ML - Understanding Data with Statistics

Introduction

While working with machine learning projects, usually we ignore two most important parts called mathematics and data. It is because, we know that ML is a data driven approach and our ML model will produce only as good or as bad results as the data we provided to it.

In the previous chapter, we discussed how we can upload CSV data into our ML project, but it would be good to understand the data before uploading it. We can understand the data by two ways, with statistics and with visualization.

In this chapter, with the help of following Python recipes, we are going to understand ML data with statistics.

Looking at Raw Data

The very first recipe is for looking at your raw data. It is important to look at raw data because the insight we will get after looking at raw data will boost our chances to better pre-processing as well as handling of data for ML projects.

Following is a Python script implemented by using head() function of Pandas DataFrame on Pima Indians diabetes dataset to look at the first 50 rows to get better understanding of it −

Example

from pandas import read_csv
path = r"C:\pima-indians-diabetes.csv"
headernames = ['preg','plas','pres','skin','test','mass','pedi','age','class']
data = read_csv(path, names=headernames)
print(data.head(50))

Output

preg plas  pres skin test   mass pedi   age      class
0     6    148  72   35     0    33.6   0.627    50     1
1     1     85  66   29     0    26.6   0.351    31     0
2     8    183  64    0     0    23.3   0.672    32     1
3     1     89  66   23    94    28.1   0.167    21     0
4     0    137  40   35   168    43.1   2.288    33     1
5     5    116  74    0     0    25.6   0.201    30     0
6     3     78  50   32    88    31.0   0.248    26     1
7    10    115   0    0     0    35.3   0.134    29     0
8     2    197  70   45   543    30.5   0.158    53     1
9     8    125  96    0     0     0.0   0.232    54     1
10    4    110  92    0     0    37.6   0.191    30     0
11   10    168  74    0     0    38.0   0.537    34     1
12   10    139  80    0     0    27.1   1.441    57     0
13    1    189  60   23   846    30.1   0.398    59     1
14    5    166  72   19   175    25.8   0.587    51     1
15    7    100   0    0     0    30.0   0.484    32     1
16    0    118  84   47   230    45.8   0.551    31     1
17    7    107  74    0     0    29.6   0.254    31     1
18    1    103  30   38    83    43.3   0.183    33     0
19    1    115  70   30    96    34.6   0.529    32     1
20    3    126  88   41   235    39.3   0.704    27     0
21    8     99  84    0     0    35.4   0.388    50     0
22    7    196  90    0     0    39.8   0.451    41     1
23    9    119  80   35     0    29.0   0.263    29     1
24   11    143  94   33   146    36.6   0.254    51     1
25   10    125  70   26   115    31.1   0.205    41     1
26    7    147  76    0     0    39.4   0.257    43     1 
27    1     97  66   15   140    23.2   0.487    22     0
28   13    145  82   19   110    22.2   0.245    57     0
29    5    117  92    0     0    34.1   0.337    38     0
30    5    109  75   26     0    36.0   0.546    60     0
31    3    158  76   36   245    31.6   0.851    28     1
32    3     88  58   11    54    24.8   0.267    22     0 
33    6     92  92    0     0    19.9   0.188    28     0
34   10    122  78   31     0    27.6   0.512    45     0 
35    4    103  60   33   192    24.0   0.966    33     0
36   11    138  76    0     0    33.2   0.420    35     0
37    9    102  76   37     0    32.9   0.665    46     1
38    2     90  68   42     0    38.2   0.503    27     1
39    4    111  72   47   207    37.1   1.390    56     1
40    3    180  64   25    70    34.0   0.271    26     0
41    7    133  84    0     0    40.2   0.696    37     0
42    7    106  92   18     0    22.7   0.235    48     0
43    9    171 110   24   240    45.4   0.721    54     1 
44    7    159  64    0     0    27.4   0.294    40     0
45    0    180  66   39     0    42.0   1.893    25     1
46    1    146  56    0     0    29.7   0.564    29     0
47    2     71  70   27     0    28.0   0.586    22     0
48    7    103  66   32     0    39.1   0.344    31     1
49    7    105   0    0     0    0.0    0.305    24     0

We can observe from the above output that first column gives the row number which can be very useful for referencing a specific observation.

Checking Dimensions of Data

It is always a good practice to know how much data, in terms of rows and columns, we are having for our ML project. The reasons behind are −

• Suppose if we have too many rows and columns then it would take long time to run the algorithm and train the model.
• Suppose if we have too less rows and columns then it we would not have enough data to well train the model.

Following is a Python script implemented by printing the shape property on Pandas Data Frame. We are going to implement it on iris data set for getting the total number of rows and columns in it.

Example

from pandas import read_csv
path = r"C:\iris.csv"
data = read_csv(path)
print(data.shape)

Output

(150, 4)

We can easily observe from the output that iris data set, we are going to use, is having 150 rows and 4 columns.

