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前回の記事(ロジスティック回帰分析)の補足コード

1.要約

 前回の記事で,収束判定を"尤度の値が変わらなくなるまで"と"係数の値が変わらなくなるまで"の2パターン紹介しました.今回の記事は,後者の収束基準に基づくプログラムを載せています.詳しい数理は前回の記事をご覧ください.

2.サンプルコード

def calc_p(beta,MatX):
    a,b = MatX.shape
    pxb = np.zeros((a,1))
    for i in range(a):
        pxb[i,0] = np.exp(beta.T.dot(MatX[i,:]))/(1+np.exp(beta.T.dot(MatX[i,:])))
        #pxb[i,0] = np.exp(beta.T.dot(MatX[i,:].reshape(b,1)))/(1+np.exp(beta.T.dot(MatX[i,:].reshape(b,1))))
    return pxb

def losgistic_estimation2(y,data,tol=10**(-4),nstart=30,maxiter=50):
    X = data.astype("float64");n,p = X.shape
    X1 = np.hstack([np.ones(n).reshape(n,1),X]).reshape(n,p+1)
    y = y.astype("float64").reshape(n,1)
    beta_hat = np.zeros(((p+1),1))
    delta_hat = np.Inf
    for _ in range(nstart):
        print("---epoc:%d ---" % (_+1))
        #initial beta
        beta = np.random.randn(p+1).reshape((p+1),1)
        delta = np.Inf
        while True:
            print("  delta: %f" % delta)
            #Newton-Raphson step
            prob = calc_p(beta,X1)
            #print(prob) #for check
            W = np.zeros((n,n))
            for i in range(n):
                W[i,i] = prob[i,0]*(1-prob[i,0])
            #print(W) # for check
            pd2 = -X1.T.dot(W).dot(X1)
            pd1 = X1.T.dot(y-prob)
            new_beta = beta - np.linalg.inv(pd2).dot(pd1)
            print("new_beta: ",new_beta)
            delta = sum((beta - new_beta)**2)
            if delta >= 0 and delta <= tol:
                print("parameters are converged")
                break
            elif np.isnan(delta)==True:
                break
            else:
                beta = new_beta
                continue
        if np.isnan(delta)==True:
            print("ERROR:delta is nan \nStop and go next epoc")
            continue
        if delta < delta_hat:
            beta_hat = new_beta
    return beta_hat

# データ行列の生成
N = 1000;p = 2
np.random.seed(10)
X = np.random.randn(N*p).reshape(N,p)
X1 = np.hstack([np.ones(N).reshape(N,1),X])
#正解ラベルの生成
y = np.zeros((N,1))
np.random.seed(100)
beta = np.random.randn(p+1).reshape(p+1,1)
prob = np.exp(X1.dot(beta))/(1+np.exp(X1.dot(beta)))
prob
for i in range(N):
    np.random.seed(i+8)
    if np.random.rand(1) < prob[i]:
        y[i] = 1
    else:
        y[i] = 0
y

losgistic_estimation2(y,X)
beta

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