预算分配Budget Allocation：Morphl-AI的营销科学解决方案（一）

文章目录

1 公司介绍
2 预算分配
3 相关案例解读
- 3.1 相关数据样式
- 3.2 2. Budget optimization - basic statistical model
- 3.3 4. Budget allocation - pseudo-revenue - first-revenue assumption - regressions
- 3.4 5. Budget allocation - pseudo-revenue - one-week assumption - regressions
4 代码测试
- 4.1 简单系数一阶收入预测
- 4.2 模型二:考虑曝光

1 公司介绍

Morphl是一家国外提供AI解决方案的公司（PS：这家公司，web UI挺好看的~）：网址：https://morphl.io/products/morphl-cloud.html

MorphL社区版 MorphL Community Edition使用大数据和机器学习来预测数字产品和服务中的用户行为，其目标是通过个性化来提高KPI（点击率，转换率等），主要涵盖的模型包括：

模型1 ：人群购物阶段模型shopping stage - 高潜力购买人群圈选；精确定位那些更有可能加入购物车、去结账或完成交易的用户。
模型2 ：购物丢失模型 cart abandonment - 加购易丢失人群圈选；精确定位那些更有可能在当前或下一回合放弃购物车的用户。
模型3 ： Customers LTV - 生命周期模型通过关注具有较低或中等客户终身价值的用户，减少客户流失，将他们转变为忠实客户。
个性化推荐模型
关联产品模型
高频购买模型
搜索意图
人群分类
流失预警

2 预算分配

在morphl理论体系里面，预算分配包含两个步骤：

计算，budge -> revence 预算到收入之间的函数关系
计算，每个活动的预算分配优化模型

第一步预算/收入预测函数

代码语言：javascript复制

f(Cost) = f(Cost(t) | Cost(t-1), Revenue(t-1), ... Cost(t0), Revenue(t0)) = Revenue function

根据历史的预算/收入数据，进行预测

第二步预算最优化问题在有了每个活动预算/收入预测函数之后，就可以开始解决预算最优化，以下有三种情况：

黄线是预算/投入金额累计线；蓝线是预算/投入效率曲线（原文表示：The blue line is the relation between the budget and the returning sum.）

曲线的顶点就是最佳的budge范围，可以帮助进行预算分配

3 相关案例解读

3.1 相关数据样式

github地址：Morphl-AI/Ecommerce-Marketing-Spend-Optimization

来看github放开的两个数据源格式：

市场花费数据，包括年份，总投入，TV/Digital 等渠道的收入
渠道转化数据，广告ID，FB活动ID，年龄，性别，曝光，点击，花费，转化等

其中的几个案例，介绍了几种他们常用的方法：

3.2 2. Budget optimization - basic statistical model

这里其实是非常简单的几种方法

收入 ~ 投入,直接除法算ROI
收入 ~ 曝光,曝光 ~ 投入,也是直接除法换算

3.3 4. Budget allocation - pseudo-revenue - first-revenue assumption - regressions

用上了回归模型来计算，Revenue~cost
举例了两种做法,Revenue ~ cost 两变量回归;rev ~ cost click等协变量这里有一个bucket index概念,还没特别看懂，猜测是一个合理的活动间隔期，类似session

Let a bucket be: Cost_B=[0, 0, 50, 20, 0, 15] , Revenue_B=[30, 100] . This means that the first revenue (30) was generated by the first two costs alone, so we merged the next bucket as well. We’ll sum them, getting C_{Sigma B}=85 and R_{Sigma B}=130 . Then, the bucket constant is: alpha_B=130/85=1.529 . Then, our pseudo-revenues will be: Pseudo-Revenue_{B} = [0*alpha_B, 0*alpha_B, 50*alpha_B, 20*alpha_B, 0*alpha_B, 15*alpha_B] = [0, 0, 76.45, 30.58, 0, 22.935] .

