversion table 
# first level - sort
data_lvl1 = data[['user_id', 'marketing_channel', 'converted']].sort_values(by=['user_id', 'marketing_channel'])

# second level - groupby userid, concat distinct marketing channel and label if any conversion took place with this channel mix
data_lvl2 = data_lvl1.groupby(['user_id'], as_index=False).agg({'marketing_channel': lambda x: ','.join(map(str,x.unique())),'converted':max})
data_lvl2.rename(columns={'marketing_channel':'marketing_channel_subset'}, inplace=True)

# third level - summing up the conversion which took place for each channel mix
data_lvl3 = data_lvl2.groupby(['marketing_channel_subset'], as_index=False).agg(sum)

Once we have prepared the dataset, we will then proceed with the set up of calculating Shapley value.

#### setting up the formulas for shapley value
###############################################################################################

### return all possible combination of the channel
def power_set(List):
    PS = [list(j) for i in range(len(List)) for j in itertools.combinations(List, i+1)]
    return PS
  
###############################################################################################

### calculating the factorial of a number
def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
       
###############################################################################################

### compute the worth of each coalition
def v_function(A,C_values):
    '''
    This function computes the worth of each coalition.
    inputs:
            - A : a coalition of channels.
            - C_values : A dictionnary containing the number of conversions that each subset of channels has yielded.
    '''
    subsets_of_A = subsets(A)
    worth_of_A=0
    for subset in subsets_of_A:
        if subset in C_values:
            worth_of_A += C_values[subset]
    return worth_of_A
      
###############################################################################################

### return all possible subsets from the channels
def subsets(s):
    '''
    This function returns all the possible subsets of a set of channels.
    input :
            - s: a set of channels.
    '''
    if len(s)==1:
        return s
    else:
        sub_channels=[]
        for i in range(1,len(s)+1):
            sub_channels.extend(map(list,itertools.combinations(s, i)))
    return list(map(",".join,map(sorted,sub_channels)))
  
###############################################################################################

def calculate_shapley(df, channel_name, conv_name):
    '''
    This function returns the shapley values
            - df: A dataframe with the two columns: ['channel_subset', 'count'].
            The channel_subset column is the channel(s) associated with the conversion and the count is the sum of the conversions. 
            - channel_name: A string that is the name of the channel column 
            - conv_name: A string that is the name of the column with conversions
            **Make sure that that each value in channel_subset is in alphabetical order. Email,PPC and PPC,Email are the same 
            in regards to this analysis and should be combined under Email,PPC.
            
    '''
    # casting the subset into dict, and getting the unique channels
    c_values = df.set_index(channel_name).to_dict()[conv_name]
    df['channels'] = df[channel_name].apply(lambda x: x if len(x.split(",")) == 1 else np.nan)
    channels = list(df['channels'].dropna().unique())
    
    v_values = {}
    for A in power_set(channels): #generate all possible channel combination
        v_values[','.join(sorted(A))] = v_function(A,c_values)
    n=len(channels) #no. of channels
    shapley_values = defaultdict(int)

    for channel in channels:
        for A in v_values.keys():
            if channel not in A.split(","):
                cardinal_A=len(A.split(","))
                A_with_channel = A.split(",")
                A_with_channel.append(channel)            
                A_with_channel=",".join(sorted(A_with_channel))
                weight = (factorial(cardinal_A)*factorial(n-cardinal_A-1)/factorial(n)) # Weight = |S|!(n-|S|-1)!/n!
                contrib = (v_values[A_with_channel]-v_values[A]) # Marginal contribution = v(S U {i})-v(S)
                shapley_values[channel] += weight * contrib
        # Add the term corresponding to the empty set
        shapley_values[channel]+= v_values[channel]/n 
        
    return shapley_values

Tejash-Shah/Multi-Touch-Attribution_ShapleyValue

Multi-Touch-Attribution_ShapleyValue