def test_isotonic_regression():
y = np.array([3, 7, 5, 9, 8, 7, 10])
y_ = np.array([3, 6, 6, 8, 8, 8, 10])
assert_array_equal(y_, isotonic_regression(y))
y = np.array([10, 0, 2])
y_ = np.array([4, 4, 4])
assert_array_equal(y_, isotonic_regression(y))
x = np.arange(len(y))
ir = IsotonicRegression(y_min=0., y_max=1.)
ir.fit(x, y)
assert_array_equal(ir.fit(x, y).transform(x), ir.fit_transform(x, y))
assert_array_equal(ir.transform(x), ir.predict(x))
# check that it is immune to permutation
perm = np.random.permutation(len(y))
ir = IsotonicRegression(y_min=0., y_max=1.)
assert_array_equal(ir.fit_transform(x[perm], y[perm]),
ir.fit_transform(x, y)[perm])
assert_array_equal(ir.transform(x[perm]), ir.transform(x)[perm])
# check we don't crash when all x are equal:
ir = IsotonicRegression()
assert_array_equal(ir.fit_transform(np.ones(len(x)), y), np.mean(y))
def train_classifier_with_calib(classifier, data, use_all_data=False, normalize=False):
X_train = data.X_train
y_train = data.y_train
X_cv = data.X_cv
y_cv = data.y_cv
if normalize:
X_train, X_cv = normalize_data(X_train, X_cv)
if not use_all_data:
ir = IR()
score, S = train(classifier, X_train, y_train, X_cv, y_cv, data.y_classes)
predictions_proba = classifier.predict_proba(X_cv)
proba = predictions_proba[:,1];
ir.fit_transform(proba,y_cv)
print proba
print ir
return {
'classifier': classifier,
'score': score,
'S_auc': S,
'IR':ir,
'prange':[np.amin(proba),np.amax(proba)]
}
else:
train_all_data(classifier, X_train, y_train, X_cv, y_cv)
return {
'classifier': classifier
}
def test_isotonic_regression():
y = np.array([3, 7, 5, 9, 8, 7, 10])
y_ = np.array([3, 6, 6, 8, 8, 8, 10])
assert_array_equal(y_, isotonic_regression(y))
y = np.array([10, 0, 2])
y_ = np.array([4, 4, 4])
assert_array_equal(y_, isotonic_regression(y))
x = np.arange(len(y))
ir = IsotonicRegression(y_min=0., y_max=1.)
ir.fit(x, y)
assert_array_equal(ir.fit(x, y).transform(x), ir.fit_transform(x, y))
assert_array_equal(ir.transform(x), ir.predict(x))
# check that it is immune to permutation
perm = np.random.permutation(len(y))
ir = IsotonicRegression(y_min=0., y_max=1.)
assert_array_equal(ir.fit_transform(x[perm], y[perm]),
ir.fit_transform(x, y)[perm])
assert_array_equal(ir.transform(x[perm]), ir.transform(x)[perm])
# check we don't crash when all x are equal:
ir = IsotonicRegression()
assert_array_equal(ir.fit_transform(np.ones(len(x)), y), np.mean(y))
def test_isotonic_regression_ties_max():
# Setup examples with ties on maximum
x = [1, 2, 3, 4, 5, 5]
y = [1, 2, 3, 4, 5, 6]
y_true = [1, 2, 3, 4, 5.5, 5.5]
# Check that we get identical results for fit/transform and fit_transform
ir = IsotonicRegression()
ir.fit(x, y)
assert_array_equal(ir.fit(x, y).transform(x), ir.fit_transform(x, y))
assert_array_equal(y_true, ir.fit_transform(x, y))
def test_isotonic_regression_ties_max():
# Setup examples with ties on maximum
x = [1, 2, 3, 4, 5, 5]
y = [1, 2, 3, 4, 5, 6]
y_true = [1, 2, 3, 4, 5.5, 5.5]
# Check that we get identical results for fit/transform and fit_transform
ir = IsotonicRegression()
ir.fit(x, y)
assert_array_equal(ir.fit(x, y).transform(x), ir.fit_transform(x, y))
assert_array_equal(y_true, ir.fit_transform(x, y))
def test_isotonic_sample_weight_parameter_default_value():
# check if default value of sample_weight parameter is one
ir = IsotonicRegression()
# random test data
rng = np.random.RandomState(42)
n = 100
x = np.arange(n)
y = rng.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n))
# check if value is correctly used
weights = np.ones(n)
y_set_value = ir.fit_transform(x, y, sample_weight=weights)
y_default_value = ir.fit_transform(x, y)
assert_array_equal(y_set_value, y_default_value)
def test_isotonic_sample_weight_parameter_default_value():
# check if default value of sample_weight parameter is one
ir = IsotonicRegression()
# random test data
rng = np.random.RandomState(42)
n = 100
x = np.arange(n)
y = rng.randint(-50, 50, size=(n, )) + 50. * np.log(1 + np.arange(n))
# check if value is correctly used
weights = np.ones(n)
y_set_value = ir.fit_transform(x, y, sample_weight=weights)
y_default_value = ir.fit_transform(x, y)
assert_array_equal(y_set_value, y_default_value)
def fit_iso_transform(self, bx, by):
with torch.no_grad():
cdf = self.eval_all(bx, by)[0].cpu().numpy()[:, 0].astype(np.float)
cdf = np.sort(cdf)
lin = np.linspace(0, 1, int(cdf.shape[0]))
# Insert an extra 0 and 1 to ensure the range is always [0, 1], and trim CDF for numerical stability
cdf = np.clip(cdf, a_max=1.0 - 1e-6, a_min=1e-6)
cdf = np.insert(np.insert(cdf, -1, 1), 0, 0)
lin = np.insert(np.insert(lin, -1, 1), 0, 0)
iso_transform = IsotonicRegression()
iso_transform.fit_transform(cdf, lin)
return iso_transform
def plot():
results = []
for f in glob('lengths*npz'):
d = np.load(f)
l = d['lengths']
l = l[l > 0.]
