Week 9 Videos¶

Logistic regression decision boundary with 3 classes¶

import altair as alt
import seaborn as sns

df = sns.load_dataset("penguins").dropna()

df.columns

Index(['species', 'island', 'bill_length_mm', 'bill_depth_mm',
       'flipper_length_mm', 'body_mass_g', 'sex'],
      dtype='object')

cols = ['bill_length_mm', 'bill_depth_mm']

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color="species"
)

from sklearn.linear_model import LogisticRegression

clf = LogisticRegression()

clf.fit(df[cols], df["species"])

LogisticRegression()

df["pred"] = clf.predict(df[cols])

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color="pred"
)

A grid of points using NumPy¶

import numpy as np
import pandas as pd

x = np.arange(32, 60, 0.2)
y = np.arange(13, 22, 0.2)

pd.DataFrame({"x":x, "y":y})

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
/var/folders/8j/gshrlmtn7dg4qtztj4d4t_w40000gn/T/ipykernel_12680/4035979450.py in <module>
----> 1 pd.DataFrame({"x":x, "y":y})

~/miniconda3/envs/math10s22/lib/python3.7/site-packages/pandas/core/frame.py in __init__(self, data, index, columns, dtype, copy)
    612         elif isinstance(data, dict):
    613             # GH#38939 de facto copy defaults to False only in non-dict cases
--> 614             mgr = dict_to_mgr(data, index, columns, dtype=dtype, copy=copy, typ=manager)
    615         elif isinstance(data, ma.MaskedArray):
    616             import numpy.ma.mrecords as mrecords

~/miniconda3/envs/math10s22/lib/python3.7/site-packages/pandas/core/internals/construction.py in dict_to_mgr(data, index, columns, dtype, typ, copy)
    463 
    464     return arrays_to_mgr(
--> 465         arrays, data_names, index, columns, dtype=dtype, typ=typ, consolidate=copy
    466     )
    467 

~/miniconda3/envs/math10s22/lib/python3.7/site-packages/pandas/core/internals/construction.py in arrays_to_mgr(arrays, arr_names, index, columns, dtype, verify_integrity, typ, consolidate)
    117         # figure out the index, if necessary
    118         if index is None:
--> 119             index = _extract_index(arrays)
    120         else:
    121             index = ensure_index(index)

~/miniconda3/envs/math10s22/lib/python3.7/site-packages/pandas/core/internals/construction.py in _extract_index(data)
    633             lengths = list(set(raw_lengths))
    634             if len(lengths) > 1:
--> 635                 raise ValueError("All arrays must be of the same length")
    636 
    637             if have_dicts:

ValueError: All arrays must be of the same length

array([32. , 32.2, 32.4, 32.6, 32.8, 33. , 33.2, 33.4, 33.6, 33.8, 34. ,
       34.2, 34.4, 34.6, 34.8, 35. , 35.2, 35.4, 35.6, 35.8, 36. , 36.2,
       36.4, 36.6, 36.8, 37. , 37.2, 37.4, 37.6, 37.8, 38. , 38.2, 38.4,
       38.6, 38.8, 39. , 39.2, 39.4, 39.6, 39.8, 40. , 40.2, 40.4, 40.6,
       40.8, 41. , 41.2, 41.4, 41.6, 41.8, 42. , 42.2, 42.4, 42.6, 42.8,
       43. , 43.2, 43.4, 43.6, 43.8, 44. , 44.2, 44.4, 44.6, 44.8, 45. ,
       45.2, 45.4, 45.6, 45.8, 46. , 46.2, 46.4, 46.6, 46.8, 47. , 47.2,
       47.4, 47.6, 47.8, 48. , 48.2, 48.4, 48.6, 48.8, 49. , 49.2, 49.4,
       49.6, 49.8, 50. , 50.2, 50.4, 50.6, 50.8, 51. , 51.2, 51.4, 51.6,
       51.8, 52. , 52.2, 52.4, 52.6, 52.8, 53. , 53.2, 53.4, 53.6, 53.8,
       54. , 54.2, 54.4, 54.6, 54.8, 55. , 55.2, 55.4, 55.6, 55.8, 56. ,
       56.2, 56.4, 56.6, 56.8, 57. , 57.2, 57.4, 57.6, 57.8, 58. , 58.2,
       58.4, 58.6, 58.8, 59. , 59.2, 59.4, 59.6, 59.8])

array([13. , 13.2, 13.4, 13.6, 13.8, 14. , 14.2, 14.4, 14.6, 14.8, 15. ,
       15.2, 15.4, 15.6, 15.8, 16. , 16.2, 16.4, 16.6, 16.8, 17. , 17.2,
       17.4, 17.6, 17.8, 18. , 18.2, 18.4, 18.6, 18.8, 19. , 19.2, 19.4,
       19.6, 19.8, 20. , 20.2, 20.4, 20.6, 20.8, 21. , 21.2, 21.4, 21.6,
       21.8])