Getting Each Attribute’s Data Type

It is another good practice to know data type of each attribute. The reason behind is that, as per to the requirement, sometimes we may need to convert one data type to another. For example, we may need to convert string into floating point or int for representing categorial or ordinal values. We can have an idea about the attribute’s data type by looking at the raw data, but another way is to use dtypes property of Pandas DataFrame. With the help of dtypes property we can categorize each attributes data type. It can be understood with the help of following Python script −

Example

from pandas import read_csv
path = r"C:\iris.csv"
data = read_csv(path)
print(data.dtypes)

Output

sepal_length   float64
sepal_width    float64
petal_length   float64
petal_width    float64
dtype: object

From the above output, we can easily get the datatypes of each attribute.

Statistical Summary of Data

We have discussed Python recipe to get the shape i.e. number of rows and columns, of data but many times we need to review the summaries out of that shape of data. It can be done with the help of describe() function of Pandas DataFrame that further provide the following 8 statistical properties of each & every data attribute −

• Count
• Mean
• Standard Deviation
• Minimum Value
• Maximum value
• 25%
• Median i.e. 50%
• 75%

Example

from pandas import read_csv
from pandas import set_option
path = r"C:\pima-indians-diabetes.csv"
names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class']
data = read_csv(path, names=names)
set_option('display.width', 100)
set_option('precision', 2)
print(data.shape)
print(data.describe())

Output

(768, 9)
       preg     plas     pres    skin     test     mass     pedi     age      class
count  768.00   768.00   768.00  768.00   768.00   768.00   768.00   768.00   768.00
mean     3.85   120.89    69.11   20.54    79.80    31.99     0.47    33.24     0.35
std      3.37    31.97    19.36   15.95   115.24     7.88     0.33    11.76     0.48
min      0.00     0.00     0.00    0.00     0.00     0.00     0.08    21.00     0.00
25%      1.00    99.00    62.00    0.00     0.00    27.30     0.24    24.00     0.00
50%      3.00   117.00    72.00   23.00    30.50    32.00     0.37    29.00     0.00
75%      6.00   140.25    80.00   32.00   127.25    36.60     0.63    41.00     1.00
max     17.00   199.00   122.00   99.00   846.00    67.10     2.42    81.00     1.00

From the above output, we can observe the statistical summary of the data of Pima Indian Diabetes dataset along with shape of data.

Reviewing Class Distribution

Class distribution statistics is useful in classification problems where we need to know the balance of class values. It is important to know class value distribution because if we have highly imbalanced class distribution i.e. one class is having lots more observations than other class, then it may need special handling at data preparation stage of our ML project. We can easily get class distribution in Python with the help of Pandas DataFrame.

Example

from pandas import read_csv
path = r"C:\pima-indians-diabetes.csv"
names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class']
data = read_csv(path, names=names)
count_class = data.groupby('class').size()
print(count_class)

Output

Class
0 500
1 268
dtype: int64

From the above output, it can be clearly seen that the number of observations with class 0 are almost double than number of observations with class 1.

Reviewing Correlation between Attributes

The relationship between two variables is called correlation. In statistics, the most common method for calculating correlation is Pearson’s Correlation Coefficient. It can have three values as follows −

• Coefficient value = 1 − It represents full positive correlation between variables.
• Coefficient value = -1 − It represents full negative correlation between variables.
• Coefficient value = 0 − It represents no correlation at all between variables.

from pandas import read_csv
from pandas import set_option
path = r"C:\pima-indians-diabetes.csv"
names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class']
data = read_csv(path, names=names)
set_option('display.width', 100)
set_option('precision', 2)
correlations = data.corr(method='pearson')
print(correlations)

preg   plas   pres   skin   test    mass    pedi    age    class
preg   1.00   0.13   0.14  -0.08   -0.07    0.02   -0.03   0.54    0.22
plas   0.13   1.00   0.15   0.06    0.33    0.22    0.14   0.26    0.47
pres   0.14   0.15   1.00   0.21    0.09    0.28    0.04   0.24    0.07
skin  -0.08   0.06   0.21   1.00    0.44    0.39    0.18  -0.11    0.07
test  -0.07   0.33   0.09   0.44    1.00    0.20    0.19  -0.04    0.13
mass   0.02   0.22   0.28   0.39    0.20    1.00    0.14   0.04    0.29
pedi  -0.03   0.14   0.04   0.18    0.19    0.14    1.00   0.03    0.17
age    0.54   0.26   0.24  -0.11   -0.04    0.04    0.03   1.00    0.24
class  0.22   0.47   0.07   0.07    0.13    0.29    0.17   0.24    1.00

from pandas import read_csv
path = r"C:\pima-indians-diabetes.csv"
names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class']
data = read_csv(path, names=names)
print(data.skew())

preg   0.90
plas   0.17
pres  -1.84
skin   0.11
test   2.27
mass  -0.43
pedi   1.92
age    1.13
class  0.64
dtype: float64