What is machine learning?

import numpy as np

area  = np.array([35, 45, 55, 65, 80, 95, 110, 130.0])      # square metres
price = np.array([40, 44, 56, 58, 76, 84, 101, 110.0])      # ₹ lakh

# SUPERVISED: every row comes with the answer we want to predict (the label)
w, b = np.polyfit(area, price, 1)
print(f"supervised: learned 'price = {w:.2f} x area + {b:.1f}' from labelled sales")
print("            prediction for an unsold 75 sq m flat:", round(float(w * 75 + b), 1), "lakh")

# UNSUPERVISED: same flats, answers hidden. Can the computer still find structure?
rng = np.random.default_rng(0)
x = (area - area.mean()) / area.std()
centres = np.array([x.min(), x.max()])                       # start two groups at the extremes
for _ in range(10):
    group = np.argmin(abs(x[:, None] - centres[None, :]), axis=1)
    centres = np.array([x[group == k].mean() for k in (0, 1)])
print("unsupervised: found two groups of flats by size alone:")
for k in (0, 1):
    print(f"            group {k}: areas {area[group == k].astype(int).tolist()}")
print("no price was used, so there is nothing to 'check' the groups against")

supervised: learned 'price = 0.78 x area + 11.2' from labelled sales
            prediction for an unsold 75 sq m flat: 69.7 lakh
unsupervised: found two groups of flats by size alone:
            group 0: areas [35, 45, 55, 65, 80]
            group 1: areas [95, 110, 130]
no price was used, so there is nothing to 'check' the groups against

import numpy as np

area  = np.array([35, 45, 55, 65, 80, 95, 110, 130.0])
price = np.array([40, 44, 56, 58, 76, 84, 101, 110.0])
a = area - area.mean()
w, level, rate_w, rate_l = 0.0, price.mean(), 0.00012, 0.06          # start from "always quote the average"

def avg_miss(w, level):
    return float(np.mean(np.abs(w * a + level - price)))

print(f"step   0: slope {w:.3f}  average miss {avg_miss(w, level):5.2f} lakh")
for step in range(1, 121):
    miss = w * a + level - price                  # 1. how wrong is the line right now?
    w     -= rate_w * np.mean(2 * miss * a)       # 2. nudge the slope so the squared miss falls
    level -= rate_l * np.mean(2 * miss)           # 3. nudge the height the same way
    if step in (1, 5, 10, 20, 40, 120):               # 4. repeat
        print(f"step {step:3d}: slope {w:.3f}  average miss {avg_miss(w, level):5.2f} lakh")

step   0: slope 0.000  average miss 21.62 lakh
step   1: slope 0.179  average miss 16.82 lakh
step   5: slope 0.567  average miss  6.37 lakh
step  10: slope 0.722  average miss  2.45 lakh
step  20: slope 0.775  average miss  2.45 lakh
step  40: slope 0.779  average miss  2.48 lakh
step 120: slope 0.779  average miss  2.48 lakh

import numpy as np

area  = np.array([35, 45, 55, 65, 80, 95, 110, 130.0])
price = np.array([40, 44, 56, 58, 76, 84, 101, 110.0])
train, test = [0, 2, 3, 5, 6, 7], [1, 4]                  # hold two flats back; the model never sees them while learning
z = (area - 80) / 30
print("degree | training miss | miss on held-back flats")
for degree in [1, 2, 3, 5]:
    coef = np.polyfit(z[train], price[train], degree)
    miss = lambda idx: float(np.mean(np.abs(np.polyval(coef, z[idx]) - price[idx])))
    print(f"{degree:6d} | {miss(train):13.2f} | {miss(test):.2f}")
coef = np.polyfit(z[train], price[train], 5)
print("degree 5 prediction for a 100 sq m flat:", round(float(np.polyval(coef, (100 - 80) / 30)), 1), "lakh  (sales near 100 sq m were about 84 to 101)")

degree | training miss | miss on held-back flats
     1 |          2.34 | 2.58
     2 |          2.29 | 2.75
     3 |          2.03 | 2.46
     5 |          0.00 | 8.83
degree 5 prediction for a 100 sq m flat: 90.1 lakh  (sales near 100 sq m were about 84 to 101)

import numpy as np

area  = np.array([35, 45, 55, 65, 80, 95, 110, 130.0])
price = np.array([40, 44, 56, 58, 76, 84, 101, 110.0])
age   = np.array([12, 3, 20, 8, 15, 2, 6, 25.0])           # a second column: years since construction
print("rows:", len(area), "| columns: area, age, price")
for name, col in [("area", area), ("age", age), ("price", price)]:
    q1, med, q3 = np.percentile(col, [25, 50, 75])
    print(f"{name:5s} min {col.min():6.1f}  median {med:6.1f}  max {col.max():6.1f}  mean {col.mean():6.1f}  std {col.std():5.1f}")
print("correlation with price: area", round(float(np.corrcoef(area, price)[0, 1]), 3), "| age", round(float(np.corrcoef(age, price)[0, 1]), 3))
z = (price - price.mean()) / price.std()
print("any price more than 2 std from the mean?", bool((abs(z) > 2).any()))
counts, edges = np.histogram(area, bins=4)
for c, lo, hi in zip(counts, edges[:-1], edges[1:]):
    print(f"area {lo:5.0f}-{hi:5.0f} | {'#' * int(c)}")

rows: 8 | columns: area, age, price
area  min   35.0  median   72.5  max  130.0  mean   76.9  std  30.9
age   min    2.0  median   10.0  max   25.0  mean   11.4  std   7.7
price min   40.0  median   67.0  max  110.0  mean   71.1  std  24.2
correlation with price: area 0.994 | age 0.26
any price more than 2 std from the mean? False
area    35-   59 | ###
area    59-   82 | ##
area    82-  106 | #
area   106-  130 | ##