A regression model is one that predicts a single numeric value, such as the income of a person based on their sex, age, State of residence, and political leaning.
In many scenarios, a simple accuracy metric of the trained model computed on the training and test data is good enough. For example:
Computing model accuracy (within 0.10 of true) Accuracy on train data = 0.8850 Accuracy on test data = 0.9250
But in some scenarios, it’s better to compute the accuracy of the trained model for various intervals of the dependent/target variable. For example:
Accuracy on training data (within 0.10 of true):
from to correct wrong count accuracy
0.00 0.25 3 1 4 0.7500
0.25 0.50 66 18 84 0.7857
0.50 0.75 99 3 102 0.9706
0.75 1.00 9 1 10 0.9000
Accuracy on test data (within 0.10 of true):
from to correct wrong count accuracy
0.00 0.25 1 0 1 1.0000
0.25 0.50 13 3 16 0.8125
0.50 0.75 22 0 22 1.0000
0.75 1.00 1 0 1 1.0000
I put together a demo with PyTorch. I used a synthetic dataset. The raw data looks like:
# people_raw.txt # sex, age, state, income, politics # F 24 michigan 29500.00 liberal M 39 oklahoma 51200.00 moderate F 63 nebraska 75800.00 conservative M 36 michigan 44500.00 moderate F 27 nebraska 28600.00 liberal . . .
The raw data is encoded and normalized and looks like:
1, 0.24, 1, 0, 0, 0.2950, 0, 0, 1 -1, 0.39, 0, 0, 1, 0.5120, 0, 1, 0 1, 0.63, 0, 1, 0, 0.7580, 1, 0, 0 -1, 0.36, 1, 0, 0, 0.4450, 0, 1, 0 1, 0.27, 0, 1, 0, 0.2860, 0, 0, 1 . . .
Sex is encoded as M = -1, F = 1. Age is normalized by dividing by 100. State is one-hot encoded as Michigan = 100, Nebraska = 010, Oklahoma = 001. Income is normalized by dividing by 100,000. Political leaning is one-hot encoded as conservative = 100, moderate = 010, liberal = 001.
There are 200 training items and 40 test items.
The demo PyTorch neural network has an 8-(10-10)-1 architecture with tanh() hidden node activation, and no output node activation (or equivalently, identity() output node activation.
For training, I used mean squared error loss, Adam optimization, a fixed learning rate of 0.10, a batch size of 10, and 100 training epochs.
When computing accuracy for a regression model, you need to specify how close a prediction is to the true target value, in order for the prediction to be considered correct. For my demo, I used 10% — if the predicted income is plus or minus 10% of the true value. The percentage to use will vary greatly according to the specific problem being examined.
My accuracy-by-interval function is named accuracy_matrix() and is:
def accuracy_matrix(model, ds, pct_close, points):
n_intervals = len(points) - 1
result = np.zeros((n_intervals,2),dtype=np.int64)
# n_corrects in col [0], n_wrongs in col [1]
for i in range(len(ds)):
X = ds[i][0] # like [1, 0.24, .. ]
Y = ds[i][1] # like [0.5678] target income
with T.no_grad():
oupt = model(X) # like [0.4156] predicted income
interval = 0
for i in range(n_intervals):
if Y.item() "gte" points[i] and \
Y.item() "lt" points[i+1]:
interval = i; break
if T.abs(oupt - Y) "lt" T.abs(pct_close * Y): # auto-conv
result[interval][0] += 1
else:
result[interval][1] += 1
return result
I implemented a separate show_acc_matrix() function to display a computed accuracy matrix:
def show_acc_matrix(am, points):
h = "from to correct wrong count accuracy"
print(" " + h)
for i in range(len(am)):
print("%8.2f" % points[i], end="")
print("%8.2f" % points[i+1], end="")
print("%8d" % am[i][0], end ="")
print("%8d" % am[i][1], end ="")
count = am[i][0] + am[i][1]
print("%8d" % count, end="")
if count == 0:
acc = 0.0
else:
acc = am[i][0] / count
print("%12.4f" % acc)
Calling the functions looks like:
income_pts = [0.0, 0.25, 0.50, 0.75, 1.0]
acc_matrix_train = \
accuracy_matrix(net, train_ds, 0.10, income_pts)
print("\nAccuracy on training data (within 0.10 of true):")
show_acc_matrix(acc_matrix_train, income_pts)
The income_pts list means compute accuracy for five intervals of target incomes: between 0 and 0.25 ($25,000), 0.25 to 0.50, 0.50 to 0.75, 0.75 to 1.00.