xx, yy = np.meshgrid(x,y)

xx

array([[32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8],
       [32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8],
       [32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8],
       ...,
       [32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8],
       [32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8],
       [32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8]])

yy

array([[13. , 13. , 13. , ..., 13. , 13. , 13. ],
       [13.2, 13.2, 13.2, ..., 13.2, 13.2, 13.2],
       [13.4, 13.4, 13.4, ..., 13.4, 13.4, 13.4],
       ...,
       [21.4, 21.4, 21.4, ..., 21.4, 21.4, 21.4],
       [21.6, 21.6, 21.6, ..., 21.6, 21.6, 21.6],
       [21.8, 21.8, 21.8, ..., 21.8, 21.8, 21.8]])

xx.shape

(45, 140)

x.size

y.size

xx.reshape(-1)

array([32. , 32.2, 32.4, ..., 59.4, 59.6, 59.8])

yy.reshape(-1)

array([13. , 13. , 13. , ..., 21.8, 21.8, 21.8])

xx.reshape(-1).size

x.size*y.size

df_sim = pd.DataFrame({"x":xx.reshape(-1), "y":yy.reshape(-1)})

df_sim

	x	y
0	32.0	13.0
1	32.2	13.0
2	32.4	13.0
3	32.6	13.0
4	32.8	13.0
...	...	...
6295	59.0	21.8
6296	59.2	21.8
6297	59.4	21.8
6298	59.6	21.8
6299	59.8	21.8

6300 rows × 2 columns

df_sim.tail()

	x	y
6295	59.0	21.8
6296	59.2	21.8
6297	59.4	21.8
6298	59.6	21.8
6299	59.8	21.8

A grid of points using itertools¶

from itertools import product

array([32. , 32.2, 32.4, 32.6, 32.8, 33. , 33.2, 33.4, 33.6, 33.8, 34. ,
       34.2, 34.4, 34.6, 34.8, 35. , 35.2, 35.4, 35.6, 35.8, 36. , 36.2,
       36.4, 36.6, 36.8, 37. , 37.2, 37.4, 37.6, 37.8, 38. , 38.2, 38.4,
       38.6, 38.8, 39. , 39.2, 39.4, 39.6, 39.8, 40. , 40.2, 40.4, 40.6,
       40.8, 41. , 41.2, 41.4, 41.6, 41.8, 42. , 42.2, 42.4, 42.6, 42.8,
       43. , 43.2, 43.4, 43.6, 43.8, 44. , 44.2, 44.4, 44.6, 44.8, 45. ,
       45.2, 45.4, 45.6, 45.8, 46. , 46.2, 46.4, 46.6, 46.8, 47. , 47.2,
       47.4, 47.6, 47.8, 48. , 48.2, 48.4, 48.6, 48.8, 49. , 49.2, 49.4,
       49.6, 49.8, 50. , 50.2, 50.4, 50.6, 50.8, 51. , 51.2, 51.4, 51.6,
       51.8, 52. , 52.2, 52.4, 52.6, 52.8, 53. , 53.2, 53.4, 53.6, 53.8,
       54. , 54.2, 54.4, 54.6, 54.8, 55. , 55.2, 55.4, 55.6, 55.8, 56. ,
       56.2, 56.4, 56.6, 56.8, 57. , 57.2, 57.4, 57.6, 57.8, 58. , 58.2,
       58.4, 58.6, 58.8, 59. , 59.2, 59.4, 59.6, 59.8])

array([13. , 13.2, 13.4, 13.6, 13.8, 14. , 14.2, 14.4, 14.6, 14.8, 15. ,
       15.2, 15.4, 15.6, 15.8, 16. , 16.2, 16.4, 16.6, 16.8, 17. , 17.2,
       17.4, 17.6, 17.8, 18. , 18.2, 18.4, 18.6, 18.8, 19. , 19.2, 19.4,
       19.6, 19.8, 20. , 20.2, 20.4, 20.6, 20.8, 21. , 21.2, 21.4, 21.6,
       21.8])

g = product(x,y)

type(g)

itertools.product

list(g)

