ML - Understanding Data with Statistics

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.
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 −
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))
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.
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 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.
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.
from pandas import read_csv
path = r"C:\iris.csv"
data = read_csv(path)
print(data.shape)
(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.
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 −
from pandas import read_csv
path = r"C:\iris.csv"
data = read_csv(path)
print(data.dtypes)
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.
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%
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())
(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.
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.
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)
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.
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 positive correlation between variables.
Coefficient value = -1 − It represents full negative correlation between variables.
Coefficient value = -1 − It represents full negative correlation between variables.
Coefficient value = 0 − It represents no correlation at all between variables.
Coefficient value = 0 − It represents no correlation at all between variables.
It is always good for us to review the pairwise correlations of the attributes in our dataset before using it into ML project because some machine learning algorithms such as linear regression and logistic regression will perform poorly if we have highly correlated attributes. In Python, we can easily calculate a correlation matrix of dataset attributes with the help of corr() function on Pandas DataFrame.
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

The matrix in above output gives the correlation between all the pairs of the attribute in dataset.
Skewness may be defined as the distribution that is assumed to be Gaussian but appears distorted or shifted in one direction or another, or either to the left or right. Reviewing the skewness of attributes is one of the important tasks due to following reasons −
Presence of skewness in data requires the correction at data preparation stage so that we can get more accuracy from our model.
Presence of skewness in data requires the correction at data preparation stage so that we can get more accuracy from our model.
Most of the ML algorithms assumes that data has a Gaussian distribution i.e. either normal of bell curved data.
Most of the ML algorithms assumes that data has a Gaussian distribution i.e. either normal of bell curved data.
In Python, we can easily calculate the skew of each attribute by using skew() function on Pandas DataFrame.
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

From the above output, positive or negative skew can be observed. If the value is closer to zero, then it shows less skew.

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