print d['mu'], l.shape
results.append([d['mu'], l.mean()])
results = sorted(results)
results = np.array(results).T
muvals, mean_length = results
f = plt.figure()
f.clf()
ax = f.gca()
iso = IsotonicRegression(increasing=False)
mean_length_iso = iso.fit_transform(np.arange(mean_length.shape[0]),
mean_length)
ax.plot(muvals, mean_length, 'k', linewidth=2, label='UMAU')
ax.plot([muvals.min(), muvals.max()], [2 * ndist.ppf(0.975)] * 2,
c='red',
label='Sample splitting',
linewidth=2)
ax.plot([muvals.min(), muvals.max()], [np.sqrt(2) * ndist.ppf(0.975)] * 2,
'k--')
ax.set_xlabel(r'$\mu$', fontsize=20)
ax.set_ylabel(r'E(|CI($\mu$)|)', fontsize=20)
ax.legend(loc='lower right')
ax.set_ylim([0, 4])
ax.set_xlim([-2, 9])
f.savefig('figure_b.pdf')
output = np.array(zip(muvals, mean_length))
np.savetxt('equal_tailed_lengths.csv', output, delimiter=',')
def apply_isotonic(arr):
n_krn = len(gus_krn)
arr_smt = np.convolve(np.hstack([np.repeat(arr[0], n_krn * 2), arr]), gus_krn, mode='same')[n_krn * 2:]
# plt.plot(range(len(arr_smt)), arr_smt, alpha=0.5, label='Smooth')
ir = IsotonicRegression(y_min=0, increasing=False)
# plt.plot(range(len(arr_smt)), bin_prd, alpha=0.5, label='Pred')
return ir.fit_transform(range(len(arr_smt)), arr_smt)
def _fit_isotonic(model,train_loader):
t_start = perf_counter()
means,stds,ys = model.mc_prediction_loader(train_loader)
N = means.shape[0]
dist = Normal(means,stds)
cdf = dist.cdf(ys)
sorted_cdf,ind = cdf.sort() #[N]
y = torch.arange(1.0,N+1)/N #[N]
ir = IsotonicRegression(out_of_bounds='clip')
x = sorted_cdf.cpu().numpy() #[N]
y = y.numpy() #[N]
x_app = np.insert(x,0,0.0)
y_app = np.insert(y,0,0.0)
y_ = ir.fit_transform(x_app, y_app)#[N]
delta = _delta(means,stds,ys)
#for synchronizing cuda calls
torch.cuda.synchronize()
#stop and measure the time taken for postprocessing method
t_stop = perf_counter()
iso_time = torch.tensor(t_stop - t_start)
return ir,delta,sorted_cdf,iso_time
def main(self):
x_field = self.fields_by_key('x')[0]
y_field = self.fields_by_key('y')[0]
x = np.array(self.slice_data(x_field,int))
y = np.array(self.slice_data(y_field,int))
n = len(x)
render = StringIO.StringIO()
###############################################################################
# Fit IsotonicRegression and LinearRegression models
ir = IsotonicRegression()
y_ = ir.fit_transform(x, y)
lr = LinearRegression()
lr.fit(x[:, np.newaxis], y) # x needs to be 2d for LinearRegression
###############################################################################
# plot result
segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]
lc = LineCollection(segments, zorder=0)
lc.set_array(np.ones(len(y)))
lc.set_linewidths(0.5 * np.ones(n))
fig = plt.figure()
plt.plot(x, y, 'r.', markersize=12)
plt.plot(x, y_, 'g.-', markersize=12)
plt.plot(x, lr.predict(x[:, np.newaxis]), 'b-')
plt.gca().add_collection(lc)
plt.legend(('Data', 'Isotonic Fit', 'Linear Fit'), loc='lower right')
plt.title('Isotonic regression')
plt.savefig(render,format='png')
return render
def test_isotonic_regression():
y = np.array([3, 7, 5, 9, 8, 7, 10])
y_ = np.array([3, 6, 6, 8, 8, 8, 10])
assert_array_equal(y_, isotonic_regression(y))
x = np.arange(len(y))
ir = IsotonicRegression(y_min=0.0, y_max=1.0)
ir.fit(x, y)
assert_array_equal(ir.fit(x, y).transform(x), ir.fit_transform(x, y))
assert_array_equal(ir.transform(x), ir.predict(x))
# check that it is immune to permutation
perm = np.random.permutation(len(y))
ir = IsotonicRegression(y_min=0.0, y_max=1.0)
assert_array_equal(ir.fit_transform(x[perm], y[perm]), ir.fit_transform(x, y)[perm])
assert_array_equal(ir.transform(x[perm]), ir.transform(x)[perm])
def pavTermFrequency(ranking_fn, cluster_names_fn, fn, plot):
ranking = dt.import2dArray(ranking_fn)
names = dt.import1dArray(cluster_names_fn)
frq = []
counter = 0
for name in names:
frq.append(readFreq(name))
pav_classes = []
for f in range(len(frq)):
print(names[f])
x = np.asarray(frq[f])
y = ranking[f]
ir = IsotonicRegression()
y_ = ir.fit_transform(x, y)
pav_classes.append(y_)
if plot:
plot(x, y, y_)
print(f)
dt.write2dArray(
pav_classes,
"../data/movies/finetune/" + file_name + "PavTermFrequency.txt")
return pav_classes
def cali(fname, predict_name, out_name, mode='ctr'):
if mode == 'ctr':
true_col = 'actual_click'
prob_col = 'ctr'
if mode == 'cvr':
true_col = 'actual_purchase'
prob_col = 'cvr'
pred_df = pd.read_csv(predict_name, names=columns)
nn = pred_df.shape[0]