借助上述例子，猜测，

为什么不是一一对应： [0,0,50,20,0,15] -> [r1,r2,r3,r4,r5] 因为投入和统计收入不是同步的，投入之后会需要一段时间来统计。
如何一一对应？可以采用一些数据插补策略，比如算一个总的bucket constant

3.4 5. Budget allocation - pseudo-revenue - one-week assumption - regressions

第四案例，可能是间断式的活动，那么第五个案例，可能是一个长期的案例，所以这里的bucket时间间隔是固定的1周，以此进行计算。

4 代码测试

github地址：Morphl-AI/Ecommerce-Marketing-Spend-Optimization

来看github放开的两个数据源格式：

市场花费数据，包括年份，总投入，TV/Digital 等渠道的收入
渠道转化数据，广告ID，FB活动ID，年龄，性别，曝光，点击，花费，转化等

4.1 简单系数一阶收入预测

对应jupyter - 2. Budget optimization - basic statistical model

就是直接 => Rev / Cost

代码语言：javascript复制

import pandas as pd

'''
模型一：直接算个总的ROI
Directly modeling f(Cost) = Revenue
'''
class StatisticalModel:
    def __init__(self):
        # This model has just a single parameter, computed as the count between targets and inputs
        self.param = np.nan
        
    def fit(self, x, t):
        assert self.param != self.param
        self.param = t.sum() / x.sum()  # 核心,非常简单的算一个ROI，作为系数进行计算
    
    def predict(self, x):
        assert self.param == self.param
        return x * self.param
    
def errorL1(y, t):
    return np.abs(y - t).mean()

def plot(model, valData, xKey, tKey):
    validCampaigns = list(valData.keys())
    ax = plt.subplots(len(validCampaigns), figsize=(5, 30))[1]
    for i, k in enumerate(validCampaigns):
        x = valData[k][xKey]
        t = valData[k][tKey]
        y = model[k].predict(x)
        ax[i].scatter(x, y, label="%s Predicted" % (tKey))
        ax[i].scatter(x, t)
        ax[i].set_title(k)
        ax[i].legend()

# 数据读入

conversion_data = pd.read_csv('Datasets/conversion_data.csv')
# marketing_spend_data = pd.read_csv('Datasets/marketing_spend_data.csv')


model_cost_revenue = {}
predictions_cost_revenue = {}
errors_cost_revenue = {}
displayDf = pd.DataFrame()
res_cost_revenue = []

campaigns = set(conversion_data['xyz_campaign_id'])
# from sklearn.model_selection import train_test_split
# X_train,X_test,y_train,y_test = train_test_split(iris.data,iris.target,test_size=0.3,random_state=0)
trainData = {}
valData = {}
for k in campaigns:
    data = conversion_data[conversion_data['xyz_campaign_id'] == k]
    num = int(len(data)*0.8)
    trainData[k] = data[:num]
    valData[k] = data[num:]

# Cost_col = 'Cost'
# Revenue_col = 'Revenue'
Cost_col = 'Spent'  # 投入
Revenue_col = 'Total_Conversion' # 产出

for k in campaigns:
    model_cost_revenue[k] = StatisticalModel()
    model_cost_revenue[k].fit(trainData[k][Cost_col], trainData[k][Revenue_col])
    predictions_cost_revenue[k] = model_cost_revenue[k].predict(valData[k][Cost_col])
    errors_cost_revenue[k] = errorL1(predictions_cost_revenue[k], valData[k][Revenue_col])
    res_cost_revenue.append([k, trainData[k][Cost_col].sum(), trainData[k][Revenue_col].sum(), 
                model_cost_revenue[k].param, errors_cost_revenue[k]])


displayDf = pd.DataFrame(res_cost_revenue, columns=["Campaign", Cost_col, Revenue_col, "Fit", "Error (L1)"])
display(displayDf)
print("Mean error:", displayDf["Error (L1)"].mean())

plot(model_cost_revenue, valData, Cost_col, Revenue_col)

