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rchq_measure_reduction.py
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rchq_measure_reduction.py
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import numpy as np
from sklearn.metrics.pairwise import euclidean_distances
import matplotlib.pyplot as plt
import functools
import time
import grlp
import emp_nys as enys
# global
lam = 1
num = 0
data = 0
data_test = 0
data_t_out = 0
k_exp_ = 0
k_exp_exp_ = 0
def gen_params(n):
return np.random.randint(num, size=n)
def preprocess(data_name):
# read data
global data, data_test, data_t_out
if data_name == '3Dnet':
data_read = np.loadtxt('data/3D_spatial_network.txt',
delimiter=',', usecols=(1, 2, 3))
else:
data_read = np.loadtxt(
'data/Combined Cycle Power Plant Data Set.txt', delimiter=',')
np.random.shuffle(data_read)
global num
num, dim = data_read.shape
if data_name == '3Dnet':
num = num // 10
data = data_read[:num, :]
for i in range(dim):
data[:, i] = (data[:, i] - np.mean(data[:, i])) / np.std(data[:, i])
data_test = data[:, dim-1:dim].reshape((num,))
data_t_out = data_test * (data[:, 0:1] >= 0).reshape((num,))
data_t_out = data_t_out * (data[:, 1:2] >= 0).reshape((num,))
global lam
lam = median_heuristics()
k_exp_comp()
k_exp_exp_comp()
def k(x, y=0, diag=False, data_k=None, lam_k=None, kernel=None):
# x, y: array of indices
if lam_k is None:
lam_k = lam
if data_k is None:
data_k = data
if np.isscalar(x):
x = np.array([x])
if diag:
return np.ones(len(x))
if np.isscalar(y):
y = np.array([y])
K = euclidean_distances(data_k[x, :], data_k[y, :], squared=True)
if kernel is None:
kernel = 'Gaussian'
if kernel == 'Gaussian':
return np.exp(- K / (2 * lam)) # Gaussian
else:
return 1 / (1 + K / (2 * lam)) # rational quadratic
def experiments(
data_name='3Dnet',
kernel='Gaussian',
times=50,
np_seed=None
):
np.random.seed(np_seed)
preprocess(data_name)
enys.k = functools.partial(k, data_k=data, lam_k=lam, kernel=kernel)
text_data = open("results_rchq/{}_{}_t{}.txt".format(
data_name, kernel, times), 'w', encoding='utf-8')
print("np_seed = {}".format(np_seed), file=text_data)
fig = plt.figure()
x_ex = [5, 10, 20, 40, 60, 80, 120, 160]
m_names = ['N. + emp + opt', 'Nyström', 'Nyström + opt',
'FNE', 'FNE + opt', 'iid Bayes']
methods = len(m_names)
results = [[] for i in range(methods)]
results_up = [[] for i in range(methods)]
results_low = [[] for i in range(methods)]
m_marks = ['x', 'o', '^', 'v', '+', '>', '<', 'd', 's']
for n in x_ex:
print("{} points. ".format(n), file=text_data)
for i in range(methods):
start_time = time.perf_counter()
res = np.zeros(times)
fails = 0
for j in range(times):
N = n*n
if 'Mercer' in m_names[i] or 'Nyström' in m_names[i]:
N = 20*n
points, weights, tmp_fails = func(
m_names[i], n, rec=N, nys=10*n)
res[j] = eval(points, weights)
fails += tmp_fails
end_time = time.perf_counter()
elapsed = (end_time - start_time)/times
res_sq = np.std(res)
res_mn = np.mean(res)
res = np.log10(res)
log_res = np.mean(res)
log_std = np.std(res)
results[i].append(np.mean(res))
results_up[i].append(log_res + log_std)
results_low[i].append(log_res - log_std)
print(" {}: {:.2e} (±{:.2e}), {:.2e}s, {} fails".format(
