Why couldn't I use ' ~ ' instead of ' /home/username/ ' when giving the file path

You need to understand that ~ is normally expanded by the shell; the programs you call never see it, they see the full pathname as inserted by bash. But this only happens when the tilde is at the start of an argument (and is not quoted).

If the Python program you are running uses a module like getopt to parse its commandline, you can give the argument of the --data-path option as a separate "word" to allow tilde expansion:

$ python ptb_word_lm.py --data_path ~/anaconda2/lib/python2.7/...

In your own code, you can use getopt or argparse for argument processing, and could also manually expand tildes as @JacobVlijm's answer suggested.

PS. The tilde is also expanded at the start of a shell variable assignment expression like DIRNAME=~/anaconda2; although the tilde in your question also follows an equals sign, this usage doesn't have special meaning for the shell (it's just something passed to a program) and doesn't trigger expansion.

Tilde expansion in python

The answer is short & simple:

python does not expand ~ unless you use:

import os
os.path.expanduser('~/your_directory')

See also here:

os.path.expanduser(path)
On Unix and Windows, return the argument with an initial component of ~ or ~user replaced by that user‘s home directory.

On Unix, an initial ~ is replaced by the environment variable HOME if it is set; otherwise the current user’s home directory is looked up in the password directory through the built-in module pwd. An initial ~user is looked up directly in the password directory.