Module: TrueskillThroughTime

Defined in:
lib/TrueskillThroughTime.rb,
lib/TrueskillThroughTime/version.rb

Defined Under Namespace

Classes: Agent, Batch, DiffMessages, DrawMessages, Error, Event, Game, Gaussian, History, Item, Player, Skill, Team, TeamVariable

Constant Summary collapse

BETA =

Configuration Constants

1.0
MU = 
0.0
SIGMA = 
BETA * 6
GAMMA = 
BETA * 0.03
P_DRAW = 
0.0
EPSILON = 
1e-6
ITERATIONS = 
30
SQRT2 =

Derived Math Constants

Math.sqrt(2)
SQRT2PI = 
Math.sqrt(2 * Math::PI)
INF = 
Float::INFINITY
N01 = 
Gaussian.new(0.0, 1.0)
N00 = 
Gaussian.new(0.0, 0.0)
NINF = 
Gaussian.new(0.0, INF)
Nms = 
Gaussian.new(MU, SIGMA)
VERSION = 
"1.0.0"

Instance Method Summary collapse

Instance Method Details

#approx(n, margin, tie) ⇒ Object

TODO: It seems like this should be a Guassian function



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# File 'lib/TrueskillThroughTime.rb', line 126

def approx(n, margin, tie) # TODO: It seems like this should be a Guassian function
  mu, sigma = trunc(n.mu, n.sigma, margin, tie)
  # if $should_debug
  #   puts "approx(#{[n, margin, tie]}) (n, margin, tie) = mu #{mu} sigma #{sigma}"
  # end
  Gaussian.new(mu, sigma)
end

#cdf(x, mu = 0, sigma = 1) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 90

def cdf(x, mu=0, sigma=1)
  0.5 * erfc(-(x - mu) / (sigma * SQRT2))
end

#clean!(agents, last_time = false) ⇒ Object

Agents is a dict in python and their implementation is whack.



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# File 'lib/TrueskillThroughTime.rb', line 670

def clean!(agents, last_time=false)
  agents.each_pair do |agent_label, agent|
    agent.message = NINF
    agent.last_time = -INF if last_time
  end
end

#compute_elapsed(last_time, actual_time) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 736

def compute_elapsed(last_time, actual_time)
  if last_time == INF
    1
  elsif last_time == -INF
    0
  else
    actual_time - last_time
  end
end

#compute_margin(p_draw, sd) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 134

def compute_margin(p_draw, sd)
  (ppf(0.5-p_draw/2.0, 0.0, sd)).abs
end

#dict_diff(old, new) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 170

def dict_diff(old, new)
  step = [0.0, 0.0]
  old.each_key do |a|
    step = max_tuple(step, old[a].delta(new[a])) # .delta is Guassian method....
  end
  step
end

#erfc(x) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 31

def erfc(x)
  # """(http://bit.ly/zOLqbc)"""
  z = x.abs
  t = 1.0 / (1.0 + z / 2.0)
  a = -0.82215223 + t * 0.17087277; b = 1.48851587 + t * a
  c = -1.13520398 + t * b; d = 0.27886807 + t * c; e = -0.18628806 + t * d
  f = 0.09678418 + t * e; g = 0.37409196 + t * f; h = 1.00002368 + t * g
  r = t * Math.exp(-z * z - 1.26551223 + t * h)
  if x.positive?
    r
  else
    2.0 - r
  end
end

#erfcinv(y) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/TrueskillThroughTime.rb', line 46

def erfcinv(y)
  raise(ArgumentError, "Argument must be non-negative numbers") if y.negative?
  return -INF if y > 2
  return INF if y.zero?

  y = 2 - y if y >= 1

  t = Math.sqrt(-2 * Math.log(y / 2.0))
  x = -0.70711 * ((2.30753 + t * 0.27061) / (1.0 + t * (0.99229 + t * 0.04481)) - t)