[(32.0, 13.0),
 (32.0, 13.2),
 (32.0, 13.399999999999999),
 (32.0, 13.599999999999998),
 (32.0, 13.799999999999997),
 (32.0, 13.999999999999996),
 (32.0, 14.199999999999996),
 (32.0, 14.399999999999995),
 (32.0, 14.599999999999994),
 (32.0, 14.799999999999994),
 (32.0, 14.999999999999993),
 (32.0, 15.199999999999992),
 (32.0, 15.399999999999991),
 (32.0, 15.59999999999999),
 (32.0, 15.79999999999999),
 (32.0, 15.99999999999999),
 (32.0, 16.19999999999999),
 (32.0, 16.399999999999988),
 (32.0, 16.599999999999987),
 (32.0, 16.799999999999986),
 (32.0, 16.999999999999986),
 (32.0, 17.199999999999985),
 (32.0, 17.399999999999984),
 (32.0, 17.599999999999984),
 (32.0, 17.799999999999983),
 (32.0, 17.999999999999982),
 (32.0, 18.19999999999998),
 (32.0, 18.39999999999998),
 (32.0, 18.59999999999998),
 (32.0, 18.79999999999998),
 (32.0, 18.99999999999998),
 (32.0, 19.199999999999978),
 (32.0, 19.399999999999977),
 (32.0, 19.599999999999977),
 (32.0, 19.799999999999976),
 (32.0, 19.999999999999975),
 (32.0, 20.199999999999974),
 (32.0, 20.399999999999974),
 (32.0, 20.599999999999973),
 (32.0, 20.799999999999972),
 (32.0, 20.99999999999997),
 (32.0, 21.19999999999997),
 (32.0, 21.39999999999997),
 (32.0, 21.59999999999997),
 (32.0, 21.79999999999997),
 (32.2, 13.0),
 (32.2, 13.2),
 (32.2, 13.399999999999999),
 (32.2, 13.599999999999998),
 (32.2, 13.799999999999997),
 (32.2, 13.999999999999996),
 (32.2, 14.199999999999996),
 (32.2, 14.399999999999995),
 (32.2, 14.599999999999994),
 (32.2, 14.799999999999994),
 (32.2, 14.999999999999993),
 (32.2, 15.199999999999992),
 (32.2, 15.399999999999991),
 (32.2, 15.59999999999999),
 (32.2, 15.79999999999999),
 (32.2, 15.99999999999999),
 (32.2, 16.19999999999999),
 (32.2, 16.399999999999988),
 (32.2, 16.599999999999987),
 (32.2, 16.799999999999986),
 (32.2, 16.999999999999986),
 (32.2, 17.199999999999985),
 (32.2, 17.399999999999984),
 (32.2, 17.599999999999984),
 (32.2, 17.799999999999983),
 (32.2, 17.999999999999982),
 (32.2, 18.19999999999998),
 (32.2, 18.39999999999998),
 (32.2, 18.59999999999998),
 (32.2, 18.79999999999998),
 (32.2, 18.99999999999998),
 (32.2, 19.199999999999978),
 (32.2, 19.399999999999977),
 (32.2, 19.599999999999977),
 (32.2, 19.799999999999976),
 (32.2, 19.999999999999975),
 (32.2, 20.199999999999974),
 (32.2, 20.399999999999974),
 (32.2, 20.599999999999973),
 (32.2, 20.799999999999972),
 (32.2, 20.99999999999997),
 (32.2, 21.19999999999997),
 (32.2, 21.39999999999997),
 (32.2, 21.59999999999997),
 (32.2, 21.79999999999997),
 (32.400000000000006, 13.0),
 (32.400000000000006, 13.2),
 (32.400000000000006, 13.399999999999999),
 (32.400000000000006, 13.599999999999998),
 (32.400000000000006, 13.799999999999997),
 (32.400000000000006, 13.999999999999996),
 (32.400000000000006, 14.199999999999996),
 (32.400000000000006, 14.399999999999995),
 (32.400000000000006, 14.599999999999994),
 (32.400000000000006, 14.799999999999994),
 (32.400000000000006, 14.999999999999993),
 (32.400000000000006, 15.199999999999992),
 (32.400000000000006, 15.399999999999991),
 (32.400000000000006, 15.59999999999999),
 (32.400000000000006, 15.79999999999999),
 (32.400000000000006, 15.99999999999999),
 (32.400000000000006, 16.19999999999999),
 (32.400000000000006, 16.399999999999988),
 (32.400000000000006, 16.599999999999987),
 (32.400000000000006, 16.799999999999986),
 (32.400000000000006, 16.999999999999986),
 (32.400000000000006, 17.199999999999985),
 (32.400000000000006, 17.399999999999984),
 (32.400000000000006, 17.599999999999984),
 (32.400000000000006, 17.799999999999983),
 (32.400000000000006, 17.999999999999982),
 (32.400000000000006, 18.19999999999998),
 (32.400000000000006, 18.39999999999998),
 (32.400000000000006, 18.59999999999998),
 (32.400000000000006, 18.79999999999998),
 (32.400000000000006, 18.99999999999998),
 (32.400000000000006, 19.199999999999978),
 (32.400000000000006, 19.399999999999977),
