Important: This notebook will only work with fastai-0.7.x. Do not try to run any fastai-1.x code from this path in the repository because it will load fastai-0.7.x
Random Forest from scratch!¶
In [ ]:
%load_ext autoreload
%autoreload 2
In [ ]:
%matplotlib inline
from fastai.imports import *
from fastai.structured import *
from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier
from IPython.display import display
from sklearn import metrics
Load in our data from last lesson¶
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PATH = "data/bulldozers/"
df_raw = pd.read_feather('tmp/bulldozers-raw')
df_trn, y_trn, nas = proc_df(df_raw, 'SalePrice')
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def split_vals(a,n): return a[:n], a[n:]
n_valid = 12000
n_trn = len(df_trn)-n_valid
X_train, X_valid = split_vals(df_trn, n_trn)
y_train, y_valid = split_vals(y_trn, n_trn)
raw_train, raw_valid = split_vals(df_raw, n_trn)
In [ ]:
x_sub = X_train[['YearMade', 'MachineHoursCurrentMeter']]
Basic data structures¶
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class TreeEnsemble():
def __init__(self, x, y, n_trees, sample_sz, min_leaf=5):
np.random.seed(42)
self.x,self.y,self.sample_sz,self.min_leaf = x,y,sample_sz,min_leaf
self.trees = [self.create_tree() for i in range(n_trees)]
def create_tree(self):
rnd_idxs = np.random.permutation(len(self.y))[:self.sample_sz]
return DecisionTree(self.x.iloc[rnd_idxs], self.y[rnd_idxs], min_leaf=self.min_leaf)
def predict(self, x):
return np.mean([t.predict(x) for t in self.trees], axis=0)
In [ ]:
class DecisionTree():
def __init__(self, x, y, idxs=None, min_leaf=5):
self.x,self.y,self.idxs,self.min_leaf = x,y,idxs,min_leaf
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m = TreeEnsemble(X_train, y_train, n_trees=10, sample_sz=1000, min_leaf=3)
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m.trees[0]
Out[ ]:
<__main__.DecisionTree at 0x7f645ec22358>
In [ ]:
class DecisionTree():
def __init__(self, x, y, idxs=None, min_leaf=5):
if idxs is None: idxs=np.arange(len(y))
self.x,self.y,self.idxs,self.min_leaf = x,y,idxs,min_leaf
self.n,self.c = len(idxs), x.shape[1]
self.val = np.mean(y[idxs])
self.score = float('inf')
self.find_varsplit()
# This just does one decision; we'll make it recursive later
def find_varsplit(self):
for i in range(self.c): self.find_better_split(i)
# We'll write this later!
def find_better_split(self, var_idx): pass
@property
def split_name(self): return self.x.columns[self.var_idx]
@property
def split_col(self): return self.x.values[self.idxs,self.var_idx]
@property
def is_leaf(self): return self.score == float('inf')
def __repr__(self):
s = f'n: {self.n}; val:{self.val}'
if not self.is_leaf:
s += f'; score:{self.score}; split:{self.split}; var:{self.split_name}'
return s
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m = TreeEnsemble(X_train, y_train, n_trees=10, sample_sz=1000, min_leaf=3)
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m.trees[0]
Out[ ]:
n: 1000; val:10.079014121552744
In [ ]:
m.trees[0].idxs
Out[ ]:
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,
100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119,
120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,
140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159,
160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179,
180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199,
200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219,
220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239,
240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259,
260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279,
280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299,