df = pd.read_csv(fname, names=columns)
n = df.shape[0]
y_true = df[true_col].values
y_prob = df[prob_col].values
#fraction_of_positives, mean_predicted_value = cali.calibration_curve(y_true, y_prob, normalize=False, n_bins=10)
#plt.figure()
#plt.plot(mean_predicted_value,fraction_of_positives)
#plt.show()
#plt.close()
ir = IsotonicRegression()
y = ir.fit_transform(y_prob, y_true)
y_pred = ir.predict(pred_df[prob_col].values)
nn = y_pred.shape[0]
h = open(out_name, 'w')
for i in range(nn):
if i < nn - 1:
h.write(str(y_pred[i]) + '\n')
else:
h.write(str(y_pred[i]))
h.close()
def test_isotonic_regression_ties_secondary_():
"""
Test isotonic regression fit, transform and fit_transform
against the "secondary" ties method and "pituitary" data from R
"isotone" package, as detailed in: J. d. Leeuw, K. Hornik, P. Mair,
Isotone Optimization in R: Pool-Adjacent-Violators Algorithm
(PAVA) and Active Set Methods
Set values based on pituitary example and
the following R command detailed in the paper above:
> library("isotone")
> data("pituitary")
> res1 <- gpava(pituitary$age, pituitary$size, ties="secondary")
> res1$x
`isotone` version: 1.0-2, 2014-09-07
R version: R version 3.1.1 (2014-07-10)
"""
x = [8, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14]
y = [21, 23.5, 23, 24, 21, 25, 21.5, 22, 19, 23.5, 25]
y_true = [22.22222, 22.22222, 22.22222, 22.22222, 22.22222, 22.22222,
22.22222, 22.22222, 22.22222, 24.25, 24.25]
# Check fit, transform and fit_transform
ir = IsotonicRegression()
ir.fit(x, y)
assert_array_almost_equal(ir.transform(x), y_true, 4)
assert_array_almost_equal(ir.fit_transform(x, y), y_true, 4)
def test_isotonic_regression_ties_secondary_():
"""
Test isotonic regression fit, transform and fit_transform
against the "secondary" ties method and "pituitary" data from R
"isotone" package, as detailed in: J. d. Leeuw, K. Hornik, P. Mair,
Isotone Optimization in R: Pool-Adjacent-Violators Algorithm
(PAVA) and Active Set Methods
Set values based on pituitary example and
the following R command detailed in the paper above:
> library("isotone")
> data("pituitary")
> res1 <- gpava(pituitary$age, pituitary$size, ties="secondary")
> res1$x
`isotone` version: 1.0-2, 2014-09-07
R version: R version 3.1.1 (2014-07-10)
"""
x = [8, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14]
y = [21, 23.5, 23, 24, 21, 25, 21.5, 22, 19, 23.5, 25]
y_true = [
22.22222, 22.22222, 22.22222, 22.22222, 22.22222, 22.22222, 22.22222,
22.22222, 22.22222, 24.25, 24.25
]
# Check fit, transform and fit_transform
ir = IsotonicRegression()
ir.fit(x, y)
assert_array_almost_equal(ir.transform(x), y_true, 4)
assert_array_almost_equal(ir.fit_transform(x, y), y_true, 4)
def test_isotonic_regression():
y = np.array([3, 7, 5, 9, 8, 7, 10])
y_ = np.array([3, 6, 6, 8, 8, 8, 10])
assert_array_equal(y_, isotonic_regression(y))
x = np.arange(len(y))
ir = IsotonicRegression(y_min=0., y_max=1.)
ir.fit(x, y)
assert_array_equal(ir.fit(x, y).transform(x), ir.fit_transform(x, y))
assert_array_equal(ir.transform(x), ir.predict(x))
# check that it is immune to permutation
perm = np.random.permutation(len(y))
ir = IsotonicRegression(y_min=0., y_max=1.)
assert_array_equal(ir.fit_transform(x[perm], y[perm]),
ir.fit_transform(x, y)[perm])
assert_array_equal(ir.transform(x[perm]), ir.transform(x)[perm])
def isoreg(filename):
ds = pd.read_csv(filename, names=["1", "2"], skiprows=1)
ds["1"] = pd.to_datetime(ds["1"], format="%Y-%m")
ds["d"] = (ds["1"] - ds["1"].min()) / np.timedelta64(1,'D')
X = ds["d"] # put your dates in here
y = ds["2"] # put your kwh in here
model = IsotonicRegression()
model.fit_transform(X, y)
X_predict = ds["d"] # put the dates of which you want to predict kwh here
y_predict = model.predict(X_predict)
fig = plt.figure(figsize=(12, 6))
plt.plot(y)
plt.plot(y_predict)
fig.savefig("files/" + str(os.path.splitext(os.path.basename(filename))[0]) + "_isoreg.png")
def compare_PAVA_implementations():
trials = 10
rs = check_random_state(0)
times = []
dimensions = [int(1e1), int(1e2), int(1e3), int(1e4), int(1e5), int(1e6)]
#dimensions = [int(1e6)]
for n in dimensions:
print 'dimensionality', n
x = np.arange(n)
for trial in range(trials):
y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n))
# scikit-learn PAVA
if n <= int(1e5):
#if n <= int(1e6):
ir = IsotonicRegression()
y_copy = np.copy(y)
start_time = time.time()
ir.fit_transform(x, y_copy)
time1 = time.time() - start_time
else: time1 = -1.