The results, shown above, suggest that the model is quite accurate for high income values, but not as accurate for low income values.
When I was a teenager, I worked at several jobs: fast food restaurant, ice cream parlor, miniature golf course, hardware store. I used some of my meager income to buy books of the Mars series written by Edgar Rice Burroughs. “Swords of Mars” is the eighth book in the series. Hero John Carter battles the Guild of Assassins on Mars, and on the Martian moon Thuria (Phobos) where the villains have kidnapped Carter’s wife, Dejah Thoris.
Left: Art for the first hardcover edition (1936) by J. Allen St. John. Center: Art for the 1973 paperback edition by Gino D’Achille. Right: Art for the 1963 paperback edition by Robert Abbett.
Demo code. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols (my blog editor chokes on symbols).
# people_income_interval_accuracy.py
# predict income from sex, age, city, politics
# PyTorch 2.1.2-CPU Anaconda3-2023.09-0 Python 3.11.5
# Windows 10/11
import numpy as np
import torch as T
device = T.device('cpu') # apply to Tensor or Module
# -----------------------------------------------------------
class PeopleDataset(T.utils.data.Dataset):
def __init__(self, src_file):
# sex age state income politics
# -1, 0.27, 0, 1, 0, 0.7610, 0, 0, 1
# +1, 0.19, 0, 0, 1, 0.6550, 1, 0, 0
tmp_x = np.loadtxt(src_file, usecols=[0,1,2,3,4,6,7,8],
delimiter=",", comments="#", dtype=np.float32)
tmp_y = np.loadtxt(src_file, usecols=5, delimiter=",",
comments="#", dtype=np.float32)
tmp_y = tmp_y.reshape(-1,1) # 2D required
# single-read approach
# tmp_xy = np.loadtxt(src_file,
# usecols=[0,1,2,3,4,5,6,7,8], delimiter=",",
# comments="#", dtype=np.float32)
# tmp_x = tmp_xy[:,[0,1,2,3,4,6,7,8]]
# tmp_y = tmp_xy[:,[5]] # already 2D
self.x_data = T.tensor(tmp_x, dtype=T.float32).to(device)
self.y_data = T.tensor(tmp_y, dtype=T.float32).to(device)
def __len__(self):
return len(self.x_data)
def __getitem__(self, idx):
preds = self.x_data[idx]
incom = self.y_data[idx]
return (preds, incom) # as a tuple
# -----------------------------------------------------------
class Net(T.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hid1 = T.nn.Linear(8, 10) # 8-(10-10)-1
self.hid2 = T.nn.Linear(10, 10)
self.oupt = T.nn.Linear(10, 1)
T.nn.init.xavier_uniform_(self.hid1.weight)
