Week 7 Videos
Contents
Week 7 Videos¶
Trying to use linear regression for classification¶
With respect to the penguins dataset, write a linear function to model the following.
Input: bill length
Output: 1 if the species is “Adelie”, 0 otherwise
import numpy as np
import pandas as pd
import altair as alt
import seaborn as sns
df = sns.load_dataset("penguins").dropna()
df["isAdelie_bool"] = (df["species"] == "Adelie")
df.head()
| species | island | bill_length_mm | bill_depth_mm | flipper_length_mm | body_mass_g | sex | isAdelie_bool | |
|---|---|---|---|---|---|---|---|---|
| 0 | Adelie | Torgersen | 39.1 | 18.7 | 181.0 | 3750.0 | Male | True |
| 1 | Adelie | Torgersen | 39.5 | 17.4 | 186.0 | 3800.0 | Female | True |
| 2 | Adelie | Torgersen | 40.3 | 18.0 | 195.0 | 3250.0 | Female | True |
| 4 | Adelie | Torgersen | 36.7 | 19.3 | 193.0 | 3450.0 | Female | True |
| 5 | Adelie | Torgersen | 39.3 | 20.6 | 190.0 | 3650.0 | Male | True |
(df["species"] == "Adelie")
0 True
1 True
2 True
4 True
5 True
...
338 False
340 False
341 False
342 False
343 False
Name: species, Length: 333, dtype: bool
(df["species"] == "Adelie").astype(float)
0 1.0
1 1.0
2 1.0
4 1.0
5 1.0
...
338 0.0
340 0.0
341 0.0
342 0.0
343 0.0
Name: species, Length: 333, dtype: float64
df["isAdelie_float"] = (df["species"] == "Adelie").astype(float)
df.tail()
| species | island | bill_length_mm | bill_depth_mm | flipper_length_mm | body_mass_g | sex | isAdelie_bool | isAdelie_float | |
|---|---|---|---|---|---|---|---|---|---|
| 338 | Gentoo | Biscoe | 47.2 | 13.7 | 214.0 | 4925.0 | Female | False | 0.0 |
| 340 | Gentoo | Biscoe | 46.8 | 14.3 | 215.0 | 4850.0 | Female | False | 0.0 |
| 341 | Gentoo | Biscoe | 50.4 | 15.7 | 222.0 | 5750.0 | Male | False | 0.0 |
| 342 | Gentoo | Biscoe | 45.2 | 14.8 | 212.0 | 5200.0 | Female | False | 0.0 |
| 343 | Gentoo | Biscoe | 49.9 | 16.1 | 213.0 | 5400.0 | Male | False | 0.0 |
alt.Chart(df).mark_circle().encode(
x="bill_length_mm",
y="isAdelie_bool"
)
alt.Chart(df).mark_circle().encode(
x="bill_length_mm",
y="isAdelie_float"
)
from sklearn.linear_model import LinearRegression
reg = LinearRegression()
reg.fit(df[["bill_length_mm"]], df["isAdelie_float"])
LinearRegression()
c = alt.Chart(df).mark_circle().encode(
x="bill_length_mm",
y="isAdelie_float"
)
df["Pred"] = reg.predict(df[["bill_length_mm"]])
df.head()
| species | island | bill_length_mm | bill_depth_mm | flipper_length_mm | body_mass_g | sex | isAdelie_bool | isAdelie_float | Pred | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Adelie | Torgersen | 39.1 | 18.7 | 181.0 | 3750.0 | Male | True | 1.0 | 0.810316 |
| 1 | Adelie | Torgersen | 39.5 | 17.4 | 186.0 | 3800.0 | Female | True | 1.0 | 0.779914 |
| 2 | Adelie | Torgersen | 40.3 | 18.0 | 195.0 | 3250.0 | Female | True | 1.0 | 0.719110 |
| 4 | Adelie | Torgersen | 36.7 | 19.3 | 193.0 | 3450.0 | Female | True | 1.0 | 0.992728 |
| 5 | Adelie | Torgersen | 39.3 | 20.6 | 190.0 | 3650.0 | Male | True | 1.0 | 0.795115 |
c1 = alt.Chart(df).mark_line(color="red").encode(
x="bill_length_mm",
y="Pred"
)
c+c1
Logistic Regression, Part 1¶
from sklearn.linear_model import LogisticRegression
clf = LogisticRegression()
clf.fit(df[["bill_length_mm"]], df["isAdelie_float"])
LogisticRegression()
df["Pred2"] = clf.predict(df[["bill_length_mm"]])
c2 = alt.Chart(df).mark_point(color="red").encode(
x="bill_length_mm",
y="Pred2"
)
c+c2
Logistic Regression, Part 2¶
clf.predict(df[["bill_length_mm"]])
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1.,
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0.,
1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
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1., 0., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
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0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
clf.classes_
array([0., 1.])
