Analytical Background Questions

# assume Spark DataFrames: df_prod, df_billing, df_crm, cust_map
# 1. build canonical customer_id
crm_clean = df_crm.selectExpr("crm_id","lower(email) as email","acquisition_channel","created_at")
cust_map = cust_map_built_from_rules  # mapping of billing_account -> customer_id

billing_clean = (df_billing
  .withColumn("ts", to_utc_timestamp(col("timestamp"),"UTC"))
  .withColumn("week", date_format(col("ts"),"yyyy-ww"))
  .withColumn("amount_cents", (col("amount")*100).cast("long"))
  .join(cust_map, on="billing_account_id", how="left")
  .withColumn("customer_id", coalesce(col("customer_id"), col("email_hash")))
  .dropDuplicates(["transaction_id"])
  .filter(col("status")=="settled")
)

events = (billing_clean.select("customer_id","week","amount_cents")
  .unionByName(prod_revenue.select(...)))
# weekly revenue per customer
weekly_rev = events.groupBy("customer_id","week").agg(sum("amount_cents").alias("rev_cents"))

# attach acquisition channel (take earliest known)
cust_acq = crm_clean.groupBy("customer_id").agg(min("created_at").alias("acq_date"),
                                              first("acquisition_channel").alias("acq_channel"))
# compute weeks since acquisition then cumulative LTV per customer-week
from pyspark.sql import Window
w = Window.partitionBy("customer_id").orderBy("week").rowsBetween(Window.unboundedPreceding,0)
cust_week = weekly_rev.join(cust_acq, on="customer_id", how="left") \
  .withColumn("week_num", week_diff(col("week"), col("acq_date"))) \
  .withColumn("ltv_cents", sum("rev_cents").over(w))

# aggregate by acquisition channel and week
result = cust_week.groupBy("acq_channel","week").agg(avg("ltv_cents").alias("avg_ltv_cents"),
                                                    sum("ltv_cents").alias("total_ltv_cents"),
                                                    countDistinct("customer_id").alias("n_customers"))

from sklearn.pipeline import Pipeline
from sklearn.compose import ColumnTransformer
from sklearn.impute import SimpleImputer
from sklearn.preprocessing import OneHotEncoder, StandardScaler
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.model_selection import RandomizedSearchCV, StratifiedKFold, cross_val_score
import numpy as np

# Example column lists
numeric_features = ['age', 'income', 'score']
categorical_features = ['city', 'occupation']

# Preprocessors
numeric_transformer = Pipeline([
    ('imputer', SimpleImputer(strategy='median')),
    ('scaler', StandardScaler())
])

categorical_transformer = Pipeline([
    ('imputer', SimpleImputer(strategy='constant', fill_value='missing')),
    ('onehot', OneHotEncoder(handle_unknown='ignore', sparse=False))
])

preprocessor = ColumnTransformer([
    ('num', numeric_transformer, numeric_features),
    ('cat', categorical_transformer, categorical_features)
], remainder='drop')

# Full pipeline
pipe = Pipeline([
    ('preproc', preprocessor),
    ('clf', GradientBoostingClassifier(random_state=42))
])

# Hyperparameter search space
param_distributions = {
    'clf__n_estimators': [100, 200, 300],
    'clf__learning_rate': [0.01, 0.05, 0.1],
    'clf__max_depth': [3, 4, 5],
    'clf__subsample': [0.6, 0.8, 1.0]
}

# Inner CV for hyperparameter tuning
inner_cv = StratifiedKFold(n_splits=3, shuffle=True, random_state=42)
random_search = RandomizedSearchCV(
    pipe,
    param_distributions=param_distributions,
    n_iter=20,
    cv=inner_cv,
    scoring='roc_auc',
    n_jobs=-1,
    random_state=42,
    verbose=1
)

# Outer CV to estimate generalization (nested CV prevents leakage)
outer_cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=1)
# cross_val_score will fit random_search on each training fold and evaluate on held-out fold
nested_scores = cross_val_score(random_search, X, y, cv=outer_cv, scoring='roc_auc', n_jobs=-1)

print("Nested CV AUC scores:", nested_scores)
print("Mean AUC (nested):", np.mean(nested_scores))

WITH steps AS (
  SELECT user_id, event_name,
         MIN(event_time) AS first_time
  FROM events
  WHERE event_name IN ('step1','step2','step3','step4','step5')
    AND event_time >= DATE_SUB(CURRENT_DATE, INTERVAL 90 DAY)
  GROUP BY user_id, event_name
),
pivoted AS (
  SELECT user_id,
    MIN(CASE WHEN event_name='step1' THEN first_time END) AS t1,
    MIN(CASE WHEN event_name='step2' THEN first_time END) AS t2,
    MIN(CASE WHEN event_name='step3' THEN first_time END) AS t3,
    MIN(CASE WHEN event_name='step4' THEN first_time END) AS t4,
    MIN(CASE WHEN event_name='step5' THEN first_time END) AS t5
  FROM steps
  GROUP BY user_id
),
ordered AS (
  SELECT *,
    -- enforce order: a step only counts if it occurs after the previous counted step and within window (e.g., 7 days between first and last)
    CASE WHEN t1 IS NOT NULL THEN t1 END AS s1,
    CASE WHEN t2 IS NOT NULL AND t1 IS NOT NULL AND t2 > t1 THEN t2 END AS s2,
    CASE WHEN t3 IS NOT NULL AND s2 IS NOT NULL AND t3 > s2 THEN t3 END AS s3,
    CASE WHEN t4 IS NOT NULL AND s3 IS NOT NULL AND t4 > s3 THEN t4 END AS s4,
    CASE WHEN t5 IS NOT NULL AND s4 IS NOT NULL AND t5 > s4 THEN t5 END AS s5
  FROM pivoted
),
final AS (
  SELECT
    COUNT(*) FILTER (WHERE s1 IS NOT NULL) AS step1_cnt,
    COUNT(*) FILTER (WHERE s2 IS NOT NULL) AS step2_cnt,
    COUNT(*) FILTER (WHERE s3 IS NOT NULL) AS step3_cnt,
    COUNT(*) FILTER (WHERE s4 IS NOT NULL) AS step4_cnt,
    COUNT(*) FILTER (WHERE s5 IS NOT NULL) AS step5_cnt
  FROM ordered
)
SELECT * FROM final;

from statsmodels.tsa.seasonal import seasonal_decompose
res = seasonal_decompose(series, model='additive', period=7)
res.plot()