How can I map a continuous variable to discrete strings, using dictionaries or otherwise in Python?

How can I map a continuous variable to discrete strings, using dictionaries or otherwise in Python?

There are several ways to map a continuous variable to discrete strings in Python. Here are a few common approaches:

Using Dictionaries

You can use a dictionary to map continuous values to discrete strings. The keys of the dictionary will be the continuous values, and the values of the dictionary will be the corresponding discrete strings. For example:

```python
mapping = {
    0: 'very low',
    1: 'low',
    2: 'medium',
    3: 'high',
    4: 'very high'
}

def map_continuous_to_discrete(value):
  """Maps a continuous value to a discrete string."""

  return mapping[value]
```

To use this function, you would simply pass in a continuous value and it would return the corresponding discrete string. For example:

```python
>>> map_continuous_to_discrete(2.5)
'medium'
```

Using Bins

Another way to map continuous variables to discrete strings is to use bins. Bins are a way of dividing a continuous range of values into a number of discrete intervals. You can then assign a different string to each bin. For example:

```python
import numpy as np

bins = np.linspace(0, 1, 5)

def map_continuous_to_discrete(value):
  """Maps a continuous value to a discrete string."""

  bin_index = np.digitize(value, bins)

  return f'bin {bin_index}'
```

To use this function, you would simply pass in a continuous value and it would return the corresponding discrete string. For example:

```python
>>> map_continuous_to_discrete(0.25)
'bin 1'
```

Using the bisect Module

The bisect module provides a function called bisect(), which can be used to find the index of a value in a sorted list. This can be used to map continuous values to discrete strings by creating a sorted list of the continuous values and then using bisect() to find the index of the value in the list. The index can then be used to look up the corresponding discrete string in a dictionary.

```python
import bisect

def map_continuous_to_discrete(value):
  """Maps a continuous value to a discrete string."""

  values = [0, 0.25, 0.5, 0.75, 1]
  strings = ['very low', 'low', 'medium', 'high', 'very high']

  index = bisect.bisect_left(values, value)

  return strings[index]
```

To use this function, you would simply pass in a continuous value and it would return the corresponding discrete string. For example:

```python
>>> map_continuous_to_discrete(0.25)
'low'
```

Using PyTorch

If you are working with PyTorch, you can use the bucketize() function to map continuous values to discrete strings. The bucketize() function takes a tensor of continuous values and a list of boundaries. The boundaries define the edges of the bins. The function will then assign each value in the tensor to the bin that it falls into. The bin index can then be used to look up the corresponding discrete string in a dictionary.

```python
import torch

values = torch.linspace(0, 1, 10)
boundaries = torch.linspace(0, 1, 5)
strings = ['very low', 'low', 'medium', 'high', 'very high']

bins = torch.bucketize(values, boundaries)

discrete_strings = [strings[bin_index] for bin_index in bins]
```

The discrete_strings list will contain the discrete strings corresponding to the continuous values in the values tensor.