# in-place PAVA
y_copy = np.copy(y)
start_time = time.time()
isotonic_regression_c_2(y_copy, 0, n)
time2 = time.time() - start_time
# in-place PAVA++
y_copy = np.copy(y)
start_time = time.time()
isotonic_regression_c(y_copy, 0, n)
time3 = time.time() - start_time
times.append([time1, time2, time3])
index = []
for n in ['1e1','1e2','1e3','1e4','1e5','1e6']: index += [n]*trials
#for n in ['1e6']: index += [n]*trials
tuples = zip()
df = pd.DataFrame(times, index=index, columns=['sklearn', 'PAVA+', 'PAVA++'])
print df
df.save('results/PAVA_comparison_5.pkl')
def mir_calibrate(logit,label,logit_eval):
p = np.exp(logit)/np.sum(np.exp(logit),1)[:,None]
p_eval = np.exp(logit_eval)/np.sum(np.exp(logit_eval),1)[:,None]
ir = IsotonicRegression(out_of_bounds='clip')
y_ = ir.fit_transform(p.flatten(), (label.flatten()))
yt_ = ir.predict(p_eval.flatten())
p = yt_.reshape(logit_eval.shape)+1e-9*p_eval
return p
def sklearn_isotonic_regression_multi(self, y, blocks):
ir = IsotonicRegression()
n = len(y)
x = np.arange(n)
z = np.zeros(n)
z[:blocks[0]] = y[:blocks[0]]
for start, end in zip(blocks, np.append(blocks[1:], [n])):
z[start:end] = ir.fit_transform(x[start:end], y[start:end])
return z
def generate_calibration_model(df, pred_col, actual_col):
ir = IsotonicRegression()
y_ = ir.fit_transform(df[pred_col], df[actual_col])
calib = {}
calib['method'] = 'ir'
calib['mod'] = ir
calib['max_obs'] = max(df[pred_col])
calib['max_cal'] = max(y_)
return calib
def test_proj_PAV(self):
n = 10
x = np.arange(n)
rs = check_random_state(0)
for i in range(10):
y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n))
ir = IsotonicRegression()
truth = ir.fit_transform(x, y)
self.assertTrue(np.linalg.norm(proj_PAV(y) - truth) < 1e-8)
def _apply_isotonic_regression(df, mag, magErr):
df.sort_values(by=[mag], inplace=True)
df = df.reset_index(drop=True)
x = df[mag]
y = df[magErr]
ir = IsotonicRegression()
y_expected = ir.fit_transform(x, y)
return ir, x, y, y_expected
def test_isotonic_min_max_boundaries():
# check if min value is used correctly
ir = IsotonicRegression(y_min=2, y_max=4)
n = 6
x = np.arange(n)
y = np.arange(n)
y_test = [2, 2, 2, 3, 4, 4]
y_result = np.round(ir.fit_transform(x, y))
assert_array_equal(y_result, y_test)
def sklearn_isotonic_regression_multi(self, y, blocks):
ir = IsotonicRegression()
n = len(y)
x = np.arange(n)
z = np.zeros(n)
z[:blocks[0]] = y[:blocks[0]]
for start, end in zip(blocks, np.append(blocks[1:], [n])):
z[start:end] = ir.fit_transform(x[start:end], y[start:end])
return z
def test_isotonic_min_max_boundaries():
# check if min value is used correctly
ir = IsotonicRegression(y_min=2, y_max=4)
n = 6
x = np.arange(n)
y = np.arange(n)
y_test = [2, 2, 2, 3, 4, 4]
y_result = np.round(ir.fit_transform(x, y))
assert_array_equal(y_result, y_test)
def test_isotonic_sample_weight():
ir = IsotonicRegression()
x = [1, 2, 3, 4, 5, 6, 7]
y = [1, 41, 51, 1, 2, 5, 24]
sample_weight = [1, 2, 3, 4, 5, 6, 7]
expected_y = [1, 13.95, 13.95, 13.95, 13.95, 13.95, 24]
received_y = ir.fit_transform(x, y, sample_weight=sample_weight)
assert_array_equal(expected_y, received_y)
def test_isotonic_sample_weight():
ir = IsotonicRegression()
x = [1, 2, 3, 4, 5, 6, 7]
y = [1, 41, 51, 1, 2, 5, 24]
sample_weight = [1, 2, 3, 4, 5, 6, 7]
expected_y = [1, 13.95, 13.95, 13.95, 13.95, 13.95, 24]
received_y = ir.fit_transform(x, y, sample_weight=sample_weight)
assert_array_equal(expected_y, received_y)
def compute_correlations(vectors, dissimilarities, distance_function):
"""
Computes the correlation between vector distances and actual dissimilarities,
using the given distance function between the vectors.
Returns a dictionary from correlation metric to its corresponding value.
For convenience, this dictionary also contains both the vector of target dissimilarities
and the vector of predicted similarities.
"""
import numpy as np
from sklearn.isotonic import IsotonicRegression
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
from scipy.stats import pearsonr, spearmanr, kendalltau
# initialize dissimilarities with ones (arbitrary, will be overwritten anyways)
dissimilarity_scores = np.ones(dissimilarities.shape)
for i in range(len(vectors)):
for j in range(len(vectors)):
vec_i = vectors[i]
vec_j = vectors[j]
score = distance_function(vec_i, vec_j)[0][0]
dissimilarity_scores[i][j] = score
# transform dissimilarity matrices into vectors for correlation computation
target_vector = np.reshape(dissimilarities, (-1, 1))
sim_vector = np.reshape(dissimilarity_scores, (-1, 1))
# compute correlations
pearson, _ = pearsonr(sim_vector, target_vector)
spearman, _ = spearmanr(sim_vector, target_vector)
kendall, _ = kendalltau(sim_vector, target_vector)
# compute least squares regression for R² metric
linear_regression = LinearRegression()
linear_regression.fit(sim_vector, target_vector)
predictions = linear_regression.predict(sim_vector)
r2_linear = r2_score(target_vector, predictions)
# compute isotonic regression for R² metric
x = np.reshape(dissimilarity_scores, (-1))
y = np.reshape(dissimilarities, (-1))
isotonic_regression = IsotonicRegression()
predictions = isotonic_regression.fit_transform(x, y)
r2_isotonic = r2_score(y, predictions)
return {
'pearson': pearson[0],
'spearman': spearman,
'kendall': kendall,
'r2_linear': r2_linear,
'r2_isotonic': r2_isotonic,
'targets': target_vector,
'predictions': sim_vector
}
def _minCllr(self, targetScoreValues, nonTargetScoreValues, ):
"""
Computes the 'minimum cost of log likelihood ratio' measure as given in IDIAP's bob calibration.py
We don't however use pavx here, as used in many other implementations, but sklearn's isotonic regression,
which is equivalent and frees us from linking to c++ code.
