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simulation.py
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simulation.py
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from random import randint
from random import random
import math
import copy
import random
import matplotlib.pyplot as plt
###############################################################################################
################## CONDITION COMPARISONS ######################################
###############################################################################################
#####################################################
######### C-BKT UPDATE ##############
#####################################################
def probability_attempted(t, time_attempted):
if t > time_attempted:
return 1
else:
return float(t) / time_attempted
def update_belief_right(sk, slip, guess):
knows_notslipped = sk*(1-slip)
notknows_guessed = (1-sk)*guess
top = knows_notslipped
bottom = knows_notslipped + notknows_guessed
return top / bottom
def update_belief_wrong(sk, slip, guess, t, attempted):
know_tried_slipped = sk*probability_attempted(t, attempted)*slip
knows_nottried = sk*(1-probability_attempted(t, attempted))
notknows_nottried = (1-sk)*(1-probability_attempted(t, attempted))
notknows_tried_notguessed = (1-sk)*probability_attempted(t, attempted)*(1-guess)
top = know_tried_slipped + knows_nottried
bottom = know_tried_slipped + knows_nottried + notknows_nottried + notknows_tried_notguessed
return top / bottom
def CBKT_get_new_belief(obs, p, task, ts):
b_round = []
for skill in range (0, len(obs)):
current_skill_obs = obs[skill]
init_belief = p.initial_belief[skill]
b = 0
for i in range (0, history_rounds):
b_ts = 0
if (i == 0):
if (obs[skill] == 0):
b_ts = update_belief_wrong(init_belief, task.skills[skill].p_slip, task.skills[skill].p_guess,ts, task.skills[skill].attempted)
history[ts].append(b_ts)
else:
b_ts = update_belief_right(init_belief, task.skills[skill].p_slip, task.skills[skill].p_guess)
history[ts].append(b_ts)
elif (ts - i) < 0:
b_ts = p.initial_belief[skill]
else:
b_ts = history[ts - i][skill]
b += b_ts
b = b / history_rounds
b_round.append(b)
return b_round
######################################################
######### BKT UPDATE FROM START #######
######################################################
def update_belief_right_traditional(sk, slip, guess):
knows_notslipped = sk*(1-slip)
notknows_guessed = (1-sk)*guess
top = knows_notslipped
bottom = knows_notslipped + notknows_guessed
return top / bottom
def update_belief_wrong_traditional(sk, slip, guess):
know_tried_slipped = sk*slip
notknows_tried_notguessed = (1-sk)*(1-guess)
top = know_tried_slipped
bottom = know_tried_slipped + notknows_tried_notguessed
return top / bottom
def BKT_get_new_belief_from_start(obs, p, task):
b_round = []
for skill in range (0, len(obs)):
current_skill_obs = obs[skill]
init_belief = p.initial_belief[skill]
b = 0
if (obs[skill] == 0):
b = update_belief_wrong_traditional(init_belief, task.skills[skill].p_slip, task.skills[skill].p_guess)
else:
b = update_belief_right_traditional(init_belief, task.skills[skill].p_slip, task.skills[skill].p_guess)
b_round.append(b)
return b_round
###############################################################################################
################## BKT UPDATE EVERY TIMESTEP ##################################
###############################################################################################