只是一个范例，

4.2 模型二:考虑曝光

类似：cost -> 曝光 -> 收入

代码语言：javascript复制

Cost x Revenue ~= Cost x Sessions   Sessions x Revenue

曝光 = a1 * cost
收入 = a2 * 曝光

分两步走，主要截取的也是2. Budget optimization - basic statistical model

代码语言：javascript复制

# 随机设定一个session
session_col = 'Impressions' # 曝光
Cost_col = 'Spent'  # 投入
Revenue_col = 'Total_Conversion' # 产出

# 第一步：曝光 = a1 * cost
model_cost_sessions = {}
predictions_cost_sessions = {}
errors_cost_sessions = {}
displayDf = pd.DataFrame()
res_cost_sessions = []
for k in campaigns:
    model_cost_sessions[k] = StatisticalModel()
    model_cost_sessions[k].fit(trainData[k][Cost_col], trainData[k][session_col])
    predictions_cost_sessions[k] = model_cost_sessions[k].predict(valData[k][Cost_col])
    errors_cost_sessions[k] = errorL1(predictions_cost_sessions[k], valData[k][session_col])
    res_cost_sessions.append([k, trainData[k][Cost_col].sum(), trainData[k][session_col].sum(), 
                model_cost_sessions[k].param, errors_cost_sessions[k]])

displayDf = pd.DataFrame(res_cost_sessions, columns=["Campaign", Cost_col, session_col, "Fit", "Error (L1)"])
display(displayDf)
print("Mean error:", displayDf["Error (L1)"].mean())

plot(model_cost_sessions, valData, Cost_col, session_col)

# 第二步：收入 = a2 * 曝光
model_sessions_revenue = {}
predictions_sessions_revenue = {}
errors_sessions_revenue = {}
displayDf = pd.DataFrame()
res_sessions_revenue = []
for k in campaigns:
    model_sessions_revenue[k] = StatisticalModel()
    model_sessions_revenue[k].fit(trainData[k][session_col], trainData[k][Revenue_col])
    predictions_sessions_revenue[k] = model_sessions_revenue[k].predict(valData[k][session_col])
    errors_sessions_revenue[k] = errorL1(predictions_sessions_revenue[k], valData[k][Revenue_col])
    res_sessions_revenue.append([k, trainData[k][session_col].sum(), trainData[k][Revenue_col].sum(), 
                model_sessions_revenue[k].param, errors_sessions_revenue[k]])

displayDf = pd.DataFrame(res_sessions_revenue, columns=["Campaign", session_col, Revenue_col, "Fit", "Error (L1)"])
display(displayDf)
print("Mean error:", displayDf["Error (L1)"].mean())

plot(model_sessions_revenue, valData, session_col, Revenue_col)

# 第三步：合并
displayDf = pd.DataFrame()
errors_cost_revenue = {}
res_cost_revenue_combined = []

class TwoModel(object):
    def __init__(self, modelA, modelB):
        self.modelA = modelA
        self.modelB = modelB
    
    def predict(self, x):
        return self.modelA.predict(self.modelB.predict(x))
models_cost_revenue = {k : TwoModel(model_cost_sessions[k], model_sessions_revenue[k]) for k in valData}

for k in campaigns:
    predictions_cost_revenue[k] = models_cost_revenue[k].predict(valData[k][Cost_col])
    errors_cost_revenue[k] = errorL1(predictions_cost_revenue[k], valData[k][Revenue_col])
    res_cost_revenue_combined.append([k, errors_cost_revenue[k]])

displayDf = pd.DataFrame(res_cost_revenue_combined, columns=["Campaign", "Error (L1)"])
display(displayDf)
print("Mean error:", displayDf["Error (L1)"].mean())


plot(models_cost_revenue, valData, Cost_col, Revenue_col)

对象存储 github git 开源编程算法

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