The PRank algorithm is a modification of the perceptron classifier. It aims to classify items into tiers, where the tiers are ordered.
def prank(stats, tiers, n_tiers, iters):
'''
Implementation of the PRank algorithm (http://papers.nips.cc/paper/2023-pranking-with-ranking.pdf)
stats: array of features, a column per feature
tiers: array of rankings, one ranking per player
n_tiers: number of tiers, tiers are numbered 0,1,2,...,n_tiers-1
iters: number of iterations of loop
'''
n_players = len(stats)
n_features = len(stats[0])
w = np.zeros([n_features]) # weight of features
b = np.zeros([n_tiers]) # cutoffs for rankings
b[-1] = np.inf
loss = 0 # total loss incurred by algorithm
for i in range(iters): # update w and b given training example x
n = i%n_players
x = stats[n].copy()
y = np.argmax(b > np.dot(x,w)) # get rank of x as determined by current w and b
y_act = tiers[n]
loss += abs(y-y_act)
if y != tiers[n]: # if predicted rank is not actual rank, update w and b
y_arr = np.repeat([1,-1],[y_act,n_tiers-1-y_act]) # create y array
t_arr = np.zeros([n_tiers-1])
y_n = np.argmax(b >= np.dot(x,w))
if y_act > y_n:
t_arr = np.repeat([0,1,0],[y_n,y_act-y_n,n_tiers-1-y_act])
else:
t_arr = np.repeat([0,-1,0],[y_act,y_n-y_act,n_tiers-1-y_n])
w = w + np.sum(t_arr)*x
b[:-1] = b[:-1] - t_arr
return w, b, 1.0*loss/iters
def rank(x,w,b):
'''
Subroutine for use in PRank
Calculates rank of example x given feature weights w and rank cutoffs b
'''
return np.argmax(b > np.dot(x,w))
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