# Maximizing your tip as a waiter

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A few weeks ago, I introduced a **target-based categorical encoder** for Statistical/Machine Learning based on correlations + **Cholesky decomposition**. That is, a way to convert explanatory variables such as the `x`

below, to **numerical variables which can be digested by ML models**.

# Have: x <- c("apple", "tomato", "banana", "apple", "pineapple", "bic mac", "banana", "bic mac", "quinoa sans gluten", "pineapple", "avocado", "avocado", "avocado", "avocado!", ...) # Need: new_x <- c(0, 1, 2, 0, 3, 4, 2, ...)

This week, I use the `tips`

dataset (available here). Imagine that **you work in a restaurant**, and also have access to the following billing information:

total_bill tip sex smoker day time size 0 16.99 1.01 Female No Sun Dinner 2 1 10.34 1.66 Male No Sun Dinner 3 2 21.01 3.50 Male No Sun Dinner 3 3 23.68 3.31 Male No Sun Dinner 2 4 24.59 3.61 Female No Sun Dinner 4 .. ... ... ... ... ... ... ... 239 29.03 5.92 Male No Sat Dinner 3 240 27.18 2.00 Female Yes Sat Dinner 2 241 22.67 2.00 Male Yes Sat Dinner 2 242 17.82 1.75 Male No Sat Dinner 2 243 18.78 3.00 Female No Thur Dinner 2 [244 rows x 7 columns]

Based on this information, you’d like to **understand how to maximize your tip** ^^. In a Statistical/Machine Learning model, nnetsauce’s Ridge2Regressor in this post, the response to be understood is the numerical variable `tip`

. The explanatory variables are `total_bill`

, `sex`

, `smoker`

, `day`

, `time`

, `size`

. However, `sex`

, `smoker`

, `day`

, `time`

are not digestible as is; they need to be numerically encoded.

So, if we let `df`

be a data frame containing all the previous information on tips, and `pseudo_tip`

be the pseudo target created as explained in this previous post using R, then by using the querier, a numerical data frame `df_numeric`

can be obtained from `df`

as:

import numpy as np import pandas as pd import querier as qr Z = qr.select(df, 'total_bill, sex, smoker, day, time, size') df_numeric = pd.DataFrame(np.zeros(Z.shape), columns=Z.columns) col_names = Z.columns.values if (qr.select(Z, col).values.dtype == np.object): # if column is not numerical # average a pseudo-target instead of the real response Z_temp = qr.summarize(df, req = col + ', avg(pseudo_tip)', group_by = col) levels = np.unique(qr.select(Z, col).values) for l in levels: qrobj = qr.Querier(Z_temp) val = qrobj\ .filtr(col + '== "' + l + '"')\ .select("avg_pseudo_tip")\ .df.values df_numeric.at[np.where(Z[col] == l)[0], col] = np.float(val) else: df_numeric[col] = Z[col]

Below **on the left**, we can observe the distribution of tips, ranging approximately from 1 to 10. **On the right**, I obtained Ridge2Regressor’s cross-validation root mean squared error (RMSE) for different values of the target correlation (50 repeats each):

Surprisingly (or not?), the result is not compatible with my intuition. Considering that we are **constructing encoded explanatory variables by using the response** (a form of subtle overfitting), I was expecting a lower cross-validation error for low target correlations – close to 0 or slightly negative. But the lowest 5-fold cross-validation error is obtained for a target correlation equal to 0.7. It will be interesting to see **how these results generalize**. Though, it’s worth noticing that accross target correlations, the volatility of Ridge2Regressor cross-validation errors – adjusted with default parameters here – remains low.

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