T.nn.init.zeros_(self.hid1.bias)
T.nn.init.xavier_uniform_(self.hid2.weight)
T.nn.init.zeros_(self.hid2.bias)
T.nn.init.xavier_uniform_(self.oupt.weight)
T.nn.init.zeros_(self.oupt.bias)
def forward(self, x):
z = T.tanh(self.hid1(x))
z = T.tanh(self.hid2(z))
z = self.oupt(z) # regression: no activation
return z
# -----------------------------------------------------------
def accuracy_matrix(model, ds, pct_close, points):
n_intervals = len(points) - 1
result = np.zeros((n_intervals,2),dtype=np.int64)
# n_corrects in col [0], n_wrongs in col [1]
for i in range(len(ds)):
X = ds[i][0] # like [1, 0.24, .. ]
Y = ds[i][1] # like [0.5678] target income
with T.no_grad():
oupt = model(X) # like [0.4156] predicted income
interval = 0
for i in range(n_intervals):
if Y.item() "gte" points[i] and \
Y.item() "lt" points[i+1]:
interval = i; break
if T.abs(oupt - Y) "lt" T.abs(pct_close * Y):
result[interval][0] += 1
else:
result[interval][1] += 1
return result
# -----------------------------------------------------------
def show_acc_matrix(am, points):
h = "from to correct wrong count accuracy"
print(" " + h)
for i in range(len(am)):
print("%8.2f" % points[i], end="")
print("%8.2f" % points[i+1], end="")
print("%8d" % am[i][0], end ="")
print("%8d" % am[i][1], end ="")
count = am[i][0] + am[i][1]
print("%8d" % count, end="")
if count == 0:
acc = 0.0
else:
acc = am[i][0] / count
print("%12.4f" % acc)
# -----------------------------------------------------------
def accuracy(model, ds, pct_close):
# assumes model.eval()
# correct within pct of true income
n_correct = 0; n_wrong = 0
for i in range(len(ds)):
X = ds[i][0] # tensor
Y = ds[i][1] # tensor target income
with T.no_grad():
oupt = model(X) # predictedd income
if T.abs(oupt - Y) "lt" T.abs(pct_close * Y):
n_correct += 1
else:
n_wrong += 1
acc = (n_correct * 1.0) / (n_correct + n_wrong)
return acc
# -----------------------------------------------------------
def accuracy_x(model, ds, pct_close):
# all-at-once (quick)
# assumes model.eval()
X = ds.x_data # all inputs
Y = ds.y_data # all targets
n_items = len(X)
with T.no_grad():
pred = model(X) # all predicted incomes
n_correct = \
T.sum((T.abs(pred - Y) "lt" T.abs(pct_close * Y)))
result = (n_correct.item() / n_items) # scalar
return result