 (32.400000000000006, 19.599999999999977),
 (32.400000000000006, 19.799999999999976),
 (32.400000000000006, 19.999999999999975),
 (32.400000000000006, 20.199999999999974),
 (32.400000000000006, 20.399999999999974),
 (32.400000000000006, 20.599999999999973),
 (32.400000000000006, 20.799999999999972),
 (32.400000000000006, 20.99999999999997),
 (32.400000000000006, 21.19999999999997),
 (32.400000000000006, 21.39999999999997),
 (32.400000000000006, 21.59999999999997),
 (32.400000000000006, 21.79999999999997),
 (32.60000000000001, 13.0),
 (32.60000000000001, 13.2),
 (32.60000000000001, 13.399999999999999),
 (32.60000000000001, 13.599999999999998),
 (32.60000000000001, 13.799999999999997),
 (32.60000000000001, 13.999999999999996),
 (32.60000000000001, 14.199999999999996),
 (32.60000000000001, 14.399999999999995),
 (32.60000000000001, 14.599999999999994),
 (32.60000000000001, 14.799999999999994),
 (32.60000000000001, 14.999999999999993),
 (32.60000000000001, 15.199999999999992),
 (32.60000000000001, 15.399999999999991),
 (32.60000000000001, 15.59999999999999),
 (32.60000000000001, 15.79999999999999),
 (32.60000000000001, 15.99999999999999),
 (32.60000000000001, 16.19999999999999),
 (32.60000000000001, 16.399999999999988),
 (32.60000000000001, 16.599999999999987),
 (32.60000000000001, 16.799999999999986),
 (32.60000000000001, 16.999999999999986),
 (32.60000000000001, 17.199999999999985),
 (32.60000000000001, 17.399999999999984),
 (32.60000000000001, 17.599999999999984),
 (32.60000000000001, 17.799999999999983),
 (32.60000000000001, 17.999999999999982),
 (32.60000000000001, 18.19999999999998),
 (32.60000000000001, 18.39999999999998),
 (32.60000000000001, 18.59999999999998),
 (32.60000000000001, 18.79999999999998),
 (32.60000000000001, 18.99999999999998),
 (32.60000000000001, 19.199999999999978),
 (32.60000000000001, 19.399999999999977),
 (32.60000000000001, 19.599999999999977),
 (32.60000000000001, 19.799999999999976),
 (32.60000000000001, 19.999999999999975),
 (32.60000000000001, 20.199999999999974),
 (32.60000000000001, 20.399999999999974),
 (32.60000000000001, 20.599999999999973),
 (32.60000000000001, 20.799999999999972),
 (32.60000000000001, 20.99999999999997),
 (32.60000000000001, 21.19999999999997),
 (32.60000000000001, 21.39999999999997),
 (32.60000000000001, 21.59999999999997),
 (32.60000000000001, 21.79999999999997),
 (32.80000000000001, 13.0),
 (32.80000000000001, 13.2),
 (32.80000000000001, 13.399999999999999),
 (32.80000000000001, 13.599999999999998),
 (32.80000000000001, 13.799999999999997),
 (32.80000000000001, 13.999999999999996),
 (32.80000000000001, 14.199999999999996),
 (32.80000000000001, 14.399999999999995),
 (32.80000000000001, 14.599999999999994),
 (32.80000000000001, 14.799999999999994),
 (32.80000000000001, 14.999999999999993),
 (32.80000000000001, 15.199999999999992),
 (32.80000000000001, 15.399999999999991),
 (32.80000000000001, 15.59999999999999),
 (32.80000000000001, 15.79999999999999),
 (32.80000000000001, 15.99999999999999),
 (32.80000000000001, 16.19999999999999),
 (32.80000000000001, 16.399999999999988),
 (32.80000000000001, 16.599999999999987),
 (32.80000000000001, 16.799999999999986),
 (32.80000000000001, 16.999999999999986),
 (32.80000000000001, 17.199999999999985),
 (32.80000000000001, 17.399999999999984),
 (32.80000000000001, 17.599999999999984),
 (32.80000000000001, 17.799999999999983),
 (32.80000000000001, 17.999999999999982),
 (32.80000000000001, 18.19999999999998),
 (32.80000000000001, 18.39999999999998),
 (32.80000000000001, 18.59999999999998),
 (32.80000000000001, 18.79999999999998),
 (32.80000000000001, 18.99999999999998),
 (32.80000000000001, 19.199999999999978),
 (32.80000000000001, 19.399999999999977),
 (32.80000000000001, 19.599999999999977),
 (32.80000000000001, 19.799999999999976),
 (32.80000000000001, 19.999999999999975),
 (32.80000000000001, 20.199999999999974),
 (32.80000000000001, 20.399999999999974),
 (32.80000000000001, 20.599999999999973),