300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319,
320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339,
340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359,
360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379,
380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399,
400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419,
420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439,
440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459,
460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479,
480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499,
500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519,
520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539,
540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559,
560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579,
580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599,
600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619,
620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639,
640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659,
660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679,
680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699,
700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719,
720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739,
740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759,
760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779,
780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799,
800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819,
820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839,
840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859,
860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879,
880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899,
900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919,
920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939,
940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959,
960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979,
980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999])
Single branch¶
Find best split given variable¶
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ens = TreeEnsemble(x_sub, y_train, 1, 1000)
tree = ens.trees[0]
x_samp,y_samp = tree.x, tree.y
x_samp.columns
Out[ ]:
Index(['YearMade', 'MachineHoursCurrentMeter'], dtype='object')
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tree
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n: 1000; val:10.079014121552744
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m = RandomForestRegressor(n_estimators=1, max_depth=1, bootstrap=False)
m.fit(x_samp, y_samp)
draw_tree(m.estimators_[0], x_samp, precision=2)
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def find_better_split(self, var_idx):
x,y = self.x.values[self.idxs,var_idx], self.y[self.idxs]
for i in range(self.n):
lhs = x<=x[i]
rhs = x>x[i]
if rhs.sum()<self.min_leaf or lhs.sum()<self.min_leaf: continue
lhs_std = y[lhs].std()
rhs_std = y[rhs].std()
curr_score = lhs_std*lhs.sum() + rhs_std*rhs.sum()
if curr_score<self.score:
self.var_idx,self.score,self.split = var_idx,curr_score,x[i]
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%timeit find_better_split(tree,1)
tree
86.9 ms ± 2 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
Out[ ]:
n: 1000; val:10.079014121552744; score:681.0184057251435; split:3744.0; var:MachineHoursCurrentMeter
In [ ]:
find_better_split(tree,0); tree
Out[ ]:
n: 1000; val:10.079014121552744; score:658.5510186055949; split:1974.0; var:YearMade
Speeding things up¶
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tree = TreeEnsemble(x_sub, y_train, 1, 1000).trees[0]