"""
# First, sort both scores.
neg = sorted(nonTargetScoreValues)
pos = sorted(targetScoreValues)
N = len(neg)
P = len(pos)
I = N + P
# Now, iterate through both score sets and add a 0 for negative and 1 for positive scores.
n, p = 0, 0
idealSequence = np.zeros(I)
neg_indices = [0] * N
pos_indices = [0] * P
for i in range(I):
if n == N or neg[n] > pos[p]:
pos_indices[p] = i
p += 1
idealSequence[i] = 1
else:
neg_indices[n] = i
n += 1
# Run the pool adjacent violaters method on the ideal LLR scores.
# pavx implements isotonic regression. Python's sklearn contains code to do just that.
ir = IsotonicRegression()
# Calculate the isotonic regression.
popt = ir.fit_transform(np.arange(len(idealSequence)), idealSequence)
# disable runtime warnings for a short time since log(0) will raise a warning.
old_warn_setup = np.seterr(divide='ignore')
# ... compute logs.
# Lets assume the prior odds on a target score is the ratio #target scores / #non target scores.
log_prior_odds = math.log(float(P) / float(N))
posterior_log_odds = np.log(popt) - np.log(1.0 - popt)
# ... activate old warnings.
np.seterr(**old_warn_setup)
llrs = posterior_log_odds - log_prior_odds
# Unmix positive and negative scores.
new_neg = np.zeros(N)
for n in range(N):
new_neg[n] = llrs[neg_indices[n]]
new_pos = np.zeros(P)
for p in range(P):
new_pos[p] = llrs[pos_indices[p]]
# Compute cllr of these new 'optimal' LLR scores.
minCllr = self._cllr(new_pos, new_neg)
return minCllr
def test_proj_PAV(self):
n = 10
x = np.arange(n)
rs = check_random_state(0)
for i in range(10):
y = rs.randint(-50, 50,
size=(n, )) + 50. * np.log(1 + np.arange(n))
ir = IsotonicRegression()
truth = ir.fit_transform(x, y)
self.assertTrue(np.linalg.norm(proj_PAV(y) - truth) < 1e-8)
def regression_monotone_initial(data_training,data_target,data): regression_data = [] #Realisation de la regression monotone qui nous donnes un bruit de fond théorique #On fit et transform les données pour chacun des replicats indépendamment ir = IsotonicRegression() for i in range(len(data_target)-1): regression = ir.fit_transform(data_training[0:len(data_training),1],data_target[i+1,0:len(data)]) regression_data.append(regression) regression_data = np.asarray(regression_data) return regression_data
def irova_calibrate(logit,label,logit_eval):
p = np.exp(logit)/np.sum(np.exp(logit),1)[:,None]
p_eval = np.exp(logit_eval)/np.sum(np.exp(logit_eval),1)[:,None]
for ii in range(p_eval.shape[1]):
ir = IsotonicRegression(out_of_bounds='clip')
y_ = ir.fit_transform(p[:,ii], label[:,ii])
p_eval[:,ii] = ir.predict(p_eval[:,ii])+1e-9*p_eval[:,ii]
return p_eval
return p_eval
def pavPPMI(cluster_names_fn,
ranking_fn,
file_name,
do_p=False,
data_type="movies",
rewrite_files=False,
limit_entities=False,
classification="genres",
lowest_amt=0,
highest_amt=2147000000):
pavPPMI_fn = "../data/" + data_type + "/finetune/" + file_name + ".txt"
all_fns = [pavPPMI_fn]
if dt.allFnsAlreadyExist(all_fns) and not rewrite_files:
print("Skipping task", pavPPMI.__name__)
return
else:
print("Running task", pavPPMI.__name__)
print("certainly still running that old pavPPMI task, yes sir")
if limit_entities is False:
classification = "all"
ranking = dt.import2dArray(ranking_fn)
names = dt.import1dArray(cluster_names_fn)
frq = []
counter = 0
for name in names:
name = name.split()[0]
if ":" in name:
name = name[:-1]
frq.append(
readPPMI(name, data_type, lowest_amt, highest_amt, classification))
pav_classes = []
for f in range(len(frq)):
try:
print(names[f])
x = np.asarray(frq[f])
y = ranking[f]
ir = IsotonicRegression()
y_ = ir.fit_transform(x, y)
pav_classes.append(y_)
if do_p:
plot(x, y, y_)
except ValueError:
print(names[f], "len ppmi",
len(frq[f], "len ranking", len(ranking[f])))
exit()
print(f)
dt.write2dArray(pav_classes, pavPPMI_fn)
return pav_classes
def cal(refn, out_fn, base_folder='data/round2models', example_folder_name='example_data'):
"""
:param refn:
:param out_fn:
:param base_folder:
:return:
"""
from sklearn.isotonic import IsotonicRegression
from sklearn.metrics import log_loss, roc_auc_score
import os
calpath = 'calibration/data/' + out_fn + '_caldata.p'
if os.path.exists(calpath):
try:
with open(calpath, 'rb')as f:
ldirs, pcal, mags = pickle.load(f)
return ldirs, pcal, mags
except:
with open(calpath, 'rb')as f:
ldirs, pcal = pickle.load(f)
return ldirs, pcal
mags = []
y = []
dirs = os.listdir(path=base_folder)
for dir in dirs:
adv_path = os.path.join(base_folder, dir, example_folder_name, refn)
if os.path.exists(adv_path):
mag = get_blur_mag(adv_path, sigma=2.0)
truth_fn = os.path.join(base_folder, dir, 'config.json')
cls = utils.get_class(truth_fn, classtype='binary', file=True)
mags.append(mag)
y.append(cls)
ir_model = IsotonicRegression(out_of_bounds='clip')
pcal = ir_model.fit_transform(mags, y)
kld = log_loss(y, pcal)
# print(kld)
roc1 = roc_auc_score(y, np.array(pcal))
print(out_fn, 'AUC:', roc1, 'KLD:', kld)
# dump(ir_model, 'data/classifiers/blur' + '_ir.joblib')
dump(ir_model, 'calibration/fitted/' + out_fn)
pcal = pcal[np.argsort(dirs)]
dirs.sort()
with open(calpath,'wb') as f:
pickle.dump([dirs, pcal, mags], f)
return dirs, pcal, mags
def test_permutation_invariance():
