def calc_Hess(B):
weights = [ lc.calc_weight(x,B) for x in X ]
oneMinusW = [ 1 - w for w in weights ]
d_elem = [None] * N
for j in range(len(weights)):
d_elem[j] = np.asscalar(m[j]) * weights[j] * oneMinusW[j]
D = np.diagflat(np.array(d_elem))
hess = X.T * D * X
return hess
def gen_D_mat(X, y, m, B):
(N, P) = np.shape(X)
weights = [lc.calc_weight(x, B) for x in X]
oneMinusW = [1 - w for w in weights]
d_elem = [None] * N
for j in range(len(weights)):
d_elem[j] = np.asscalar(m[j]) * weights[j] * oneMinusW[j]
D = np.matrix(np.diagflat(np.array(d_elem)))
return D
def calc_llh_point_contribution(B, x, y, m):
"""
Calculates the contribution to the total likelihood of the selected sample point
B: (cvector) -- Current guess for beta
x: (cvector) -- Predictors of a single sample point
y: (scalar) -- Response of sample point
m: (scalar) -- Number of trials on this sample point, m_i
"""
# -L_i(B) = y_i \log(w_i) + (m_i - y_i) \log(1 - w_i)
w = lc.calc_weight(x.T, B)
return -np.asscalar(y * math.log(w) + (m - y) * math.log(1 - w))