clf.predict_proba(df[["bill_length_mm"]])
array([[1.30799652e-02, 9.86920035e-01],
[2.05066613e-02, 9.79493339e-01],
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[9.99632041e-01, 3.67958508e-04],
[6.69501446e-01, 3.30498554e-01],
[9.99947275e-01, 5.27251927e-05],
[9.77950677e-01, 2.20493235e-02],
[9.99999139e-01, 8.60837276e-07],
[9.98846866e-01, 1.15313383e-03],
[9.92862513e-01, 7.13748666e-03],
[9.88771519e-01, 1.12284806e-02],
[9.99814636e-01, 1.85363789e-04],
[9.33956925e-01, 6.60430749e-02],
[9.99671773e-01, 3.28226694e-04]])
A = clf.predict_proba(df[["bill_length_mm"]])
df["Pred3"] = A[:,1]
c3 = alt.Chart(df).mark_line(color="red").encode(
x="bill_length_mm",
y="Pred3"
)
c+c3
Logistic Regression, Part 3¶
clf = LogisticRegression()
clf.fit(df[["bill_length_mm"]], df["species"])
LogisticRegression()
df["Pred4"] = clf.predict(df[["bill_length_mm"]])
df.head()
| species | island | bill_length_mm | bill_depth_mm | flipper_length_mm | body_mass_g | sex | isAdelie_bool | isAdelie_float | Pred | Pred2 | Pred3 | Pred4 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Adelie | Torgersen | 39.1 | 18.7 | 181.0 | 3750.0 | Male | True | 1.0 | 0.810316 | 1.0 | 0.986920 | Adelie |
| 1 | Adelie | Torgersen | 39.5 | 17.4 | 186.0 | 3800.0 | Female | True | 1.0 | 0.779914 | 1.0 | 0.979493 | Adelie |
| 2 | Adelie | Torgersen | 40.3 | 18.0 | 195.0 | 3250.0 | Female | True | 1.0 | 0.719110 | 1.0 | 0.950350 | Adelie |
| 4 | Adelie | Torgersen | 36.7 | 19.3 | 193.0 | 3450.0 | Female | True | 1.0 | 0.992728 | 1.0 | 0.999148 | Adelie |
| 5 | Adelie | Torgersen | 39.3 | 20.6 | 190.0 | 3650.0 | Male | True | 1.0 | 0.795115 | 1.0 | 0.983615 | Adelie |
df["Pred4"].value_counts()
Gentoo 173
Adelie 150
Chinstrap 10
Name: Pred4, dtype: int64
df["species"].value_counts()
Adelie 146
Gentoo 119
Chinstrap 68
Name: species, dtype: int64
alt.Chart(df).mark_circle().encode(
x="bill_length_mm",
y="flipper_length_mm",
color="species"
)
clf.score(df[["bill_length_mm"]], df["species"])
0.7537537537537538
clf.classes_
array(['Adelie', 'Chinstrap', 'Gentoo'], dtype=object)
clf.predict_proba(df[["bill_length_mm"]])
array([[9.87130539e-01, 2.03702100e-03, 1.08324397e-02],
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[1.60571852e-04, 4.28261330e-01, 5.71578098e-01],
[6.46480424e-02, 2.65619915e-01, 6.69732042e-01],
[2.88832350e-04, 4.13302974e-01, 5.86408194e-01]])
clf2 = LogisticRegression()
clf2.fit(df[["bill_length_mm","flipper_length_mm"]], df["species"])
LogisticRegression()
clf2.score(df[["bill_length_mm","flipper_length_mm"]], df["species"])
0.9579579579579579
clf2.predict(df[["bill_length_mm","flipper_length_mm"]])
array(['Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Chinstrap', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Chinstrap', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Gentoo',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Chinstrap', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Gentoo', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie', 'Adelie',
'Adelie', 'Adelie', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Adelie', 'Chinstrap', 'Adelie',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Adelie', 'Chinstrap', 'Adelie',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Gentoo', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Gentoo',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Adelie', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Chinstrap', 'Adelie', 'Chinstrap', 'Chinstrap', 'Chinstrap',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Chinstrap', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo',
'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo', 'Gentoo'], dtype=object)
clf2.predict(df[["bill_length_mm","flipper_length_mm"]]) == df["species"]
0 True
1 True
2 True
4 True
5 True
...
338 True
340 True
341 True
342 True
343 True
Name: species, Length: 333, dtype: bool
(clf2.predict(df[["bill_length_mm","flipper_length_mm"]]) == df["species"]).mean()
0.9579579579579579