def test_factor_graph_agrees_with_two_team_explicit(self):
# given
p1 = Gaussian(mu=MU, sigma=SIGMA)
p2 = Gaussian(mu=MU, sigma=SIGMA)
p3 = Gaussian(mu=MU, sigma=SIGMA)
losing_team = {"player3": p3, "player2": p2}
winning_team = {"player1": p1}
teams = [winning_team] + [losing_team]
# when
# we update skills with the factor graph
ts = TrueSkillEnv(teams)
new_ratings = ts.update_ratings()
# and update skills with the analytic method
update_ratings_in_team(winning_team, losing_team)
# then
self.assertAlmostEqual(new_ratings["player1"].mu,
winning_team["player1"].mu, 2)
self.assertAlmostEqual(new_ratings["player2"].mu,
losing_team["player2"].mu, 2)
self.assertAlmostEqual(new_ratings["player3"].mu,
losing_team["player3"].mu, 2)
self.assertAlmostEqual(new_ratings["player1"].sigma,
winning_team["player1"].sigma, 2)
self.assertAlmostEqual(new_ratings["player2"].sigma,
new_ratings["player2"].sigma, 2)
self.assertAlmostEqual(new_ratings["player3"].sigma,
losing_team["player3"].sigma, 2)
def test_three_team_converges(self):
# given
p1 = Gaussian(mu=MU, sigma=SIGMA)
p2 = Gaussian(mu=MU, sigma=SIGMA)
p3 = Gaussian(mu=MU, sigma=SIGMA)
teams = [{"player1": p1}, {"player2": p2}, {"player3": p3}]
# when
ts = TrueSkillEnv(teams)
ts.update_ratings()
def test_gaussian_multiply(self):
# given
x = Gaussian(pi=3, tau=4)
y = Gaussian(pi=5, tau=6)
# when
z = x * y
# then
self.assertEqual(z.tau, x.tau + y.tau)
self.assertEqual(z.pi, x.pi + y.pi)
def test_update_player_rating(self):
# given
player = 'foo'
rating = Gaussian(mu=1, sigma=1)
self.source.data[player] = Gaussian(mu=0, sigma=10)
# when
self.source.update_player_rating(player, rating)
# then
self.assertEqual(self.source.data[player], rating)
def test_gaussian_divide(self):
# given
x = Gaussian(pi=4, tau=8)
y = Gaussian(pi=2, tau=2)
# when
z = x / y
# then
self.assertEqual(z.tau, x.tau - y.tau)
self.assertEqual(z.pi, x.pi - y.pi)
def test_prior_factor_down(self):
# given
var = Variable("player1")
dyn_fact = 0.5
val = Gaussian(mu=MU, sigma=SIGMA)
pf = PriorFactor(var, val, dyn_fact)
# when
pf.down()
# then
expected_pi = 1 / (SIGMA**2 + dyn_fact**2)
expected_marginal = Gaussian(pi=expected_pi, tau=val.tau)
self.assertEqual(expected_marginal, pf.var.marginal)
def test_sum_factor_helper(self):
# given
var = Variable()
var1, var2 = Variable(), Variable()
var1.pi, var2.pi, var1.tau, var2.tau = [1] * 4
perf_vars = [var1, var2]
perf_messages = [Gaussian(), Gaussian()]
coeffs = [1, 2]
sf = SumFactor(var, perf_vars, coeffs)
# when
sf._update_helper(var, perf_vars, perf_messages, coeffs)
# then
expected_pi = 1 / (1 / 1 + 1 / 2)
expected_tau = expected_pi * (1 + 2)
var.messages[sf] = Gaussian(pi=expected_pi, tau=expected_tau)
def update_ratings_in_team(winning_team: Dict[str, Gaussian],
losing_team: Dict[str, Gaussian],
perf_noise_sigma=PERFORMANCE_NOISE,
dynamics_factor=DYNAMIC_FACTOR):
"""Does TrueSkill update for players in a two team game.
