LASSO迴歸，概念與實現(轉)

概念部分參考知乎一大哥的文章：

https://zhuanlan.zhihu.com/p/30535220

代碼實現(哈哈，我懶得敲，也給拿過來了)：

def lasso_regression(X, y, lambd=0.2, threshold=0.1):
    ''' 通過座標下降(coordinate descent)法獲取LASSO迴歸係數
    '''
    # 計算殘差平方和
    rss = lambda X, y, w: (y - X*w).T*(y - X*w)
    # 初始化迴歸係數w.
    m, n = X.shape
    w = np.matrix(np.zeros((n, 1)))
    r = rss(X, y, w)
    # 使用座標下降法優化迴歸係數w
    niter = itertools.count(1)
    for it in niter:
        for k in range(n):
            # 計算常量值z_k和p_k
            z_k = (X[:, k].T*X[:, k])[0, 0]
            p_k = 0
            for i in range(m):
                p_k += X[i, k]*(y[i, 0] - sum([X[i, j]*w[j, 0] for j in range(n) if j != k]))
            if p_k < -lambd/2:
                w_k = (p_k + lambd/2)/z_k
            elif p_k > lambd/2:
                w_k = (p_k - lambd/2)/z_k
            else:
                w_k = 0
            w[k, 0] = w_k
        r_prime = rss(X, y, w)
        delta = abs(r_prime - r)[0, 0]
        r = r_prime
        print('Iteration: {}, delta = {}'.format(it, delta))
        if delta < threshold:
            break
    return w

if '__main__' == __name__:
    X, y = load_data('abalone.txt')
    X, y = standarize(X), standarize(y)
    w = lasso_regression(X, y, lambd=10)
    y_prime = X*w
    # 計算相關係數
    corrcoef = get_corrcoef(np.array(y.reshape(1, -1)),
                            np.array(y_prime.reshape(1, -1)))
    print('Correlation coefficient: {}'.format(corrcoef))

# LASSO迴歸係數軌跡
# 類似嶺軌跡，我們也可以改變λλ的值得到不同的迴歸係數，通過作圖可以看到迴歸係數的軌跡

ntest = 30
# 繪製軌跡
ws = lasso_traj(X, y, ntest)
fig = plt.figure()
ax = fig.add_subplot(111)
lambdas = [i-10 for i in range(ntest)]
ax.plot(lambdas, ws)
plt.show()

# Lasso中不斷有係數變爲0