 (32.80000000000001, 20.799999999999972),
 (32.80000000000001, 20.99999999999997),
 (32.80000000000001, 21.19999999999997),
 (32.80000000000001, 21.39999999999997),
 (32.80000000000001, 21.59999999999997),
 (32.80000000000001, 21.79999999999997),
 (33.000000000000014, 13.0),
 (33.000000000000014, 13.2),
 (33.000000000000014, 13.399999999999999),
 (33.000000000000014, 13.599999999999998),
 (33.000000000000014, 13.799999999999997),
 (33.000000000000014, 13.999999999999996),
 (33.000000000000014, 14.199999999999996),
 (33.000000000000014, 14.399999999999995),
 (33.000000000000014, 14.599999999999994),
 (33.000000000000014, 14.799999999999994),
 (33.000000000000014, 14.999999999999993),
 (33.000000000000014, 15.199999999999992),
 (33.000000000000014, 15.399999999999991),
 (33.000000000000014, 15.59999999999999),
 (33.000000000000014, 15.79999999999999),
 (33.000000000000014, 15.99999999999999),
 (33.000000000000014, 16.19999999999999),
 (33.000000000000014, 16.399999999999988),
 (33.000000000000014, 16.599999999999987),
 (33.000000000000014, 16.799999999999986),
 (33.000000000000014, 16.999999999999986),
 (33.000000000000014, 17.199999999999985),
 (33.000000000000014, 17.399999999999984),
 (33.000000000000014, 17.599999999999984),
 (33.000000000000014, 17.799999999999983),
 (33.000000000000014, 17.999999999999982),
 (33.000000000000014, 18.19999999999998),
 (33.000000000000014, 18.39999999999998),
 (33.000000000000014, 18.59999999999998),
 (33.000000000000014, 18.79999999999998),
 (33.000000000000014, 18.99999999999998),
 (33.000000000000014, 19.199999999999978),
 (33.000000000000014, 19.399999999999977),
 (33.000000000000014, 19.599999999999977),
 (33.000000000000014, 19.799999999999976),
 (33.000000000000014, 19.999999999999975),
 (33.000000000000014, 20.199999999999974),
 (33.000000000000014, 20.399999999999974),
 (33.000000000000014, 20.599999999999973),
 (33.000000000000014, 20.799999999999972),
 (33.000000000000014, 20.99999999999997),
 (33.000000000000014, 21.19999999999997),
 (33.000000000000014, 21.39999999999997),
 (33.000000000000014, 21.59999999999997),
 (33.000000000000014, 21.79999999999997),
 (33.20000000000002, 13.0),
 (33.20000000000002, 13.2),
 (33.20000000000002, 13.399999999999999),
 (33.20000000000002, 13.599999999999998),
 (33.20000000000002, 13.799999999999997),
 (33.20000000000002, 13.999999999999996),
 (33.20000000000002, 14.199999999999996),
 (33.20000000000002, 14.399999999999995),
 (33.20000000000002, 14.599999999999994),
 (33.20000000000002, 14.799999999999994),
 (33.20000000000002, 14.999999999999993),
 (33.20000000000002, 15.199999999999992),
 (33.20000000000002, 15.399999999999991),
 (33.20000000000002, 15.59999999999999),
 (33.20000000000002, 15.79999999999999),
 (33.20000000000002, 15.99999999999999),
 (33.20000000000002, 16.19999999999999),
 (33.20000000000002, 16.399999999999988),
 (33.20000000000002, 16.599999999999987),
 (33.20000000000002, 16.799999999999986),
 (33.20000000000002, 16.999999999999986),
 (33.20000000000002, 17.199999999999985),
 (33.20000000000002, 17.399999999999984),
 (33.20000000000002, 17.599999999999984),
 (33.20000000000002, 17.799999999999983),
 (33.20000000000002, 17.999999999999982),
 (33.20000000000002, 18.19999999999998),
 (33.20000000000002, 18.39999999999998),
 (33.20000000000002, 18.59999999999998),
 (33.20000000000002, 18.79999999999998),
 (33.20000000000002, 18.99999999999998),
 (33.20000000000002, 19.199999999999978),
 (33.20000000000002, 19.399999999999977),
 (33.20000000000002, 19.599999999999977),
 (33.20000000000002, 19.799999999999976),
 (33.20000000000002, 19.999999999999975),
 (33.20000000000002, 20.199999999999974),
 (33.20000000000002, 20.399999999999974),
 (33.20000000000002, 20.599999999999973),
 (33.20000000000002, 20.799999999999972),
 (33.20000000000002, 20.99999999999997),
 (33.20000000000002, 21.19999999999997),
 (33.20000000000002, 21.39999999999997),