# -----------------------------------------------------------
def train(model, ds, bs, lr, me, le):
# dataset, bat_size, lrn_rate, max_epochs, log interval
train_ldr = T.utils.data.DataLoader(ds, batch_size=bs,
shuffle=True)
loss_func = T.nn.MSELoss()
optimizer = T.optim.Adam(model.parameters(), lr=lr)
for epoch in range(0, me):
epoch_loss = 0.0 # for one full epoch
for (b_idx, batch) in enumerate(train_ldr):
X = batch[0] # predictors
y = batch[1] # target income
optimizer.zero_grad()
oupt = model(X)
loss_val = loss_func(oupt, y) # a tensor
epoch_loss += loss_val.item() # accumulate
loss_val.backward() # compute gradients
optimizer.step() # update weights
if epoch % le == 0:
print("epoch = %4d | loss = %0.4f" % \
(epoch, epoch_loss))
# -----------------------------------------------------------
def main():
# 0. get started
print("\nBegin People predict income ")
T.manual_seed(0)
np.random.seed(0)
# 1. create Dataset objects
print("\nCreating People Dataset objects ")
train_file = ".\\Data\\people_train.txt"
train_ds = PeopleDataset(train_file) # 200 rows
test_file = ".\\Data\\people_test.txt"
test_ds = PeopleDataset(test_file) # 40 rows
# 2. create network
print("\nCreating 8-(10-10)-1 neural network ")
net = Net().to(device)
# -----------------------------------------------------------
# 3. train model
print("\nbat_size = 10 ")
print("loss = MSELoss() ")
print("optimizer = Adam ")
print("lrn_rate = 0.01 ")
print("\nStarting training")
net.train()
train(net, train_ds, bs=10, lr=0.01, me=120, le=20)
print("Done ")
# -----------------------------------------------------------
# 4. evaluate model accuracy
print("\nComputing model accuracy (within 0.10 of true) ")
net.eval()
acc_train = accuracy(net, train_ds, 0.10) # item-by-item
print("Accuracy on train data = %0.4f" % acc_train)
acc_test = accuracy_x(net, test_ds, 0.10) # all-at-once
print("Accuracy on test data = %0.4f" % acc_test)
income_pts = [0.0, 0.25, 0.50, 0.75, 1.0]
acc_matrix_train = \
accuracy_matrix(net, train_ds, 0.10, income_pts)
print("\nAccuracy on training data (within 0.10 of true):")
show_acc_matrix(acc_matrix_train, income_pts)
acc_matrix_test = \
accuracy_matrix(net, test_ds, 0.10, income_pts)
print("\nAccuracy on test data (within 0.10 of true):")
show_acc_matrix(acc_matrix_test, income_pts)