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def std_agg(cnt, s1, s2): return math.sqrt((s2/cnt) - (s1/cnt)**2)
def find_better_split(self, var_idx):
x,y = self.x.values[self.idxs,var_idx], self.y[self.idxs]
sort_idx = np.argsort(x)
sort_y,sort_x = y[sort_idx], x[sort_idx]
rhs_cnt,rhs_sum,rhs_sum2 = self.n, sort_y.sum(), (sort_y**2).sum()
lhs_cnt,lhs_sum,lhs_sum2 = 0,0.,0.
for i in range(0,self.n-self.min_leaf):
xi,yi = sort_x[i],sort_y[i]
lhs_cnt += 1; rhs_cnt -= 1
lhs_sum += yi; rhs_sum -= yi
lhs_sum2 += yi**2; rhs_sum2 -= yi**2
if i<self.min_leaf-1 or xi==sort_x[i+1]:
continue
lhs_std = std_agg(lhs_cnt, lhs_sum, lhs_sum2)
rhs_std = std_agg(rhs_cnt, rhs_sum, rhs_sum2)
curr_score = lhs_std*lhs_cnt + rhs_std*rhs_cnt
if curr_score<self.score:
self.var_idx,self.score,self.split = var_idx,curr_score,xi
In [ ]:
%timeit find_better_split(tree,1)
tree
1.73 ms ± 3.58 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
Out[ ]:
n: 1000; val:10.079014121552744; score:681.0184057251353; split:3744.0; var:MachineHoursCurrentMeter
In [ ]:
find_better_split(tree,0); tree
Out[ ]:
n: 1000; val:10.079014121552744; score:658.5510186055565; split:1974.0; var:YearMade
In [ ]:
DecisionTree.find_better_split = find_better_split
In [ ]:
tree = TreeEnsemble(x_sub, y_train, 1, 1000).trees[0]; tree
Out[ ]:
n: 1000; val:10.079014121552744; score:658.5510186055565; split:1974.0; var:YearMade
Full single tree¶
In [ ]:
m = RandomForestRegressor(n_estimators=1, max_depth=2, bootstrap=False)
m.fit(x_samp, y_samp)
draw_tree(m.estimators_[0], x_samp, precision=2)
In [ ]:
def find_varsplit(self):
for i in range(self.c): self.find_better_split(i)
if self.is_leaf: return
x = self.split_col
lhs = np.nonzero(x<=self.split)[0]
rhs = np.nonzero(x>self.split)[0]
self.lhs = DecisionTree(self.x, self.y, self.idxs[lhs])
self.rhs = DecisionTree(self.x, self.y, self.idxs[rhs])
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DecisionTree.find_varsplit = find_varsplit
In [ ]:
tree = TreeEnsemble(x_sub, y_train, 1, 1000).trees[0]; tree
Out[ ]:
n: 1000; val:10.079014121552744; score:658.5510186055565; split:1974.0; var:YearMade
In [ ]:
tree.lhs
Out[ ]:
n: 159; val:9.660892662981706; score:76.82696888346362; split:2800.0; var:MachineHoursCurrentMeter
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tree.rhs
Out[ ]:
n: 841; val:10.158064432982941; score:571.4803525045031; split:2005.0; var:YearMade
In [ ]:
tree.lhs.lhs
Out[ ]:
n: 150; val:9.619280538108496; score:71.15906938383463; split:1000.0; var:YearMade
In [ ]:
tree.lhs.rhs
Out[ ]:
n: 9; val:10.354428077535193
Predictions¶
In [ ]:
cols = ['MachineID', 'YearMade', 'MachineHoursCurrentMeter', 'ProductSize', 'Enclosure',
'Coupler_System', 'saleYear']
In [ ]:
%time tree = TreeEnsemble(X_train[cols], y_train, 1, 1000).trees[0]
x_samp,y_samp = tree.x, tree.y
CPU times: user 325 ms, sys: 3.98 ms, total: 329 ms Wall time: 328 ms
In [ ]:
m = RandomForestRegressor(n_estimators=1, max_depth=3, bootstrap=False)
m.fit(x_samp, y_samp)
draw_tree(m.estimators_[0], x_samp, precision=2, ratio=0.9, size=7)
In [ ]:
def predict(self, x): return np.array([self.predict_row(xi) for xi in x])
DecisionTree.predict = predict
In [ ]:
if something:
x= do1()
else:
x= do2()
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x = do1() if something else do2()
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x = something ? do1() : do2()
In [ ]:
In [ ]:
def predict_row(self, xi):
if self.is_leaf: return self.val
t = self.lhs if xi[self.var_idx]<=self.split else self.rhs
return t.predict_row(xi)
DecisionTree.predict_row = predict_row
In [ ]:
%time preds = tree.predict(X_valid[cols].values)
CPU times: user 94.4 ms, sys: 0 ns, total: 94.4 ms Wall time: 93.4 ms
In [ ]:
plt.scatter(preds, y_valid, alpha=0.05)
Out[ ]:
<matplotlib.collections.PathCollection at 0x7ffb14937780>
In [ ]:
metrics.r2_score(preds, y_valid)
Out[ ]:
0.4840854669925271
In [ ]:
m = RandomForestRegressor(n_estimators=1, min_samples_leaf=5, bootstrap=False)
%time m.fit(x_samp, y_samp)
preds = m.predict(X_valid[cols].values)
plt.scatter(preds, y_valid, alpha=0.05)
CPU times: user 8 ms, sys: 0 ns, total: 8 ms Wall time: 8.48 ms
Out[ ]:
<matplotlib.collections.PathCollection at 0x7f645dee8860>
In [ ]:
metrics.r2_score(preds, y_valid)
Out[ ]:
0.47541053100694797
Putting it together¶
In [ ]:
class TreeEnsemble():
def __init__(self, x, y, n_trees, sample_sz, min_leaf=5):
np.random.seed(42)
self.x,self.y,self.sample_sz,self.min_leaf = x,y,sample_sz,min_leaf
self.trees = [self.create_tree() for i in range(n_trees)]
def create_tree(self):
idxs = np.random.permutation(len(self.y))[:self.sample_sz]
return DecisionTree(self.x.iloc[idxs], self.y[idxs],
idxs=np.array(range(self.sample_sz)), min_leaf=self.min_leaf)
def predict(self, x):
return np.mean([t.predict(x) for t in self.trees], axis=0)
def std_agg(cnt, s1, s2): return math.sqrt((s2/cnt) - (s1/cnt)**2)
In [ ]:
class DecisionTree():
def __init__(self, x, y, idxs, min_leaf=5):
self.x,self.y,self.idxs,self.min_leaf = x,y,idxs,min_leaf
self.n,self.c = len(idxs), x.shape[1]
self.val = np.mean(y[idxs])
self.score = float('inf')
self.find_varsplit()
def find_varsplit(self):
for i in range(self.c): self.find_better_split(i)
if self.score == float('inf'): return
x = self.split_col
lhs = np.nonzero(x<=self.split)[0]
rhs = np.nonzero(x>self.split)[0]
self.lhs = DecisionTree(self.x, self.y, self.idxs[lhs])
self.rhs = DecisionTree(self.x, self.y, self.idxs[rhs])
def find_better_split(self, var_idx):
x,y = self.x.values[self.idxs,var_idx], self.y[self.idxs]
sort_idx = np.argsort(x)
sort_y,sort_x = y[sort_idx], x[sort_idx]
rhs_cnt,rhs_sum,rhs_sum2 = self.n, sort_y.sum(), (sort_y**2).sum()
lhs_cnt,lhs_sum,lhs_sum2 = 0,0.,0.
for i in range(0,self.n-self.min_leaf):
xi,yi = sort_x[i],sort_y[i]
lhs_cnt += 1; rhs_cnt -= 1
lhs_sum += yi; rhs_sum -= yi
lhs_sum2 += yi**2; rhs_sum2 -= yi**2
if i<self.min_leaf-1 or xi==sort_x[i+1]:
continue
lhs_std = std_agg(lhs_cnt, lhs_sum, lhs_sum2)
rhs_std = std_agg(rhs_cnt, rhs_sum, rhs_sum2)
curr_score = lhs_std*lhs_cnt + rhs_std*rhs_cnt
if curr_score<self.score:
self.var_idx,self.score,self.split = var_idx,curr_score,xi
@property
def split_name(self): return self.x.columns[self.var_idx]
@property
def split_col(self): return self.x.values[self.idxs,self.var_idx]
@property
def is_leaf(self): return self.score == float('inf')
def __repr__(self):
s = f'n: {self.n}; val:{self.val}'
if not self.is_leaf:
s += f'; score:{self.score}; split:{self.split}; var:{self.split_name}'
return s
def predict(self, x):
return np.array([self.predict_row(xi) for xi in x])
def predict_row(self, xi):
if self.is_leaf: return self.val
t = self.lhs if xi[self.var_idx]<=self.split else self.rhs
return t.predict_row(xi)
In [ ]:
ens = TreeEnsemble(X_train[cols], y_train, 5, 1000)
In [ ]:
preds = ens.predict(X_valid[cols].values)
In [ ]:
plt.scatter(y_valid, preds, alpha=0.1, s=6);
In [ ]:
metrics.r2_score(y_valid, preds)
Out[ ]:
0.7025757322910476
In [ ]:
%load_ext Cython
In [ ]:
def fib1(n):
a, b = 0, 1
while b < n:
a, b = b, a + b
In [ ]:
%%cython
def fib2(n):
a, b = 0, 1
while b < n:
a, b = b, a + b
In [ ]:
%%cython
def fib3(int n):
cdef int b = 1
cdef int a = 0
cdef int t = 0
while b < n:
t = a
a = b
b = t + b
In [ ]:
%timeit fib1(50)
698 ns ± 10.2 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
In [ ]:
%timeit fib2(50)
291 ns ± 13.8 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
In [ ]:
%timeit fib3(50)
49 ns ± 1.1 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
In [ ]:
In [ ]: