inference

.py

School

University of California, Berkeley *

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188

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Computer Science

Date

Apr 26, 2024

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Uploaded by ElderMongoose4017 on coursehero.com

# inference.py # ------------ # Licensing Information: You are free to use or extend these projects for # educational purposes provided that (1) you do not distribute or publish # solutions, (2) you retain this notice, and (3) you provide clear # attribution to UC Berkeley, including a link to http://ai.berkeley.edu. # # Attribution Information: The Pacman AI projects were developed at UC Berkeley. # The core projects and autograders were primarily created by John DeNero # (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). # Student side autograding was added by Brad Miller, Nick Hay, and # Pieter Abbeel (pabbeel@cs.berkeley.edu). import random import itertools from typing import List, Dict, Tuple import busters import game import bayesNet as bn from bayesNet import normalize import hunters from util import manhattanDistance, raiseNotDefined from factorOperations import joinFactorsByVariableWithCallTracking, joinFactors from factorOperations import eliminateWithCallTracking ########### ########### ########### ########### QUESTION 1 ########### ########### ########### ########### def constructBayesNet(gameState: hunters.GameState): """ Construct an empty Bayes net according to the structure given in Figure 1 of the project description. You *must* name all variables using the constants in this function. In this method, you should: - populate `variables` with the Bayes Net nodes - populate `edges` with every edge in the Bayes Net. we will represent each edge as a tuple `(from, to)`. - set each `variableDomainsDict[var] = values`, where `values` is a list of the possible assignments to `var`. - each agent position is a tuple (x, y) where x and y are 0-indexed - each observed distance is a noisy Manhattan distance: it's non-negative and |obs - true| <= MAX_NOISE - this uses slightly simplified mechanics vs the ones used later for simplicity """ # constants to use PAC = "Pacman" GHOST0 = "Ghost0" GHOST1 = "Ghost1" OBS0 = "Observation0" OBS1 = "Observation1" X_RANGE = gameState.getWalls().width Y_RANGE = gameState.getWalls().height MAX_NOISE = 7 variables = []

edges = [] variableDomainsDict = {} "*** YOUR CODE HERE ***" # raiseNotDefined() variables = [PAC, GHOST0, GHOST1, OBS0, OBS1] edges = [(GHOST0, OBS0), (PAC, OBS0), (PAC, OBS1), (GHOST1, OBS1)] variableDomainsDict[PAC]= [(x,y) for x in range(X_RANGE) for y in range(Y_RANGE)] variableDomainsDict[GHOST0] = [(x,y) for x in range(X_RANGE) for y in range(Y_RANGE)] variableDomainsDict[GHOST1]= [(x,y) for x in range(X_RANGE) for y in range(Y_RANGE)] variableDomainsDict[OBS0] = range(X_RANGE+Y_RANGE + MAX_NOISE - 1) variableDomainsDict[OBS1]= range(X_RANGE+Y_RANGE + MAX_NOISE - 1) "*** END YOUR CODE HERE ***" net = bn.constructEmptyBayesNet(variables, edges, variableDomainsDict) return net def inferenceByEnumeration(bayesNet: bn, queryVariables: List[str], evidenceDict: Dict): """ An inference by enumeration implementation provided as reference. This function performs a probabilistic inference query that returns the factor: P(queryVariables | evidenceDict) bayesNet: The Bayes Net on which we are making a query. queryVariables: A list of the variables which are unconditioned in the inference query. evidenceDict: An assignment dict {variable : value} for the variables which are presented as evidence (conditioned) in the inference query. """ callTrackingList = [] joinFactorsByVariable = joinFactorsByVariableWithCallTracking(callTrackingList) eliminate = eliminateWithCallTracking(callTrackingList) # initialize return variables and the variables to eliminate evidenceVariablesSet = set(evidenceDict.keys()) queryVariablesSet = set(queryVariables) eliminationVariables = (bayesNet.variablesSet() - evidenceVariablesSet) - queryVariablesSet # grab all factors where we know the evidence variables (to reduce the size of the tables) currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict) # join all factors by variable for joinVariable in bayesNet.variablesSet(): currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, joinVariable) currentFactorsList.append(joinedFactor) # currentFactorsList should contain the connected components of the graph now as factors, must join the connected components