# check that fit is permuation invariant.
# regression test of missing sorting of sample-weights
ir = IsotonicRegression()
x = [1, 2, 3, 4, 5, 6, 7]
y = [1, 41, 51, 1, 2, 5, 24]
sample_weight = [1, 2, 3, 4, 5, 6, 7]
x_s, y_s, sample_weight_s = shuffle(x, y, sample_weight, random_state=0)
y_transformed = ir.fit_transform(x, y, sample_weight=sample_weight)
y_transformed_s = ir.fit(x_s, y_s, sample_weight=sample_weight_s).transform(x)
assert_array_equal(y_transformed, y_transformed_s)
def test_permutation_invariance():
# check that fit is permutation invariant.
# regression test of missing sorting of sample-weights
ir = IsotonicRegression()
x = [1, 2, 3, 4, 5, 6, 7]
y = [1, 41, 51, 1, 2, 5, 24]
sample_weight = [1, 2, 3, 4, 5, 6, 7]
x_s, y_s, sample_weight_s = shuffle(x, y, sample_weight, random_state=0)
y_transformed = ir.fit_transform(x, y, sample_weight=sample_weight)
y_transformed_s = ir.fit(x_s, y_s, sample_weight=sample_weight_s).transform(x)
assert_array_equal(y_transformed, y_transformed_s)
def test_isotonic_regression(self):
self.setUp()
times = []
rs = check_random_state(0)
for n in [int(1e1), int(1e2), int(1e3), int(1e4)]:
x = np.arange(n)
y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n))
ir = IsotonicRegression()
start_time = time.time()
y1 = ir.fit_transform(x, y)
times.append(time.time() - start_time)
print 'test isotonic_regression'
print times
def regression_monotone(data_target,data): regression_data = [] #Realisation de la regression monotone qui nous donnes un bruit de fond théorique #On fit et transform les données pour chacun des replicats indépendamment ir = IsotonicRegression() #data_target_transpose = np.transpose(data_target) for replicat in data_target: regression = ir.fit_transform(np.arange(0,len(replicat),1),replicat) regression_data.append(regression) regression_data = np.asarray(regression_data) #print(len(regression_data)) return regression_data
def test_isotonic_regression(self):
self.setUp()
times = []
rs = check_random_state(0)
for n in [int(1e1), int(1e2), int(1e3), int(1e4)]:
x = np.arange(n)
y = rs.randint(-50, 50,
size=(n, )) + 50. * np.log(1 + np.arange(n))
ir = IsotonicRegression()
start_time = time.time()
y1 = ir.fit_transform(x, y)
times.append(time.time() - start_time)
print 'test isotonic_regression'
print times
def fit(self, counts_matrix, lengths=None):
'''
NMDS fit Function, scale low dimension matrix to high dimension
Parameters
----------
counts_matrix: ndarray
Returns
----------
fit_matrix: ndarray
'''
if not sparse.isspmatrix_coo(counts_matrix):
counts_matrix = sparse.coo_matrix(counts_matrix)
for i in range(self.max_iter_outer):
if i == 0:
fit_matrix = Multi_Dimensional_Scaling_Base.estimate_model(
counts_matrix,
alpha=self.alpha,
beta=self.beta,
ini=self.init,
verbose=self.verbose,
precompute_distances=self.precompute_distances,
use_zero_entries=False,
random_state=self.random_state,
bias=self.bias,
factr=self.factr,
maxiter=self.max_iter)
else:
ir = IsotonicRegression()
distances = np.sqrt(
((fit_matrix[counts_matrix.row] -
fit_matrix[counts_matrix.col])**2).sum(axis=1))
wish_distances = ir.fit_transform(1. / counts_matrix.data,
distances)
fit_matrix = Multi_Dimensional_Scaling_Base.estimate_model(
sparse.coo_matrix(
(wish_distances, (counts_matrix.row,
counts_matrix.col))),
alpha=self.alpha,
beta=self.beta,
ini=fit_matrix,
verbose=self.verbose,
use_zero_entries=False,
precompute_distances='precomputed',
random_state=self.random_state,
factr=self.factr,
maxiter=self.max_iter,
)
return fit_matrix
def isotonic_regression(ax, x, y, w=[]):
"""
INPUT:
ax: an Axes object
x: (N, ) np.array
y: (N, ) np.array
w: None or a list of length N.