m_names[i], res_mn, res_sq, elapsed, fails), file=text_data)
x = np.log10(x_ex)
for i in range(methods):
plt.plot(x, results[i], label=m_names[i], marker=m_marks[i])
plt.fill_between(x, results_low[i], results_up[i], alpha=0.3)
# plt.xscale("log", nonposx='clip')
# plt.yscale("log", nonposy='clip')
plt.legend(loc='lower left', fontsize=12)
plt.xlabel("$\mathrm{log}_{10} n$", fontsize=20)
plt.ylabel("$\mathrm{log}_{10} (\mathrm{wce})^2$", fontsize=20)
plt.tight_layout()
# plt.show()
fig.savefig("results_rchq/{}_{}_t{}.pdf".format(data_name, kernel, times))
text_data.close()
def func(name, n, rec=0, nys=0):
x = []
w = []
idx = []
fails = 0
if 'FNE' in name:
pts_rec = gen_params(rec)
pts_nys = gen_params(nys)
idx, w = enys.recombination(
pts_rec, pts_nys, n, use_obj=False, rand_SVD=True)
x = pts_rec[idx]
if 'N. + emp' in name:
pts_rec = gen_params(rec)
pts_nys = gen_params(nys)
idx, w = enys.recombination(
pts_rec, pts_nys, n, use_obj=True, rand_SVD=False)
x = pts_rec[idx]
elif name == 'iid Bayes':
x, w = mc_bayes(n)
elif 'Nyström' in name:
fails = -1
pts_nys = gen_params(nys)
svs, U_nys = enys.ker_svd_sparsify(
pts_nys, n - 1, rand_SVD=False)
while len(idx) == 0:
fails += 1
pts_rec = gen_params(rec)
idx, w = rchq_nys(pts_rec, pts_nys, n, U_nys, svs, use_obj=True)
x = pts_rec[idx]
if 'opt' in name:
w = grlp.QP(k(x, x), k_exp(x), k_exp_exp(), nonnegative=True)
return x, w, fails
def k_exp_exp():
return k_exp_exp_
def k_exp_exp_comp(): # post computation
global k_exp_exp_
k_exp_exp_ = np.sum(k_exp_) / num
def k_exp(x):
return k_exp_[x]
def k_exp_comp(): # post computation
r = np.ones((num,))
r /= num
xal = np.arange(num)
xsp = np.array_split(xal, np.minimum(50, len(xal)))
dots = [k(x, xal) @ r for x in xsp]
global k_exp_
k_exp_ = np.concatenate(dots)
def median_heuristics():
num_mh = np.minimum(10000, num)
xal = np.arange(num_mh)
xsp = np.array_split(xal, np.minimum(50, len(xal)))
tmp = np.zeros(num_mh)
for x in xsp:
tmp = np.append(tmp, euclidean_distances(
data[x, :], data[xal, :], squared=True).reshape(num_mh * len(x)))
return np.median(tmp) / 2
def eval(x, w, pr=False):
if pr == True:
print(w)
if len(x) == 0:
return 10000000000
m = len(x)
tmp = np.transpose(w) @ k_exp(x)
ret = (k_exp_exp() - tmp) + (np.transpose(w) @ k(x, x) @ w - tmp)
return ret
def mc_bayes(m, nn=False):
pt = gen_params(m)
return pt, grlp.QP(k(pt, pt), k_exp(pt), k_exp_exp(), nonnegative=nn)
def rchq_nys(samp, pt, s, U, svs=0, use_obj=False):
obj = 0
if use_obj:
obj = k(samp, diag=True)
idx_feasible = svs >= 1e-10
inv_svs = np.zeros(len(svs))
inv_svs[idx_feasible] = np.sqrt(1/svs[idx_feasible])
sur_svs = np.reshape(inv_svs, (-1, 1))
N = len(samp)
rem = N - s * (N // s)
for i in range(N//s):
mat = k(pt, samp[s*i:s*(i+1)])
mat = U @ mat
mat = np.multiply(mat, sur_svs)
obj[s*i:s*(i+1)] -= np.sum(mat**2, axis=0)
if rem:
mat = k(pt, samp[N-rem:N])
mat = U @ mat
mat = np.multiply(mat, sur_svs)
obj[N-rem:N] -= np.sum(mat**2, axis=0)
K = np.ones((s, len(samp)))
B = np.ones(s,)
B[:s-1] = U @ k_exp(pt)
K[:s-1, :] = U @ k(pt, samp)
sol = grlp.LP(K, B, set_objective=use_obj, obj=obj)
idx = []
weights = []
for a, w_a in sol:
idx += [a]
weights += [w_a]
return idx, weights