def BKT_get_new_belief_every_timestep(obs, p, task):
b_round = []
for skill in range (0, len(obs)):
current_skill_obs = obs[skill]
current_belief = p.belief[-1][skill]
b = 0
if (obs[skill] == 0):
b = update_belief_wrong_traditional(current_belief, task.skills[skill].p_slip, task.skills[skill].p_guess)
else:
b = update_belief_right_traditional(current_belief, task.skills[skill].p_slip, task.skills[skill].p_guess)
b_round.append(b)
return b_round
###############################################################################################
################## AUXILIARY FUNCTIONS ########################################
###############################################################################################
def decision(probability):
v = random.uniform(0.0, 1.0)
if (v < probability):
return 1
else:
return 0
def write_file(name,info):
f = open(name+".txt", "w")
for el in info:
f.write(str(round(el,2)) + "\n")
f.close()
###############################################################################################
################## PERSON, SKILL, AND TASKS ###################################
###############################################################################################
class Person():
def __init__(self, p_id, task):
self.p_id = p_id
self.mastery = []
self.initial_belief = []
self.belief = []
self.start_b = random.uniform(0.5, 0.5)
self.prev_obs = []
for i in range(0, task.number_skills):
self.prev_obs.append(0)
m = random.randint(0,1)
self.mastery.append(m)
self.initial_belief.append(self.start_b)
self.belief.append([self.start_b]*task.number_skills) #set to just have the initial belief (complete uncertianty) at the start
def get_obs(self, task, ts):
obs = []
for i in range (0, task.number_skills):
p_att = probability_attempted(ts, task.skills[i].attempted)
has_attempted = decision(p_att)
can_do = self.mastery[i]
if (has_attempted == 0):
obs.append(0)
else:
if (can_do == 1):
probability = 1 - task.skills[i].p_slip
obs.append(decision(probability))
else:
probability = task.skills[i].p_guess
obs.append(decision(probability))
return obs
class Skill():
def __init__(self, name):
self.name = name
self.p_guess = random.uniform(0.1, 0.25)
self.p_slip = random.uniform(0.1, 0.25)
self.attempted = random.randint(40, 150)
class Task():
def __init__(self):
self.skills = []
self.number_skills = random.randint(5,10)
# ~ self.number_skills = 1
for i in range (0, self.number_skills):
skill = Skill(i)
self.skills.append(skill)
###############################################################################################
################## MEASURES AND REWARD FUNCTIONS ##############################
###############################################################################################
def distance_kld(b1, b2):
d = []
for ts in range (0, len(b1)):
d_ts = 0
for sk in range (0, len(b1[0])):
d_ts += b1[ts][sk] * math.log(b1[ts][sk]+0.001 / (b2[ts][sk]+0.001)) + (1-b1[ts][sk]+0.001) * math.log((1-b1[ts][sk]+0.001)/ (1-b2[ts][sk]+0.001))
d.append(d_ts / len(b1[0]))
return d
###############################################################################################
################## 100 ROUNDS OF SIMULATION ######################################
###############################################################################################
history_rounds = 10 #amount of rounds it will average over
n_timesteps = 180
rounds = 1000
distance_C_BKT = []
distance_I_BKT = []
distance_E_BKT = []
distance_T_BKT = []