# -----------------------------------------------------------
# 5. make a prediction
print("\nPredicting income for M 34 Oklahoma moderate: ")
x = np.array([[-1, 0.34, 0,0,1, 0,1,0]],
dtype=np.float32)
x = T.tensor(x, dtype=T.float32).to(device)
with T.no_grad():
pred_inc = net(x)
pred_inc = pred_inc.item() # scalar
print("$%0.2f" % (pred_inc * 100_000)) # un-normalized
# -----------------------------------------------------------
# 6. save model (state_dict approach)
print("\nSaving trained model state")
fn = ".\\Models\\people_income_model.pt"
T.save(net.state_dict(), fn)
# model = Net()
# model.load_state_dict(T.load(fn))
# use model to make prediction(s)
print("\nEnd People income demo ")
if __name__ == "__main__":
main()
Training data:
# people_train.txt # # sex (-1 = male, 1 = female), age / 100, # state (michigan = 100, nebraska = 010, oklahoma = 001), # income / 100_000, # politics (conservative = 100, moderate = 010, liberal = 001) # 1, 0.24, 1, 0, 0, 0.2950, 0, 0, 1 -1, 0.39, 0, 0, 1, 0.5120, 0, 1, 0 1, 0.63, 0, 1, 0, 0.7580, 1, 0, 0 -1, 0.36, 1, 0, 0, 0.4450, 0, 1, 0 1, 0.27, 0, 1, 0, 0.2860, 0, 0, 1 1, 0.50, 0, 1, 0, 0.5650, 0, 1, 0 1, 0.50, 0, 0, 1, 0.5500, 0, 1, 0 -1, 0.19, 0, 0, 1, 0.3270, 1, 0, 0 1, 0.22, 0, 1, 0, 0.2770, 0, 1, 0 -1, 0.39, 0, 0, 1, 0.4710, 0, 0, 1 1, 0.34, 1, 0, 0, 0.3940, 0, 1, 0 -1, 0.22, 1, 0, 0, 0.3350, 1, 0, 0 1, 0.35, 0, 0, 1, 0.3520, 0, 0, 1 -1, 0.33, 0, 1, 0, 0.4640, 0, 1, 0 1, 0.45, 0, 1, 0, 0.5410, 0, 1, 0 1, 0.42, 0, 1, 0, 0.5070, 0, 1, 0 -1, 0.33, 0, 1, 0, 0.4680, 0, 1, 0 1, 0.25, 0, 0, 1, 0.3000, 0, 1, 0 -1, 0.31, 0, 1, 0, 0.4640, 1, 0, 0 1, 0.27, 1, 0, 0, 0.3250, 0, 0, 1 1, 0.48, 1, 0, 0, 0.5400, 0, 1, 0 -1, 0.64, 0, 1, 0, 0.7130, 0, 0, 1 1, 0.61, 0, 1, 0, 0.7240, 1, 0, 0 1, 0.54, 0, 0, 1, 0.6100, 1, 0, 0 1, 0.29, 1, 0, 0, 0.3630, 1, 0, 0 1, 0.50, 0, 0, 1, 0.5500, 0, 1, 0 1, 0.55, 0, 0, 1, 0.6250, 1, 0, 0 1, 0.40, 1, 0, 0, 0.5240, 1, 0, 0 1, 0.22, 1, 0, 0, 0.2360, 0, 0, 1 1, 0.68, 0, 1, 0, 0.7840, 1, 0, 0 -1, 0.60, 1, 0, 0, 0.7170, 0, 0, 1 -1, 0.34, 0, 0, 1, 0.4650, 0, 1, 0 -1, 0.25, 0, 0, 1, 0.3710, 1, 0, 0 -1, 0.31, 0, 1, 0, 0.4890, 0, 1, 0 1, 0.43, 0, 0, 1, 0.4800, 0, 1, 0 1, 0.58, 0, 1, 0, 0.6540, 0, 0, 1 -1, 0.55, 0, 1, 0, 0.6070, 0, 0, 1 -1, 0.43, 0, 1, 0, 0.5110, 0, 1, 0 -1, 0.43, 0, 0, 1, 0.5320, 0, 1, 0 -1, 0.21, 1, 0, 0, 0.3720, 1, 0, 0 1, 0.55, 0, 0, 1, 0.6460, 1, 