 (33.20000000000002, 21.59999999999997),
 (33.20000000000002, 21.79999999999997),
 (33.40000000000002, 13.0),
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 (35.60000000000005, 13.799999999999997),
 (35.60000000000005, 13.999999999999996),
 (35.60000000000005, 14.199999999999996),
 (35.60000000000005, 14.399999999999995),
 (35.60000000000005, 14.599999999999994),
 (35.60000000000005, 14.799999999999994),
 (35.60000000000005, 14.999999999999993),
 (35.60000000000005, 15.199999999999992),
 (35.60000000000005, 15.399999999999991),
 (35.60000000000005, 15.59999999999999),
 (35.60000000000005, 15.79999999999999),
 (35.60000000000005, 15.99999999999999),
 (35.60000000000005, 16.19999999999999),
 (35.60000000000005, 16.399999999999988),
 (35.60000000000005, 16.599999999999987),
 (35.60000000000005, 16.799999999999986),
 (35.60000000000005, 16.999999999999986),
 (35.60000000000005, 17.199999999999985),
 (35.60000000000005, 17.399999999999984),
 (35.60000000000005, 17.599999999999984),
 (35.60000000000005, 17.799999999999983),
 (35.60000000000005, 17.999999999999982),
 (35.60000000000005, 18.19999999999998),
 (35.60000000000005, 18.39999999999998),
 (35.60000000000005, 18.59999999999998),
 (35.60000000000005, 18.79999999999998),
 (35.60000000000005, 18.99999999999998),
 (35.60000000000005, 19.199999999999978),
 (35.60000000000005, 19.399999999999977),
 (35.60000000000005, 19.599999999999977),
 (35.60000000000005, 19.799999999999976),
 (35.60000000000005, 19.999999999999975),
 (35.60000000000005, 20.199999999999974),
 (35.60000000000005, 20.399999999999974),
 (35.60000000000005, 20.599999999999973),
 (35.60000000000005, 20.799999999999972),
 (35.60000000000005, 20.99999999999997),
 (35.60000000000005, 21.19999999999997),
 (35.60000000000005, 21.39999999999997),
 (35.60000000000005, 21.59999999999997),
 (35.60000000000005, 21.79999999999997),
 (35.800000000000054, 13.0),
 (35.800000000000054, 13.2),
 (35.800000000000054, 13.399999999999999),
 (35.800000000000054, 13.599999999999998),
 (35.800000000000054, 13.799999999999997),
 (35.800000000000054, 13.999999999999996),
 (35.800000000000054, 14.199999999999996),
 (35.800000000000054, 14.399999999999995),
 (35.800000000000054, 14.599999999999994),
 (35.800000000000054, 14.799999999999994),
 (35.800000000000054, 14.999999999999993),
 (35.800000000000054, 15.199999999999992),
 (35.800000000000054, 15.399999999999991),
 (35.800000000000054, 15.59999999999999),
 (35.800000000000054, 15.79999999999999),
 (35.800000000000054, 15.99999999999999),
 (35.800000000000054, 16.19999999999999),
 (35.800000000000054, 16.399999999999988),
 (35.800000000000054, 16.599999999999987),
 (35.800000000000054, 16.799999999999986),
 (35.800000000000054, 16.999999999999986),
 (35.800000000000054, 17.199999999999985),
 (35.800000000000054, 17.399999999999984),
 (35.800000000000054, 17.599999999999984),
 (35.800000000000054, 17.799999999999983),
 (35.800000000000054, 17.999999999999982),
 (35.800000000000054, 18.19999999999998),
 (35.800000000000054, 18.39999999999998),
 (35.800000000000054, 18.59999999999998),
 (35.800000000000054, 18.79999999999998),
 (35.800000000000054, 18.99999999999998),
 (35.800000000000054, 19.199999999999978),
 (35.800000000000054, 19.399999999999977),
 (35.800000000000054, 19.599999999999977),
 (35.800000000000054, 19.799999999999976),
 (35.800000000000054, 19.999999999999975),
 (35.800000000000054, 20.199999999999974),
 (35.800000000000054, 20.399999999999974),
 (35.800000000000054, 20.599999999999973),
 (35.800000000000054, 20.799999999999972),
 (35.800000000000054, 20.99999999999997),
 (35.800000000000054, 21.19999999999997),
 (35.800000000000054, 21.39999999999997),
 (35.800000000000054, 21.59999999999997),
 (35.800000000000054, 21.79999999999997),
 (36.00000000000006, 13.0),
 (36.00000000000006, 13.2),
 (36.00000000000006, 13.399999999999999),
 (36.00000000000006, 13.599999999999998),
 (36.00000000000006, 13.799999999999997),