Args:
winning_team: A dictionary of the skills of each player
losing_team: A dictionary of the skills of each player
perf_noise_sigma: Standard deviation of the performance noise
dynamics_factor: Additional factor which allows uncertainty in skill
to vary over time
"""
total_players = len(winning_team) + len(losing_team)
winning_mu = sum(winning_team[p].mu for p in winning_team)
losing_mu = sum(losing_team[p].mu for p in losing_team)
delta_mu = winning_mu - losing_mu
c = math.sqrt(
sum(winning_team[p].sigma**2 for p in winning_team) +
sum(losing_team[p].sigma**2
for p in losing_team) + total_players * perf_noise_sigma**2)
# compute the additive and multiplicative correction factors
v_game = v_truncate(delta_mu / c)
w_game = w_truncate(delta_mu / c)
# update the winning teams skills in place
for player in winning_team:
skill = winning_team[player]
adjusted_var = skill.sigma**2 + dynamics_factor**2
mu_multiplier = adjusted_var / c
sigma_multiplier = adjusted_var / c**2
mu = skill.mu + mu_multiplier * v_game
sigma = math.sqrt(adjusted_var * (1 - w_game * sigma_multiplier))
winning_team[player] = Gaussian(mu=mu, sigma=sigma)
# update the losing teams skills in place
for player in losing_team:
skill = losing_team[player]
adjusted_var = skill.sigma**2 + dynamics_factor**2
mu_multiplier = adjusted_var / c
sigma_multiplier = adjusted_var / c**2
mu = skill.mu - mu_multiplier * v_game
sigma = math.sqrt(adjusted_var * (1 - w_game * sigma_multiplier))
losing_team[player] = Gaussian(mu=mu, sigma=sigma)
def test_gaussian_multiply_throws_type_error(self):
# given
x = Gaussian()
y = 3
# when, then
with self.assertRaises(TypeError):
x * y
def test_sum_factor_down(self, mock_helper):
# given
var = Variable()
var1, var2 = Variable(), Variable()
var1.pi, var2.pi, var1.tau, var2.tau = [1] * 4
perf_vars = [var1, var2]
perf_messages = [Gaussian(), Gaussian()]
coeffs = [1, 2]
sf = SumFactor(var, perf_vars, coeffs)
# when
sf.down()
# then
expected_messages = [var1.messages[sf], var2.messages[sf]]
mock_helper.assert_called_with(var, perf_vars, expected_messages,
coeffs)
def update_rating(winner: Gaussian,
loser: Gaussian,
perf_noise_sigma=PERFORMANCE_NOISE,
dynamics_factor=DYNAMIC_FACTOR) -> Tuple[Gaussian, Gaussian]:
"""Updates the skills of two players in a 1vs1 match.
Args:
winner: Skill of the winner
loser: Skill of the loser
perf_noise_sigma: The standard devication of the performance noise.
dynamics_factor: The standard deviation of the dynamics factor on the
prior skill which allows uncertainty in skill to vary over time.
Returns:
Two new Gaussian objects containing the updated winner skill and
updated loser skill respectively.
"""
c = math.sqrt(winner.sigma**2 + loser.sigma**2 + 2 * perf_noise_sigma**2)
winner_adjusted_var = winner.sigma**2 + dynamics_factor**2
loser_adjusted_var = loser.sigma**2 + dynamics_factor**2
winning_mu = winner.mu
losing_mu = loser.mu
delta_mu = winning_mu - losing_mu
# calculate the additive and multiplicative correction factors
v_game = v_truncate(delta_mu / c)
w_game = w_truncate(delta_mu / c)
# update the winner
mu_multiplier = winner_adjusted_var / c
sigma_multiplier = winner_adjusted_var / c**2
new_mu = winning_mu + mu_multiplier * v_game
new_sigma = math.sqrt(winner_adjusted_var *
(1 - w_game * sigma_multiplier))
updated_winner = Gaussian(mu=new_mu, sigma=new_sigma)
# update the loser
mu_multiplier = loser_adjusted_var / c
sigma_multiplier = loser_adjusted_var / c**2
new_mu = losing_mu - mu_multiplier * v_game
new_sigma = math.sqrt(loser_adjusted_var * (1 - w_game * sigma_multiplier))
updated_loser = Gaussian(mu=new_mu, sigma=new_sigma)
return updated_winner, updated_loser
def up(self):
c = self.var.pi - self.var.messages[self].pi
d = self.var.tau - self.var.messages[self].tau
pi = c / (1 - w_truncate(d / math.sqrt(c)))
tau = ((d + math.sqrt(c) * v_truncate(d / math.sqrt(c))) /
(1 - w_truncate(d / math.sqrt(c))))
old_marginal = self.var.marginal
self.var.update_marginal(self, Gaussian(pi=pi, tau=tau))
return old_marginal.kl_divergence(self.var.marginal)
def connect_to_source(self, data_dir='.'):
if os.path.exists(os.path.join(data_dir, self.DATA_SOURCE)):
with open(os.path.join(data_dir, self.DATA_SOURCE), 'r') as f:
line = f.readline().strip('\n')
while line:
name, mu, sigma = line.split(',')
