AI002. 归一化与线性预测

# Min-Max 用训练集的列 min/max(常量列归 0),查询同参数换算不截断;
# 批量 GD:MSE 梯度带 2/n 系数,一轮内基于旧参数算完全部梯度再同步更新。
import sys


def solve() -> None:
    data = sys.stdin.buffer.read().split()
    if not data:
        return
    it = iter(data)
    n, d, m, epochs = (int(next(it)) for _ in range(4))
    eta = float(next(it))
    x, y = [], []
    for _ in range(n):
        x.append([float(next(it)) for _ in range(d)])
        y.append(float(next(it)))
    query = [[float(next(it)) for _ in range(d)] for _ in range(m)]

    lo = [min(row[j] for row in x) for j in range(d)]
    hi = [max(row[j] for row in x) for j in range(d)]

    def norm(row):
        return [0.0 if hi[j] == lo[j] else (row[j] - lo[j]) / (hi[j] - lo[j]) for j in range(d)]

    train = [norm(row) for row in x]
    weights = [0.0] * d
    bias = 0.0
    for _ in range(epochs):
        grad_w = [0.0] * d
        grad_b = 0.0
        for row, target in zip(train, y):
            error = bias + sum(weights[j] * row[j] for j in range(d)) - target
            grad_b += error
            for j in range(d):
                grad_w[j] += error * row[j]
        scale = 2.0 / n
        bias -= eta * scale * grad_b
        for j in range(d):
            weights[j] -= eta * scale * grad_w[j]

    out = []
    for row in query:
        row = norm(row)
        value = bias + sum(weights[j] * row[j] for j in range(d))
        if abs(value) < 0.00005:
            value = 0.0
        out.append(f"{value:.4f}")
    print("\n".join(out))


if __name__ == "__main__":
    solve()