OUTPUT:
ax: an Axes object
"""
if len(w) == 0:
w = [1.0 for _ in y]
n = len(y)
# Fit IsotonicRegression and LinearRegression models
ir = IsotonicRegression()
y_ = ir.fit_transform(x, y, sample_weight=w)
lr = LinearRegression()
lr.fit(x[:, np.newaxis], y,
sample_weight=w) # x needs to be 2d for LinearRegression
# Plot result
segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]
ax.plot(x, y, 'r.', markersize=12, alpha=0.2)
ax.plot(x, y_, 'g^', markersize=12, alpha=0.2)
ax.plot(x, lr.predict(x[:, np.newaxis]), 'b-')
ax.set_xlim(-0.1, 1.1)
ax.set_ylim(-0.1, 1.1)
# compute ece and acc after calibration
ece = EceEval(np.array([1 - y_, y_]).T, y, num_bins=20)
y_predict = y_ > 0.5
acc = (y_predict == y).mean()
ax.text(0.05,
0.8,
'ECE=%.4f\nACC=%.4f' % (ece, acc),
size=14,
ha='left',
va='center',
bbox={
'facecolor': 'green',
'alpha': 0.5,
'pad': 4
})
return ax
def sklearn_pav(y_true, y_score):
"""
Binary PAV algorithm, algorithm to solve Isotonic regression
NOTE: sklearn isotonic regression is used
y_true: 1D array
y_score: 1D array
"""
id_permute = np.argsort(y_score)
y_sort = y_true[id_permute]
p_sort = np.sort(y_score)
ir = IsotonicRegression()
p_calibrated = ir.fit_transform(p_sort, y_sort)
return y_sort, p_calibrated
def ensure_monotone_increasing(arr_, fromright=True, fromleft=True, newmode=True):
r"""
Args:
arr_ (ndarray):
Returns:
ndarray: arr
CommandLine:
python -m vtool.math --test-ensure_monotone_increasing --show
Example:
>>> # DISABLE_DOCTEST
>>> from vtool.math import * # NOQA
>>> rng = np.random.RandomState(0)
>>> size_ = 100
>>> domain = np.arange(size_)
>>> offset = ut.get_argval('--offset', type_=float, default=2.3)
>>> arr_ = np.sin(np.pi * (domain / 100) - offset) + (rng.rand(len(domain)) - .5) * .1
>>> arr = ensure_monotone_increasing(arr_, fromleft=False, fromright=True)
>>> result = str(arr)
>>> print(result)
>>> ut.quit_if_noshow()
>>> import plottool as pt
>>> pt.plot2(domain, arr_, 'r-', fnum=1, pnum=(2, 1, 1), title='before', equal_aspect=False)
>>> pt.plot2(domain, arr, 'r-', fnum=1, pnum=(2, 1, 2), title='after monotonization (increasing)', equal_aspect=False)
>>> ut.show_if_requested()
"""
if newmode:
from sklearn.isotonic import IsotonicRegression
ir = IsotonicRegression()
arr = ir.fit_transform(np.arange(len(arr_)), arr_)
else:
arr = arr_.copy()
size = len(arr)
# Ensure increasing from right
if fromright:
for lx in range(1, size):
rx = (size - lx - 1)
if arr[rx] > arr[rx + 1]:
arr[rx] = arr[rx + 1]
if fromleft:
# ensure increasing from left
for lx in range(0, size - 1):
if arr[lx] > arr[lx + 1]:
arr[lx + 1] = arr[lx]
return arr
def test_isotonic_regression_auto_increasing():
# Set y and x for decreasing
y = np.array([5, 6.1, 6, 7, 10, 9, 10])
x = np.arange(len(y))
# Create model and fit_transform
ir = IsotonicRegression(increasing='auto')
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
y_ = ir.fit_transform(x, y)
# work-around for pearson divide warnings in scipy <= 0.17.0
assert_true(all(["invalid value encountered in "
in str(warn.message) for warn in w]))
# Check that relationship increases
is_increasing = y_[0] < y_[-1]
assert_true(is_increasing)
def plot():
results = []
for f in glob('umau_lengths*npz'):
d = np.load(f)
l = d['lengths']
l = l[~np.isnan(l)]
l = l[np.isfinite(l)]
l = l[l>0]
results.append([d['mu'], l.mean()])
for f in glob('miller/lengths*npz'):
d = np.load(f)
if d['mu'] not in [r[0] for r in results]:
l = d['lengths']
l = l[np.isfinite(l)]
l = l[~np.isnan(l)]
l = l[l>0]
results.append([d['mu'], l.mean()])
else:
idx = [r[0] for r in results].index(d['mu'])
l = d['lengths']
l = l[np.isfinite(l)]
l = l[~np.isnan(l)]
l = l[l>0]
results[idx][1] = 0.5 * (results[idx][1] + l.mean())
results = sorted(results)
results = np.array(results).T
muvals, mean_length = results
f = plt.figure()
f.clf()
ax = f.gca()
iso = IsotonicRegression(increasing=False)
mean_length_iso = iso.fit_transform(np.arange(mean_length.shape[0]), mean_length)
ax.plot(muvals, mean_length, 'k', linewidth=2, label='UMAU')
ax.plot([muvals.min(), muvals.max()], [2*ndist.ppf(0.975)]*2, c='red', label='Sample splitting', linewidth=2)
ax.plot([muvals.min(), muvals.max()], [np.sqrt(2)*ndist.ppf(0.975)]*2, 'k--')
ax.set_xlabel(r'$\mu$', fontsize=20)
ax.set_ylabel(r'E(|CI($\mu$)|)', fontsize=20)
ax.legend(loc='lower right')
ax.set_ylim([0,4])
ax.set_xlim([-2,9])
f.savefig('figure_b_umau.pdf')
def fit(self, counts, lengths=None):
"""
"""
if not sparse.isspmatrix_coo(counts):
counts = sparse.coo_matrix(counts)
for i in range(self.max_iter_outer):
if i == 0:
X = estimate_X(
counts,
alpha=self.alpha,
beta=self.beta,
ini=self.init,