 (36.00000000000006, 13.999999999999996),
 (36.00000000000006, 14.199999999999996),
 (36.00000000000006, 14.399999999999995),
 (36.00000000000006, 14.599999999999994),
 (36.00000000000006, 14.799999999999994),
 (36.00000000000006, 14.999999999999993),
 (36.00000000000006, 15.199999999999992),
 (36.00000000000006, 15.399999999999991),
 (36.00000000000006, 15.59999999999999),
 (36.00000000000006, 15.79999999999999),
 (36.00000000000006, 15.99999999999999),
 (36.00000000000006, 16.19999999999999),
 (36.00000000000006, 16.399999999999988),
 (36.00000000000006, 16.599999999999987),
 (36.00000000000006, 16.799999999999986),
 (36.00000000000006, 16.999999999999986),
 (36.00000000000006, 17.199999999999985),
 (36.00000000000006, 17.399999999999984),
 (36.00000000000006, 17.599999999999984),
 (36.00000000000006, 17.799999999999983),
 (36.00000000000006, 17.999999999999982),
 (36.00000000000006, 18.19999999999998),
 (36.00000000000006, 18.39999999999998),
 (36.00000000000006, 18.59999999999998),
 (36.00000000000006, 18.79999999999998),
 (36.00000000000006, 18.99999999999998),
 (36.00000000000006, 19.199999999999978),
 (36.00000000000006, 19.399999999999977),
 (36.00000000000006, 19.599999999999977),
 (36.00000000000006, 19.799999999999976),
 (36.00000000000006, 19.999999999999975),
 (36.00000000000006, 20.199999999999974),
 (36.00000000000006, 20.399999999999974),
 (36.00000000000006, 20.599999999999973),
 (36.00000000000006, 20.799999999999972),
 (36.00000000000006, 20.99999999999997),
 (36.00000000000006, 21.19999999999997),
 (36.00000000000006, 21.39999999999997),
 (36.00000000000006, 21.59999999999997),
 (36.00000000000006, 21.79999999999997),
 (36.20000000000006, 13.0),
 (36.20000000000006, 13.2),
 (36.20000000000006, 13.399999999999999),
 (36.20000000000006, 13.599999999999998),
 (36.20000000000006, 13.799999999999997),
 (36.20000000000006, 13.999999999999996),
 (36.20000000000006, 14.199999999999996),
 (36.20000000000006, 14.399999999999995),
 (36.20000000000006, 14.599999999999994),
 (36.20000000000006, 14.799999999999994),
 (36.20000000000006, 14.999999999999993),
 (36.20000000000006, 15.199999999999992),
 (36.20000000000006, 15.399999999999991),
 (36.20000000000006, 15.59999999999999),
 (36.20000000000006, 15.79999999999999),
 (36.20000000000006, 15.99999999999999),
 (36.20000000000006, 16.19999999999999),
 (36.20000000000006, 16.399999999999988),
 (36.20000000000006, 16.599999999999987),
 (36.20000000000006, 16.799999999999986),
 (36.20000000000006, 16.999999999999986),
 (36.20000000000006, 17.199999999999985),
 (36.20000000000006, 17.399999999999984),
 (36.20000000000006, 17.599999999999984),
 (36.20000000000006, 17.799999999999983),
 (36.20000000000006, 17.999999999999982),
 (36.20000000000006, 18.19999999999998),
 (36.20000000000006, 18.39999999999998),
 (36.20000000000006, 18.59999999999998),
 (36.20000000000006, 18.79999999999998),
 (36.20000000000006, 18.99999999999998),
 (36.20000000000006, 19.199999999999978),
 (36.20000000000006, 19.399999999999977),
 (36.20000000000006, 19.599999999999977),
 (36.20000000000006, 19.799999999999976),
 (36.20000000000006, 19.999999999999975),
 (36.20000000000006, 20.199999999999974),
 (36.20000000000006, 20.399999999999974),
 (36.20000000000006, 20.599999999999973),
 (36.20000000000006, 20.799999999999972),
 (36.20000000000006, 20.99999999999997),
 (36.20000000000006, 21.19999999999997),
 (36.20000000000006, 21.39999999999997),
 (36.20000000000006, 21.59999999999997),
 (36.20000000000006, 21.79999999999997),
 (36.40000000000006, 13.0),
 (36.40000000000006, 13.2),
 (36.40000000000006, 13.399999999999999),
 (36.40000000000006, 13.599999999999998),
 (36.40000000000006, 13.799999999999997),
 (36.40000000000006, 13.999999999999996),
 (36.40000000000006, 14.199999999999996),
 (36.40000000000006, 14.399999999999995),
 (36.40000000000006, 14.599999999999994),
 (36.40000000000006, 14.799999999999994),
 ...]

list(g)[-5:]

[]

g2 = product(x,y)

list(g2)[-5:]

[(59.800000000000395, 20.99999999999997),
 (59.800000000000395, 21.19999999999997),
 (59.800000000000395, 21.39999999999997),
 (59.800000000000395, 21.59999999999997),
 (59.800000000000395, 21.79999999999997)]

g = product(x,y)

pd.DataFrame(g)

	0	1
0	32.0	13.0
1	32.0	13.2
2	32.0	13.4
3	32.0	13.6
4	32.0	13.8
...	...	...
6295	59.8	21.0
6296	59.8	21.2
6297	59.8	21.4
6298	59.8	21.6
6299	59.8	21.8

6300 rows × 2 columns

cols

['bill_length_mm', 'bill_depth_mm']

pd.DataFrame(g, columns=cols)

	bill_length_mm	bill_depth_mm

df_sim2 = pd.DataFrame(product(x,y), columns=cols)

df_sim2

	bill_length_mm	bill_depth_mm
0	32.0	13.0
1	32.0	13.2
2	32.0	13.4
3	32.0	13.6
4	32.0	13.8
...	...	...
6295	59.8	21.0
6296	59.8	21.2
6297	59.8	21.4
6298	59.8	21.6
6299	59.8	21.8

6300 rows × 2 columns

Using the grid of points to visualize the decision boundary¶

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color="pred"
)

df_sim2["pred"] = clf.predict(df_sim2)

len(df_sim2)

df_sim2_sub = df_sim2.sample(5000)

df_sim2_sub

	bill_length_mm	bill_depth_mm	pred
1626	39.2	14.2	Gentoo
5656	57.0	19.2	Chinstrap
4517	52.0	16.4	Gentoo
2949	45.0	17.8	Chinstrap
2213	41.8	14.6	Gentoo
...	...	...	...
5562	56.6	18.4	Chinstrap
2103	41.2	19.6	Adelie
1903	40.4	15.6	Gentoo
1551	38.8	17.2	Adelie
687	35.0	15.4	Adelie

5000 rows × 3 columns

len(df_sim2_sub)

alt.Chart(df_sim2_sub).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color="pred"
)

What penguins were misclassified?¶

df_sim2

	bill_length_mm	bill_depth_mm	pred
0	32.0	13.0	Adelie
1	32.0	13.2	Adelie
2	32.0	13.4	Adelie
3	32.0	13.6	Adelie
4	32.0	13.8	Adelie
...	...	...	...
6295	59.8	21.0	Chinstrap
6296	59.8	21.2	Chinstrap
6297	59.8	21.4	Chinstrap
6298	59.8	21.6	Chinstrap
6299	59.8	21.8	Chinstrap

6300 rows × 3 columns

df

	species	island	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g	sex	pred
0	Adelie	Torgersen	39.1	18.7	181.0	3750.0	Male	Adelie
1	Adelie	Torgersen	39.5	17.4	186.0	3800.0	Female	Adelie
2	Adelie	Torgersen	40.3	18.0	195.0	3250.0	Female	Adelie
4	Adelie	Torgersen	36.7	19.3	193.0	3450.0	Female	Adelie
5	Adelie	Torgersen	39.3	20.6	190.0	3650.0	Male	Adelie
...	...	...	...	...	...	...	...	...
338	Gentoo	Biscoe	47.2	13.7	214.0	4925.0	Female	Gentoo
340	Gentoo	Biscoe	46.8	14.3	215.0	4850.0	Female	Gentoo
341	Gentoo	Biscoe	50.4	15.7	222.0	5750.0	Male	Gentoo
342	Gentoo	Biscoe	45.2	14.8	212.0	5200.0	Female	Gentoo
343	Gentoo	Biscoe	49.9	16.1	213.0	5400.0	Male	Gentoo

333 rows × 8 columns

df["species"] == df["pred"]

    True
    True
    True
    True
    True
       ... 
  True
  True
  True
  True
  True
Length: 333, dtype: bool

df["correct"] = (df["species"] == df["pred"])

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color="pred"
)

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color="correct"
)

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color=alt.condition(alt.datum.correct, alt.value("black"), alt.value("red"))
)

df.correct.unique()

array([ True, False])

alt.Chart(df).mark_circle().encode(
    x=alt.X(cols[0], scale=alt.Scale(zero=False)),
    y=alt.Y(cols[1], scale=alt.Scale(zero=False)),
    color=alt.Color("correct", scale=alt.Scale(domain=[True, False], range=["black", "red"]))
)

UC Irvine Math 10 S22

Week 9 Videos

Contents

Week 9 Videos¶

Logistic regression decision boundary with 3 classes¶

A grid of points using NumPy¶

A grid of points using itertools¶

Using the grid of points to visualize the decision boundary¶

What penguins were misclassified?¶