0, 0 1, 0.64, 0, 1, 0, 0.7480, 1, 0, 0 -1, 0.41, 1, 0, 0, 0.5880, 0, 1, 0 1, 0.64, 0, 0, 1, 0.7270, 1, 0, 0 -1, 0.56, 0, 0, 1, 0.6660, 0, 0, 1 1, 0.31, 0, 0, 1, 0.3600, 0, 1, 0 -1, 0.65, 0, 0, 1, 0.7010, 0, 0, 1 1, 0.55, 0, 0, 1, 0.6430, 1, 0, 0 -1, 0.25, 1, 0, 0, 0.4030, 1, 0, 0 1, 0.46, 0, 0, 1, 0.5100, 0, 1, 0 -1, 0.36, 1, 0, 0, 0.5350, 1, 0, 0 1, 0.52, 0, 1, 0, 0.5810, 0, 1, 0 1, 0.61, 0, 0, 1, 0.6790, 1, 0, 0 1, 0.57, 0, 0, 1, 0.6570, 1, 0, 0 -1, 0.46, 0, 1, 0, 0.5260, 0, 1, 0 -1, 0.62, 1, 0, 0, 0.6680, 0, 0, 1 1, 0.55, 0, 0, 1, 0.6270, 1, 0, 0 -1, 0.22, 0, 0, 1, 0.2770, 0, 1, 0 -1, 0.50, 1, 0, 0, 0.6290, 1, 0, 0 -1, 0.32, 0, 1, 0, 0.4180, 0, 1, 0 -1, 0.21, 0, 0, 1, 0.3560, 1, 0, 0 1, 0.44, 0, 1, 0, 0.5200, 0, 1, 0 1, 0.46, 0, 1, 0, 0.5170, 0, 1, 0 1, 0.62, 0, 1, 0, 0.6970, 1, 0, 0 1, 0.57, 0, 1, 0, 0.6640, 1, 0, 0 -1, 0.67, 0, 0, 1, 0.7580, 0, 0, 1 1, 0.29, 1, 0, 0, 0.3430, 0, 0, 1 1, 0.53, 1, 0, 0, 0.6010, 1, 0, 0 -1, 0.44, 1, 0, 0, 0.5480, 0, 1, 0 1, 0.46, 0, 1, 0, 0.5230, 0, 1, 0 -1, 0.20, 0, 1, 0, 0.3010, 0, 1, 0 -1, 0.38, 1, 0, 0, 0.5350, 0, 1, 0 1, 0.50, 0, 1, 0, 0.5860, 0, 1, 0 1, 0.33, 0, 1, 0, 0.4250, 0, 1, 0 -1, 0.33, 0, 1, 0, 0.3930, 0, 1, 0 1, 0.26, 0, 1, 0, 0.4040, 1, 0, 0 1, 0.58, 1, 0, 0, 0.7070, 1, 0, 0 1, 0.43, 0, 0, 1, 0.4800, 0, 1, 0 -1, 0.46, 1, 0, 0, 0.6440, 1, 0, 0 1, 0.60, 1, 0, 0, 0.7170, 1, 0, 0 -1, 0.42, 1, 0, 0, 0.4890, 0, 1, 0 -1, 0.56, 0, 0, 1, 0.5640, 0, 0, 1 -1, 0.62, 0, 1, 0, 0.6630, 0, 0, 1 -1, 0.50, 1, 0, 0, 0.6480, 0, 1, 0 1, 0.47, 0, 0, 1, 0.5200, 0, 1, 0 -1, 0.67, 0, 1, 0, 0.8040, 0, 0, 1 -1, 0.40, 0, 0, 1, 0.5040, 0, 1, 0 1, 0.42, 0, 1, 0, 0.4840, 0, 1, 0 1, 0.64, 1, 0, 0, 0.7200, 1, 0, 0 -1, 0.47, 1, 0, 0, 0.5870, 0, 0, 1 1, 0.45, 0, 1, 0, 0.5280, 0, 1, 0 -1, 0.25, 0, 0, 1, 0.4090, 1, 0, 0 1, 0.38, 1, 0, 0, 0.4840, 1, 0, 0 1, 0.55, 0, 0, 1, 0.6000, 0, 1, 0 -1, 0.44, 1, 0, 0, 0.6060, 0, 1, 0 1, 0.33, 1, 0, 0, 0.4100, 0, 1, 0 1, 0.34, 0, 0, 1, 0.3900, 0, 1, 0 1, 0.27, 0, 1, 0, 0.3370, 0, 0, 1 1, 0.32, 0, 1, 0, 0.4070, 0, 1, 0 1, 0.42, 0, 0, 1, 0.4700, 0, 1, 0 -1, 0.24, 0, 0, 1, 0.4030, 1, 0, 0 1, 0.42, 0, 1, 0, 0.5030, 0, 1, 0 1, 0.25, 0, 0, 1, 0.2800, 0, 0, 1 1, 0.51, 0, 1, 0, 0.5800, 0, 1, 0 -1, 0.55, 0, 1, 0, 0.6350, 0, 0, 1 1, 0.44, 1, 0, 0, 0.4780, 0, 0, 1 -1, 0.18, 1, 0, 0, 0.3980, 1, 0, 0 -1, 0.67, 0, 1, 0, 0.7160, 0, 0, 1 1, 0.45, 