  3.times do
    err = erfc(x) - y
    x += err / (1.12837916709551257 * Math.exp(-(x**2)) - x * err)
  end

  y < 1 ? x : -x
end

#game_example(mu = MU, sigma = SIGMA, beta = BETA, p_draw = P_DRAW) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 1066

def game_example(mu=MU, sigma=SIGMA, beta=BETA, p_draw=P_DRAW)
  a1 = Player.new(Gaussian.new(mu-500, sigma), beta=beta)
  a2 = Player.new(Gaussian.new(mu-500, sigma), beta=beta)
  a3 = Player.new(Gaussian.new(mu, sigma), beta=beta)
  a4 = Player.new(Gaussian.new(mu, sigma), beta=beta)
  a5 = Player.new(Gaussian.new(mu+5000, sigma), beta=beta)
  a6 = Player.new(Gaussian.new(mu+5000, sigma), beta=beta)
  team_a = [ a1, a2 ]
  team_b = [ a3, a4 ]
  team_c = [ a5, a6 ]
  teams = [team_a, team_b, team_c]
  result = [0.0, 1.0, 2.0]
  g = Game.new(teams, result, p_draw=p_draw)
  puts "Teams: #{g.teams}"
  puts "Likelihoods: #{g.likelihoods}"
  puts "Evidence: #{g.evidence}"
  puts "Posteriors: #{g.posteriors}"
  (0...teams.length).each do |i|
    puts "#{i}: #{g.performance(i)}"
  end
end

#get_composition(events) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 728

def get_composition(events)
  events.map {|event| event.teams.map {|team| team.items.map {|item| item.name} } }
end

#get_results(events) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 732

def get_results(events)
  events.map {|event| event.teams.map {|team| team.output } }
end

#gr_tuple(tup, threshold) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 154

def gr_tuple(tup, threshold)
  tup.max > threshold
end

#history_example(mu = MU, sigma = SIGMA, beta = BETA, p_draw = P_DRAW) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 1088

def history_example(mu=MU, sigma=SIGMA, beta=BETA, p_draw=P_DRAW)
  c1 = [["a"], ["b"]]
  c2 = [["b"], ["c"]]
  c3 = [["c"], ["a"]]
  composition = [c1, c2, c3]
  h = History.new(composition, gamma: 0.0)
  puts "#{h.learning_curves["a"]}"
  # [(1, N(mu=3.339, sigma=4.985)), (3, N(mu=-2.688, sigma=3.779))]
  puts "#{h.learning_curves["b"]}"
  # [(1, N(mu=-3.339, sigma=4.985)), (2, N(mu=0.059, sigma=4.218))]
  h.convergence
  puts "#{h.learning_curves["a"]}"
  # [[1, N(mu= 1.1776221018565704e-07, sigma= 2.3948083841791528)], [3, N(mu= -9.875327098012653e-08, sigma= 2.3948083506699978)]]
  puts "#{h.learning_curves["b"]}"
  # [[1, N(mu= -6.743217353120669e-08, sigma= 2.3948083803990317)], [2, N(mu= -6.888059735564812e-08, sigma= 2.394808375074641)]]
  puts "#{h.log_evidence}"
  puts "Foo"
end

#liquid_example(path: "./example_data/liquid_t2_tournament_results.json") ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 1107

def liquid_example(path:"./example_data/liquid_t2_tournament_results.json")
  json_data = JSON.load(File.open(path))
  tournaments = {}
  json_data["tournament_positions"].each_pair do |k, v| # Symbolise keys and convert to dates, remove fake tournaments, remove tournaments with draws
    next unless v["results"].length > 2 # fake tournaments have < 3 teams

    results = {}
    had_ties = false
    v["results"].each_pair do |rk, rv| # numberise keys, then sort the results by them
      if rv.length > 1
        had_ties = true
        break
      else
        results[rk.to_f] = rv
      end
    end
    unless had_ties
      tournaments[k] = { :results => results.sort,
                         :day => DateTime.strptime(v["date"], "%Y-%m-%d %H:%M:%S").to_time.to_i / (60 * 60 * 24) }
    end
  end
  tournaments = tournaments.sort_by {|k, v| v[:day]}.to_h
  # Need to get to compositions, results, times: results needs to be inverse of position
  compositions = []
  results = []
  times = []
  tournaments.each_pair do |tournament_name, t_data|
    times << t_data[:day]
    t_results = []
    t_compositions = []
    t_data[:results].each_with_index do |(position, composition), i|
      t_results << t_data[:results].length - i
      # t_compositions << composition.map {|player| [player]}
      t_compositions << composition.flatten
    end
    compositions << t_compositions
    results << t_results
  end