mu, sigma = float(mu), float(sigma)
rating = Gaussian(mu=mu, sigma=sigma)
self.data[name] = rating
line = f.readline().strip('\n')
def test_load_player_ratings_for_new_player(self):
# given
new_player = 'hello TrueSkill'
# when
self.source.load_player_ratings(new_player)
# then
expected_rating = Gaussian(mu=MU, sigma=SIGMA)
self.assertEqual(self.source.data[new_player], expected_rating)
def update_ratings(self):
self._run() # run the message passing algorithm
new_ratings = {}
for player in self.players:
name = player.name
pi = player.pi
tau = player.tau
new_ratings[name] = Gaussian(pi=pi, tau=tau)
return new_ratings
def test_sum_factor_up(self, mock_helper):
# given
var = Variable()
var1, var2 = Variable(), Variable()
var1.pi, var2.pi, var1.tau, var2.tau = [1] * 4
perf_vars = [var1, var2]
perf_messages = [Gaussian(), Gaussian()]
coeffs = [1, 2]
sf = SumFactor(var, perf_vars, coeffs)
# when
sf.up(0)
# then
# expect all variables except that at index 0
expected_vars = [var2, var]
expected_messages = [var2.messages[sf], var.messages[sf]]
expected_coeffs = [-2, 1] # coefficients of rearranged equation
mock_helper.assert_called_with(var1, expected_vars, expected_messages,
expected_coeffs)
def test_load_player_ratings_for_existing_player(self):
# given
existing_player = 'A True Skill Veteran'
existing_rating = Gaussian(mu=1, sigma=1)
self.source.data[existing_player] = existing_rating
# when
self.source.load_player_ratings(existing_player)
# then
self.assertEqual(self.source.data[existing_player], existing_rating)
def test_factor_graph_agrees_with_two_player_explicit(self):
# given
winner = Gaussian(mu=MU, sigma=SIGMA)
loser = Gaussian(mu=MU, sigma=SIGMA)
teams = [{"winner": winner}, {"loser": loser}]
# when
# we update the skills with the analytic method
updated_winner, updated_loser = update_rating(winner, loser)
# and we update the skills with the factor graph
ts = TrueSkillEnv(teams)
new_ratings = ts.update_ratings()
# then
# expect the results to be almost equal due to floating point errors
# TODO check that this level of error is expected.
self.assertAlmostEqual(new_ratings["winner"].mu, updated_winner.mu, 2)
self.assertAlmostEqual(new_ratings["loser"].mu, updated_loser.mu, 2)
self.assertAlmostEqual(new_ratings["winner"].sigma,
updated_loser.sigma, 2)
self.assertAlmostEqual(new_ratings["loser"].sigma, updated_loser.sigma,
2)
def _update_helper(self, var: Variable, perf_vars: List[Variable],
perf_messages: List[Gaussian], coeffs: List[float]):
# TODO: Make variables, messages and coeffs a list of named tuples.
assert len(perf_vars) == len(perf_messages) == len(coeffs)
pi = 1.0 / sum([
coeffs[i]**2 / (perf_vars[i].pi - perf_messages[i].pi)
for i in range(len(coeffs))
])
tau = pi * sum([
coeffs[i] * (perf_vars[i].tau - perf_messages[i].tau) /
(perf_vars[i].pi - perf_messages[i].pi) for i in range(len(coeffs))
])
new_message = Gaussian(pi=pi, tau=tau)
var.update_message(self, new_message)
def test_truncate_factor_updates_marginal(self, mock_v, mock_w, mock_kl):
# given
var = Variable()
var.pi, var.tau = [1] * 2
tf = TruncateFactor(var)
# when
tf.up()
# then
expected_tau = 1
expected_pi = 1
expected_marginal = Gaussian(pi=expected_pi, tau=expected_tau)
self.assertEqual(var.marginal, expected_marginal)
def test_truncate_factor_calls_kl_divergence(self, mock_v, mock_w,
mock_kl):
# given
var = Variable()
var.pi, var.tau = [1] * 2
tf = TruncateFactor(var)
# when
tf.up()
# then
expected_tau = 1
expected_pi = 1
expected_marginal = Gaussian(pi=expected_pi, tau=expected_tau)
mock_kl.assert_called_with(expected_marginal)
def marginal(self):
return Gaussian(pi=self.pi, tau=self.tau)
def _update_helper(self, variable_one: Variable, variable_two: Variable):
msg = variable_one / variable_one.messages[self]
a = 1 / (1 + self.beta**2 * msg.pi)
message = Gaussian(pi=a * msg.pi, tau=a * msg.tau)
variable_two.update_message(self, message)
def down(self):
pi = 1 / (self.value.pi**-1 + self.dynamic**2)
value = Gaussian(pi=pi, tau=self.value.tau)
self.var.update_marginal(self, value)
def __init__(self, variables):
self.vars = variables
for var in self.vars:
var.messages[self] = Gaussian()
def load_player_ratings(self, player_name):
if player_name not in self.data:
self.data[player_name] = Gaussian(mu=MU, sigma=SIGMA)
return self.data[player_name]