0, 0, 1, 0.5000, 0, 1, 0 1, 0.48, 1, 0, 0, 0.5580, 0, 1, 0 -1, 0.25, 0, 1, 0, 0.3900, 0, 1, 0 -1, 0.67, 1, 0, 0, 0.7830, 0, 1, 0 1, 0.37, 0, 0, 1, 0.4200, 0, 1, 0 -1, 0.32, 1, 0, 0, 0.4270, 0, 1, 0 1, 0.48, 1, 0, 0, 0.5700, 0, 1, 0 -1, 0.66, 0, 0, 1, 0.7500, 0, 0, 1 1, 0.61, 1, 0, 0, 0.7000, 1, 0, 0 -1, 0.58, 0, 0, 1, 0.6890, 0, 1, 0 1, 0.19, 1, 0, 0, 0.2400, 0, 0, 1 1, 0.38, 0, 0, 1, 0.4300, 0, 1, 0 -1, 0.27, 1, 0, 0, 0.3640, 0, 1, 0 1, 0.42, 1, 0, 0, 0.4800, 0, 1, 0 1, 0.60, 1, 0, 0, 0.7130, 1, 0, 0 -1, 0.27, 0, 0, 1, 0.3480, 1, 0, 0 1, 0.29, 0, 1, 0, 0.3710, 1, 0, 0 -1, 0.43, 1, 0, 0, 0.5670, 0, 1, 0 1, 0.48, 1, 0, 0, 0.5670, 0, 1, 0 1, 0.27, 0, 0, 1, 0.2940, 0, 0, 1 -1, 0.44, 1, 0, 0, 0.5520, 1, 0, 0 1, 0.23, 0, 1, 0, 0.2630, 0, 0, 1 -1, 0.36, 0, 1, 0, 0.5300, 0, 0, 1 1, 0.64, 0, 0, 1, 0.7250, 1, 0, 0 1, 0.29, 0, 0, 1, 0.3000, 0, 0, 1 -1, 0.33, 1, 0, 0, 0.4930, 0, 1, 0 -1, 0.66, 0, 1, 0, 0.7500, 0, 0, 1 -1, 0.21, 0, 0, 1, 0.3430, 1, 0, 0 1, 0.27, 1, 0, 0, 0.3270, 0, 0, 1 1, 0.29, 1, 0, 0, 0.3180, 0, 0, 1 -1, 0.31, 1, 0, 0, 0.4860, 0, 1, 0 1, 0.36, 0, 0, 1, 0.4100, 0, 1, 0 1, 0.49, 0, 1, 0, 0.5570, 0, 1, 0 -1, 0.28, 1, 0, 0, 0.3840, 1, 0, 0 -1, 0.43, 0, 0, 1, 0.5660, 0, 1, 0 -1, 0.46, 0, 1, 0, 0.5880, 0, 1, 0 1, 0.57, 1, 0, 0, 0.6980, 1, 0, 0 -1, 0.52, 0, 0, 1, 0.5940, 0, 1, 0 -1, 0.31, 0, 0, 1, 0.4350, 0, 1, 0 -1, 0.55, 1, 0, 0, 0.6200, 0, 0, 1 1, 0.50, 1, 0, 0, 0.5640, 0, 1, 0 1, 0.48, 0, 1, 0, 0.5590, 0, 1, 0 -1, 0.22, 0, 0, 1, 0.3450, 1, 0, 0 1, 0.59, 0, 0, 1, 0.6670, 1, 0, 0 1, 0.34, 1, 0, 0, 0.4280, 0, 0, 1 -1, 0.64, 1, 0, 0, 0.7720, 0, 0, 1 1, 0.29, 0, 0, 1, 0.3350, 0, 0, 1 -1, 0.34, 0, 1, 0, 0.4320, 0, 1, 0 -1, 0.61, 1, 0, 0, 0.7500, 0, 0, 1 1, 0.64, 0, 0, 1, 0.7110, 1, 0, 0 -1, 0.29, 1, 0, 0, 0.4130, 1, 0, 0 1, 0.63, 0, 1, 0, 0.7060, 1, 0, 0 -1, 0.29, 0, 1, 0, 0.4000, 1, 0, 0 -1, 0.51, 1, 0, 0, 0.6270, 0, 1, 0 -1, 0.24, 0, 0, 1, 0.3770, 1, 0, 0 1, 0.48, 0, 1, 0, 0.5750, 0, 1, 0 1, 0.18, 1, 0, 0, 0.2740, 1, 0, 0 1, 0.18, 1, 0, 0, 0.2030, 0, 0, 1 1, 0.33, 0, 1, 0, 0.3820, 0, 0, 1 -1, 0.20, 0, 0, 1, 0.3480, 1, 0, 0 1, 0.29, 0, 0, 1, 0.3300, 0, 0, 1 -1, 0.44, 0, 0, 1, 0.6300, 1, 0, 0 -1, 0.65, 0, 0, 1, 0.8180, 1, 0, 0 -1, 0.56, 1, 0, 0, 0.6370, 0, 0, 1 -1, 0.52, 0, 0, 1, 0.5840, 0, 1, 0 -1, 0.29, 0, 1, 0, 0.4860, 1, 0, 0 -1, 0.47, 0, 1, 0, 0.5890, 0, 1, 0 1, 0.68, 1, 