TBKT_30 = []
CBKT_30 = []
IBKT_30 = []
EBKT_30 = []
TBKT_80 = []
CBKT_80 = []
IBKT_80 = []
EBKT_80 = []
TBKT_130 = []
CBKT_130 = []
IBKT_130 = []
EBKT_130 = []
TBKT_180 = []
CBKT_180 = []
IBKT_180 = []
EBKT_180 = []
for round_n in range (0, rounds):
task = Task()
p = Person(round_n, task)
# ~ print (p.mastery)
p_C_BKT = copy.deepcopy(p)
# ~ p_T_BKT = copy.deepcopy(p)
p_I_BKT = copy.deepcopy(p)
p_E_BKT = copy.deepcopy(p)
p_T_BKT = copy.deepcopy(p)
True_State = copy.deepcopy(p)
True_State.belief = [True_State.mastery]
history = [ [] for _ in range(n_timesteps) ]
for ts in range (0, n_timesteps):
obs = p.get_obs(task, ts)
# ~ print (obs)
#update for C-BKT
b_C_BKT = CBKT_get_new_belief(obs, p_C_BKT, task, ts)
p_C_BKT.belief.append(b_C_BKT )
#update for I-BKT
b_I_BKT = BKT_get_new_belief_from_start(obs, p_I_BKT, task)
p_I_BKT.belief.append(b_I_BKT)
#update for E-BKT
b_E_BKT = BKT_get_new_belief_every_timestep(obs, p_E_BKT, task)
p_E_BKT.belief.append(b_E_BKT)
b_T_BKT = p_T_BKT.initial_belief
p_T_BKT.belief.append(b_T_BKT)
#the true state belief, will be whether they have mastery or not
True_State.belief.append(p.mastery)
d_C_BKT = distance_kld(p_C_BKT.belief, True_State.belief)
d_I_BKT = distance_kld(p_I_BKT.belief, True_State.belief)
d_E_BKT = distance_kld(p_E_BKT.belief, True_State.belief)
d_T_BKT = distance_kld(p_T_BKT.belief, True_State.belief)
for ts in range (0, len(d_T_BKT)):
if (ts == 30):
TBKT_30.append(d_T_BKT[ts])
CBKT_30.append(d_C_BKT[ts])
IBKT_30.append(d_I_BKT[ts])
EBKT_30.append(d_E_BKT[ts])
if (ts == 80):
TBKT_80.append(d_T_BKT[ts])
CBKT_80.append(d_C_BKT[ts])
IBKT_80.append(d_I_BKT[ts])
EBKT_80.append(d_E_BKT[ts])
if (ts == 130):
TBKT_130.append(d_T_BKT[ts])
CBKT_130.append(d_C_BKT[ts])
IBKT_130.append(d_I_BKT[ts])
EBKT_130.append(d_E_BKT[ts])
if (ts == 180):
TBKT_180.append(d_T_BKT[ts])
CBKT_180.append(d_C_BKT[ts])
IBKT_180.append(d_I_BKT[ts])
EBKT_180.append(d_E_BKT[ts])
# ~ print (d_C_BKT)
distance_C_BKT.append(d_C_BKT)
distance_I_BKT.append(d_I_BKT)
distance_E_BKT.append(d_E_BKT)
distance_T_BKT.append(d_T_BKT)
write_file("TBKT_30", TBKT_30 )
write_file("CBKT_30",CBKT_30)
write_file("IBKT_30",IBKT_30)
write_file("EBKT_30", EBKT_30)
write_file("TBKT_80", TBKT_80)
write_file("CBKT_80", CBKT_80)
write_file("IBKT_80", IBKT_80)
write_file("EBKT_80", EBKT_80)
write_file("TBKT_130", TBKT_130)
write_file("CBKT_130", CBKT_130)
write_file("IBKT_130", IBKT_130)
write_file("EBKT_130", EBKT_130)
write_file("TBKT_180", TBKT_180)
write_file("CBKT_180", CBKT_180)
write_file("IBKT_180", IBKT_180)
write_file("EBKT_180", EBKT_180)
average_C_BKT = [sum(x)/rounds for x in zip(*distance_C_BKT)]
average_I_BKT = [sum(x)/rounds for x in zip(*distance_I_BKT)]
average_E_BKT = [sum(x)/rounds for x in zip(*distance_E_BKT)]
average_T_BKT = [sum(x)/rounds for x in zip(*distance_T_BKT)]
# ~ print (p_E_BKT.belief)
# ~ print (average_E_BKT)
plt.rcParams['font.family'] = 'serif'
plt.rcParams['font.serif'] = ['Times New Roman'] + plt.rcParams['font.serif']
plt.rcParams.update({'font.size': 15})
# ~ plt.figure(figsize=(8,5))
# ~ plt.gcf().subplots_adjust(bottom=0.15)
# ~ plt.title('KLD Distance to True Skill State')
plt.plot(average_C_BKT, color='#ff1f5b', linewidth = 3)
plt.plot(average_I_BKT, color='#009ade', linewidth = 3)
plt.plot(average_E_BKT, color='#00cd6c', linewidth = 3)
plt.plot(average_T_BKT, color='#ffc61e', linewidth = 3)
# ~ plt.axis([0, n_timesteps, 0, 1])
plt.xlabel('time-steps')
plt.ylabel("Kullback-Leibler Divergence")
plt.show()