fullJoint = joinFactors(currentFactorsList) # marginalize all variables that aren't query or evidence incrementallyMarginalizedJoint = fullJoint for eliminationVariable in eliminationVariables: incrementallyMarginalizedJoint = eliminate(incrementallyMarginalizedJoint, eliminationVariable) fullJointOverQueryAndEvidence = incrementallyMarginalizedJoint # normalize so that the probability sums to one # the input factor contains only the query variables and the evidence variables, # both as unconditioned variables queryConditionedOnEvidence = normalize(fullJointOverQueryAndEvidence) # now the factor is conditioned on the evidence variables # the order is join on all variables, then eliminate on all elimination variables return queryConditionedOnEvidence ########### ########### ########### ########### QUESTION 4 ########### ########### ########### ########### def inferenceByVariableEliminationWithCallTracking(callTrackingList=None): def inferenceByVariableElimination(bayesNet: bn, queryVariables: List[str], evidenceDict: Dict, eliminationOrder: List[str]): """ This function should perform a probabilistic inference query that returns the factor: P(queryVariables | evidenceDict) It should perform inference by interleaving joining on a variable and eliminating that variable, in the order of variables according to eliminationOrder. See inferenceByEnumeration for an example on how to use these functions. You need to use joinFactorsByVariable to join all of the factors that contain a variable in order for the autograder to recognize that you performed the correct interleaving of joins and eliminates. If a factor that you are about to eliminate a variable from has only one unconditioned variable, you should not eliminate it and instead just discard the factor. This is since the result of the eliminate would be 1 (you marginalize all of the unconditioned variables), but it is not a valid factor. So this simplifies using the result of eliminate. The sum of the probabilities should sum to one (so that it is a true conditional probability, conditioned on the evidence). bayesNet: The Bayes Net on which we are making a query. queryVariables: A list of the variables which are unconditioned in the inference query. evidenceDict: An assignment dict {variable : value} for the

variables which are presented as evidence (conditioned) in the inference query. eliminationOrder: The order to eliminate the variables in. Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional Probability Tables even if an empty dict (or None) is passed in for evidenceDict. In this case it will not specialize any variable domains in the CPTs. Useful functions: BayesNet.getAllCPTsWithEvidence normalize eliminate joinFactorsByVariable joinFactors """ # this is for autograding -- don't modify joinFactorsByVariable = joinFactorsByVariableWithCallTracking(callTrackingList) eliminate = eliminateWithCallTracking(callTrackingList) if eliminationOrder is None: # set an arbitrary elimination order if None given eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\ set(evidenceDict.keys()) eliminationOrder = sorted(list(eliminationVariables)) "*** YOUR CODE HERE ***" # raiseNotDefined() currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict) for var in eliminationOrder: currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, var) length = len(joinedFactor.unconditionedVariables()) if length > 1: currentFactorsList.append(eliminate(joinedFactor, var)) joined = joinFactors(currentFactorsList) return normalize(joined) "*** END YOUR CODE HERE ***" return inferenceByVariableElimination inferenceByVariableElimination = inferenceByVariableEliminationWithCallTracking() def sampleFromFactorRandomSource(randomSource=None): if randomSource is None: randomSource = random.Random() def sampleFromFactor(factor, conditionedAssignments=None): """ Sample an assignment for unconditioned variables in factor with probability equal to the probability in the row of factor corresponding to that assignment. factor: The factor to sample from.

conditionedAssignments: A dict of assignments for all conditioned variables in the factor. Can only be None if there are no conditioned variables in factor, otherwise must be nonzero. Useful for inferenceByLikelihoodWeightingSampling Returns an assignmentDict that contains the conditionedAssignments but also a random assignment of the unconditioned variables given their probability. """ if conditionedAssignments is None and len(factor.conditionedVariables()) > 0: raise ValueError("Conditioned assignments must be provided since \n" + "this factor has conditionedVariables: " + "\n" + str(factor.conditionedVariables())) elif conditionedAssignments is not None: conditionedVariables = set([var for var in conditionedAssignments.keys()]) if not conditionedVariables.issuperset(set(factor.conditionedVariables())): raise ValueError("Factor's conditioned variables need to be a subset of the \n" + "conditioned assignments passed in. \n" + \ "conditionedVariables: " + str(conditionedVariables) + "\n" + "factor.conditionedVariables: " + str(set(factor.conditionedVariables()))) # Reduce the domains of the variables that have been # conditioned upon for this factor newVariableDomainsDict = factor.variableDomainsDict() for (var, assignment) in conditionedAssignments.items(): newVariableDomainsDict[var] = [assignment] # Get the (hopefully) smaller conditional probability table # for this variable CPT = factor.specializeVariableDomains(newVariableDomainsDict) else: CPT = factor # Get the probability of each row of the table (along with the # assignmentDict that it corresponds to) assignmentDicts = sorted([assignmentDict for assignmentDict in CPT.getAllPossibleAssignmentDicts()]) assignmentDictProbabilities = [CPT.getProbability(assignmentDict) for assignmentDict in assignmentDicts] # calculate total probability in the factor and index each row by the # cumulative sum of probability up to and including that row currentProbability = 0.0 probabilityRange = [] for i in range(len(assignmentDicts)): currentProbability += assignmentDictProbabilities[i] probabilityRange.append(currentProbability) totalProbability = probabilityRange[-1]

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