0, 0, 0.7260, 0, 0, 1 1, 0.31, 0, 0, 1, 0.3600, 0, 1, 0 1, 0.61, 0, 1, 0, 0.6250, 0, 0, 1 1, 0.19, 0, 1, 0, 0.2150, 0, 0, 1 1, 0.38, 0, 0, 1, 0.4300, 0, 1, 0 -1, 0.26, 1, 0, 0, 0.4230, 1, 0, 0 1, 0.61, 0, 1, 0, 0.6740, 1, 0, 0 1, 0.40, 1, 0, 0, 0.4650, 0, 1, 0 -1, 0.49, 1, 0, 0, 0.6520, 0, 1, 0 1, 0.56, 1, 0, 0, 0.6750, 1, 0, 0 -1, 0.48, 0, 1, 0, 0.6600, 0, 1, 0 1, 0.52, 1, 0, 0, 0.5630, 0, 0, 1 -1, 0.18, 1, 0, 0, 0.2980, 1, 0, 0 -1, 0.56, 0, 0, 1, 0.5930, 0, 0, 1 -1, 0.52, 0, 1, 0, 0.6440, 0, 1, 0 -1, 0.18, 0, 1, 0, 0.2860, 0, 1, 0 -1, 0.58, 1, 0, 0, 0.6620, 0, 0, 1 -1, 0.39, 0, 1, 0, 0.5510, 0, 1, 0 -1, 0.46, 1, 0, 0, 0.6290, 0, 1, 0 -1, 0.40, 0, 1, 0, 0.4620, 0, 1, 0 -1, 0.60, 1, 0, 0, 0.7270, 0, 0, 1 1, 0.36, 0, 1, 0, 0.4070, 0, 0, 1 1, 0.44, 1, 0, 0, 0.5230, 0, 1, 0 1, 0.28, 1, 0, 0, 0.3130, 0, 0, 1 1, 0.54, 0, 0, 1, 0.6260, 1, 0, 0
Test data:
# people_test.txt # -1, 0.51, 1, 0, 0, 0.6120, 0, 1, 0 -1, 0.32, 0, 1, 0, 0.4610, 0, 1, 0 1, 0.55, 1, 0, 0, 0.6270, 1, 0, 0 1, 0.25, 0, 0, 0, 0.2620, 0, 0, 1 1, 0.33, 0, 0, 0, 0.3730, 0, 0, 1 -1, 0.29, 0, 1, 0, 0.4620, 1, 0, 0 1, 0.65, 1, 0, 0, 0.7270, 1, 0, 0 -1, 0.43, 0, 1, 0, 0.5140, 0, 1, 0 -1, 0.54, 0, 1, 0, 0.6480, 0, 0, 1 1, 0.61, 0, 1, 0, 0.7270, 1, 0, 0 1, 0.52, 0, 1, 0, 0.6360, 1, 0, 0 1, 0.30, 0, 1, 0, 0.3350, 0, 0, 1 1, 0.29, 1, 0, 0, 0.3140, 0, 0, 1 -1, 0.47, 0, 0, 0, 0.5940, 0, 1, 0 1, 0.39, 0, 1, 0, 0.4780, 0, 1, 0 1, 0.47, 0, 0, 0, 0.5200, 0, 1, 0 -1, 0.49, 1, 0, 0, 0.5860, 0, 1, 0 -1, 0.63, 0, 0, 0, 0.6740, 0, 0, 1 -1, 0.30, 1, 0, 0, 0.3920, 1, 0, 0 -1, 0.61, 0, 0, 0, 0.6960, 0, 0, 1 -1, 0.47, 0, 0, 0, 0.5870, 0, 1, 0 1, 0.30, 0, 0, 0, 0.3450, 0, 0, 1 -1, 0.51, 0, 0, 0, 0.5800, 0, 1, 0 -1, 0.24, 1, 0, 0, 0.3880, 0, 1, 0 -1, 0.49, 1, 0, 0, 0.6450, 0, 1, 0 1, 0.66, 0, 0, 0, 0.7450, 1, 0, 0 -1, 0.65, 1, 0, 0, 0.7690, 1, 0, 0 -1, 0.46, 0, 1, 0, 0.5800, 1, 0, 0 -1, 0.45, 0, 0, 0, 0.5180, 0, 1, 0 -1, 0.47, 1, 0, 0, 0.6360, 1, 0, 0 -1, 0.29, 1, 0, 0, 0.4480, 1, 0, 0 -1, 0.57, 0, 0, 0, 0.6930, 0, 0, 1 -1, 0.20, 1, 0, 0, 0.2870, 0, 0, 1 -1, 0.35, 1, 0, 0, 0.4340, 0, 1, 0 -1, 0.61, 0, 0, 0, 0.6700, 0, 0, 1 -1, 0.31, 0, 0, 0, 0.3730, 0, 1, 0 1, 0.18, 1, 0, 0, 0.2080, 0, 0, 1 1, 0.26, 0, 0, 0, 0.2920, 0, 0, 1 -1, 0.28, 1, 0, 0, 0.3640, 0, 0, 1 -1, 0.59, 0, 0, 0, 0.6940, 0, 0, 1
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