# probFactors.py - Factor manipulation for graphical models # AIFCA Python3 code Version 0.8.6 Documentation at http://aipython.org # Artificial Intelligence: Foundations of Computational Agents # http://artint.info # Copyright David L Poole and Alan K Mackworth 2017-2020. # This work is licensed under a Creative Commons # Attribution-NonCommercial-ShareAlike 4.0 International License. # See: http://creativecommons.org/licenses/by-nc-sa/4.0/deed.en from functools import reduce #from probVariables import Variable class Factor(object): nextid=0 # each factor has a unique identifier; for printing def __init__(self,variables): """variables is the ordered list of variables """ self.variables = variables # ordered list of variables # Compute the size and the offsets for the variables self.var_offsets = {} self.size = 1 for i in range(len(variables)-1,-1,-1): self.var_offsets[variables[i]]=self.size self.size *= variables[i].size self.id = Factor.nextid self.name = "f"+str(self.id) Factor.nextid += 1 def get_value(self,assignment): raise NotImplementedError("get_value") # abstract method def __str__(self, variables=None): """returns a string representation of the factor. Allows for an arbitrary variable ordering. variables is a list of the variables in the factor (can contain other variables)""" if variables==None: variables = self.variables else: variables = [v for v in variables if v in self.variables] res = "" for v in variables: res += str(v) + "\t" res += self.name+"\n" for i in range(self.size): asst = self.index_to_assignment(i) for v in variables: res += str(asst[v])+"\t" res += str(self.get_value(asst)) res += "\n" return res def brief(self): """returns a string representing a summary of the factor""" res = self.name+"(" for i in range(0,len(self.variables)-1): res += str(self.variables[i])+"," if len(self.variables)>0: res += str(self.variables[len(self.variables)-1]) res += ")" return res __repr__ = brief def assignment_to_index(self,assignment): """returns the index where the variable:value assignment is stored""" index = 0 for var in self.variables: index += var.val_to_index[assignment[var]]*self.var_offsets[var] return index def index_to_assignment(self,index): """gives a dict representation of the variable assignment for index """ asst = {} for i in range(len(self.variables)-1,-1,-1): asst[self.variables[i]] = self.variables[i].domain[index % self.variables[i].size] index = index // self.variables[i].size return asst class Factor_stored(Factor): def __init__(self,variables,values): Factor.__init__(self, variables) self.values = values def get_value(self,assignment): return self.values[self.assignment_to_index(assignment)] class Factor_observed(Factor): def __init__(self,factor,obs): Factor.__init__(self, [v for v in factor.variables if v not in obs]) self.observed = obs self.orig_factor = factor def get_value(self,assignment): ass = assignment.copy() for ob in self.observed: ass[ob]=self.observed[ob] return self.orig_factor.get_value(ass) class Factor_sum(Factor_stored): def __init__(self,var,factors): self.var_summed_out = var self.factors = factors vars = [] for fac in factors: for v in fac.variables: if v is not var and v not in vars: vars.append(v) Factor_stored.__init__(self,vars,None) self.values = [None]*self.size def get_value(self,assignment): """lazy implementation: if not saved, compute it. Return saved value""" index = self.assignment_to_index(assignment) if self.values[index]: return self.values[index] else: total = 0 new_asst = assignment.copy() for val in self.var_summed_out.domain: new_asst[self.var_summed_out] = val prod = 1 for fac in self.factors: prod *= fac.get_value(new_asst) total += prod self.values[index] = total return total def factor_times(variable,factors): """when factors are factors just on variable (or on no variables)""" prods= [] facs = [f for f in factors if variable in f.variables] for val in variable.domain: prod = 1 ast = {variable:val} for f in facs: prod *= f.get_value(ast) prods.append(prod) return prods class Prob(Factor_stored): """A factor defined by a conditional probability table""" def __init__(self,var,pars,cpt): """Creates a factor from a conditional probability table, cptf. The cpt values are assumed to be for the ordering par+[var] """ Factor_stored.__init__(self,pars+[var],cpt) self.child = var self.parents = pars assert self.size==len(cpt),"Table size incorrect "+str(self) def cond_dist(self,par_assignment): """returns the distribution (a val:prob dictionary) over the child given assignment to the parents par_assignment is a variable:value dictionary that assigns values to parents """ index = 0 for var in self.parents: index += var.val_to_index[par_assignment[var]]*self.var_offsets[var] # index is the position where the disgribution starts return {self.child.domain[i]:self.values[index+i] for i in range(len(self.child.domain))} def cond_prob(self,par_assignment,child_value): """returns the probability child has child_value given assignment to the parents par_assignment is a variable:value dictionary that assigns values to parents child_value is a value to the child """ index = self.child.val_to_index[child_value] for var in self.parents: index += var.val_to_index[par_assignment[var]]*self.var_offsets[var] return self.values[index] class Factor_rename(Factor): def __init__(self,fac,renaming): Factor.__init__(self,list(renaming.keys())) self.orig_fac = fac self.renaming = renaming def get_value(self,assignment): return self.orig_fac.get_value({self.renaming[var]:val for (var,val) in assignment.items() if var in self.variables})