Parsing, executing, and calculating expected information gain for program-form questions.
Question Programs & Expected Information Gain
This is a package for parsing/executing questions and calculating Expected Information Gain (EIG) for question programs defined on the Battleship Dataset in the paper "Question Asking as Program Generation".
This package provide a Pure python version (slow) and a Python/C++ hybrid version (fast). Both versions have the same API but different implementations.
This package can be installed using pip
pip install expected-information-gain
The following example shows how to execute a program on a given board
# define a board using BattleshipHypothesis from eig.battleship import Ship, BattleshipHypothesis, Parser, Executor ships = [Ship(ship_label=1, topleft=(0, 0), size=2, orientation='V'), Ship(ship_label=2, topleft=(1, 2), size=2, orientation='V') hypothesis = BattleshipHypothesis(grid_size=3, ships=ships) # the board looks like this # B W W # B W R # W W R # parse and execute the program question = Parser.parse("(bottomright (coloredTiles Red))") executor = Executor(question) executor.execute(hypothesis) # (2, 2) # we can also evaluate general arithmic and logical expressions, with whatever hypothesis provided question2 = Parser.parse("(and (not (< 4 9)) (== (+ 1 3) 4))") executor2 = Executor(question) executor.execute(hypothesis) # False
The next example shows how to calculate Expected Information Gain on a partly revealed board
# first we need to construct a hypothesis space # We suggest to do this as an initialization step, and use this instance every time # Because this step is time consuming, and may take several seconds to finish. from eig.battleship import BattleshipHypothesisSpace hypotheses = BattleshipHypothesisSpace(grid_size=6, ship_labels=[1, 2, 3], ship_sizes=[2, 3, 4], orientations=['V', 'H']) # suppose we have a program and a partly revealed board import numpy as np program = "..." board = np.array([...]) # next we can calculate EIG as follows from eig import compute_eig_basic from eig.battleship.program import ProgramSyntaxError try: score = compute_eig_basic(hypotheses, program, board) except ProgramSyntaxError: # if the program is invalid, a ProgramSyntaxError will be raised # do something except RuntimeError: # if error happens during execution, a RuntimeError will be raised # do something
We also provide some advanced interfaces, which are more efficient when the users need to calculate EIG for many programs on one given board, and they also allows users to incorporate more complicated distributions.
# construct the hypothesis space from eig.battleship import BattleshipHypothesisSpace hypotheses = BattleshipHypothesisSpace(grid_size=6, ship_labels=[1, 2, 3], ship_sizes=[2, 3, 4], orientations=['V', 'H']) # calculate EIG as follows from eig import compute_eig, Bayes, Context from eig.battleship import Parser, Executor from eig.battleship.program import ProgramSyntaxError try: ast = Parser.parse(program) # parse the program into abstract syntax tree executor = Executor(ast) # obtain an executor to execute the program prior = EqualSizesDistribution(ship_labels=[1, 2, 3]) # a more cognitive inspired prior distribution belief = eig.Bayes(hypotheses, prior) # a prior belief given the hypothesis space context = eig.Context(hypotheses, belief) # context stores the posterior belief context.observe(board) # update posterior belief given the board score = eig.compute_eig(executor, context) # compute EIG given program and posterior belief except ProgramSyntaxError: # if the program is invalid, a ProgramSyntaxError will be raised # do something except RuntimeError: # if error happens during execution, a RuntimeError will be raised # do something
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