  h = History.new(compositions, results:results, times:times, mu:1200, sigma:400, beta:1320, gamma:19, p_draw: 0.01375)

  puts h.log_evidence
  h.convergence(epsilon: 0.01, iterations: 60, verbose: true)
  puts h.log_evidence
  puts h.learning_curves.first

  h.evidence.each_with_index do |ev, idx|
    puts "#{idx}\t#{ev}\t#{tournaments.keys[idx]}"
  end

end

#max_tuple(t1, t2) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 138

def max_tuple(t1, t2)
  # Let's emulate python nan sorting behaviour!
  responses = [0.0, 0.0]
  responses[0] = if t1[0].to_f.nan? || t2[0].to_f.nan?
                   t1[0]
                 else
                   [t1[0], t2[0]].max
                 end
  responses[1] = if t1[1].to_f.nan? || t2[1].to_f.nan?
                   t1[1]
                 else
                   [t1[1], t2[1]].max
                 end
  responses
end

#mu_sigma(tau_, pi_) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/TrueskillThroughTime.rb', line 77

def mu_sigma(tau_, pi_)
  raise(ArgumentError, "Sigma must be greater than 0.") if (pi_ + 1e-5) < 0.0

  if pi_ > 0.0
    sigma = Math.sqrt(1.0/pi_)
    mu = tau_ / pi_.to_f
  else
    sigma = INF
    mu = 0.0
  end
  [mu, sigma] # again tuple in original
end

#pdf(x, mu, sigma) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 94

def pdf(x, mu, sigma)
  normaliser = (SQRT2PI * sigma)**-1
  functional = Math.exp(-((x - mu)**2) / (2*sigma**2))
  normaliser * functional
end

#podium(xs) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 158

def podium(xs)
  sortperm(xs)
end

#ppf(p, mu, sigma) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 100

def ppf(p, mu, sigma)
  mu - sigma * SQRT2 * erfcinv(2 * p)
end

#sortperm(xs, reverse = false) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 162

def sortperm(xs, reverse=false)
  sorted_indices = xs.each_with_index
                     .sort_by { |v, i| v }
                     .map { |v, i| i }
  sorted_indices.reverse! if reverse
  sorted_indices
end

#tau_pi(mu, sigma) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/TrueskillThroughTime.rb', line 64

def tau_pi(mu, sigma)
  raise(ArgumentError, "Sigma must be greater than 0.") if (sigma + 1e-5) < 0.0

  if sigma > 0.0
    pi_ = sigma ** -2
    tau_ = pi_ * mu
  else
    pi_ = INF
    tau_ = INF
  end
  [tau_, pi_] # python returns tuple
end

#trunc(mu, sigma, margin, tie) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 119

def trunc(mu, sigma, margin, tie)
  v, w = v_w(mu, sigma, margin, tie)
  mu_trunc = mu + sigma * v
  sigma_trunc = sigma * Math.sqrt(1-w)
  [mu_trunc, sigma_trunc]
end

#v_w(mu, sigma, margin, tie) ⇒ Object 



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# File 'lib/TrueskillThroughTime.rb', line 104

def v_w(mu, sigma, margin, tie)
  if tie
    _alpha = (-margin-mu)/sigma
    _beta  = ( margin-mu)/sigma
    v = (pdf(_alpha, 0, 1)-pdf(_beta, 0, 1))/(cdf(_beta, 0, 1)-cdf(_alpha, 0, 1))
    u = (_alpha*pdf(_alpha, 0, 1)-_beta*pdf(_beta, 0, 1))/(cdf(_beta, 0, 1)-cdf(_alpha, 0, 1))
    w = - ( u - v**2 )
  else
    _alpha = (margin-mu)/sigma
    v = pdf(-_alpha, 0, 1) / cdf(-_alpha, 0, 1)
    w = v * (v + (-_alpha))
  end
  [v, w] # again, a tuple
end