verbose=self.verbose,
use_zero_entries=False,
random_state=self.random_state,
bias=self.bias,
factr=self.factr,
maxiter=self.max_iter,
)
else:
ir = IsotonicRegression()
dis = np.sqrt(((X[counts.row] - X[counts.col]) ** 2).sum(axis=1))
wish_distances = ir.fit_transform(1.0 / counts.data, dis)
X = estimate_X(
sparse.coo_matrix((wish_distances, (counts.row, counts.col))),
alpha=self.alpha,
beta=self.beta,
ini=X,
verbose=self.verbose,
use_zero_entries=False,
precompute_distances="precomputed",
random_state=self.random_state,
bias=self.bias,
factr=self.factr,
maxiter=self.max_iter,
)
print "writing wish distances"
return X
def isotonic_deg_sequence(deg_seq, eps):
# index-sort deg_seq
idx = [i[0] for i in sorted(enumerate(deg_seq), key=lambda x:x[1])]
sorted_deg_seq = [deg_seq[idx[i]] for i in range(len(deg_seq))]
alpha = math.exp(-eps/4) # global seensitivity = 4
s1 = [0.0 for _ in range(len(deg_seq))]
# s1 (sorted)
for i in range(len(deg_seq)):
s1[i] = sorted_deg_seq[i] + geometric_mechanism(alpha, 1) # Geometric noise
# s
ir = IsotonicRegression()
s = ir.fit_transform(range(len(deg_seq)), s1)
#
return s, s1, sorted_deg_seq
def test_isotonic_regression_with_ties_in_differently_sized_groups():
"""
Non-regression test to handle issue 9432:
https://github.com/scikit-learn/scikit-learn/issues/9432
Compare against output in R:
> library("isotone")
> x <- c(0, 1, 1, 2, 3, 4)
> y <- c(0, 0, 1, 0, 0, 1)
> res1 <- gpava(x, y, ties="secondary")
> res1$x
`isotone` version: 1.1-0, 2015-07-24
R version: R version 3.3.2 (2016-10-31)
"""
x = np.array([0, 1, 1, 2, 3, 4])
y = np.array([0, 0, 1, 0, 0, 1])
y_true = np.array([0., 0.25, 0.25, 0.25, 0.25, 1.])
ir = IsotonicRegression()
ir.fit(x, y)
assert_array_almost_equal(ir.transform(x), y_true)
assert_array_almost_equal(ir.fit_transform(x, y), y_true)
def _smacof_single_p(similarities, n_uq, metric=True, n_components=2, init=None,
max_iter=300, verbose=0, eps=1e-3, random_state=None):
"""
Computes multidimensional scaling using SMACOF algorithm
Parameters
----------
n_uq
similarities: symmetric ndarray, shape [n * n]
similarities between the points
metric: boolean, optional, default: True
compute metric or nonmetric SMACOF algorithm
n_components: int, optional, default: 2
number of dimension in which to immerse the similarities
overwritten if initial array is provided.
init: {None or ndarray}, optional
if None, randomly chooses the initial configuration
if ndarray, initialize the SMACOF algorithm with this array
max_iter: int, optional, default: 300
Maximum number of iterations of the SMACOF algorithm for a single run
verbose: int, optional, default: 0
level of verbosity
eps: float, optional, default: 1e-6
relative tolerance w.r.t stress to declare converge
random_state: integer or numpy.RandomState, optional
The generator used to initialize the centers. If an integer is
given, it fixes the seed. Defaults to the global numpy random
number generator.
Returns
-------
X: ndarray (n_samples, n_components), float
coordinates of the n_samples points in a n_components-space
stress_: float
The final value of the stress (sum of squared distance of the
disparities and the distances for all constrained points)
n_iter : int
Number of iterations run.
"""
similarities = check_symmetric(similarities, raise_exception=True)
n_samples = similarities.shape[0]
random_state = check_random_state(random_state)
W = np.ones((n_samples, n_samples))
W[:n_uq, :n_uq] = 0.0
W[n_uq:, n_uq:] = 0.0
# W[np.arange(len(W)), np.arange(len(W))] = 0.0
V = -W
V[np.arange(len(V)), np.arange(len(V))] = W.sum(axis=1)
e = np.ones((n_samples, 1))
Vp = np.linalg.inv(V + np.dot(e, e.T)/n_samples) - np.dot(e, e.T)/n_samples
# Vp = np.linalg.pinv(V)
# sim_flat = ((1 - np.tri(n_samples)) * similarities).ravel()
sim_flat = similarities.ravel()
sim_flat_w = sim_flat[sim_flat != 0]
if init is None:
# Randomly choose initial configuration
X = random_state.rand(n_samples * n_components)
X = X.reshape((n_samples, n_components))
else:
# overrides the parameter p
n_components = init.shape[1]
if n_samples != init.shape[0]:
raise ValueError("init matrix should be of shape (%d, %d)" %
(n_samples, n_components))
X = init
old_stress = None
ir = IsotonicRegression()
for it in range(max_iter):
# Compute distance and monotonic regression
dis = euclidean_distances(X)
if metric:
disparities = similarities
else:
# dis_flat = dis.ravel()
# # similarities with 0 are considered as missing values
# dis_flat_w = dis_flat[sim_flat != 0]
# # Compute the disparities using a monotonic regression
# disparities_flat = ir.fit_transform(sim_flat_w, dis_flat_w)
# disparities = dis_flat.copy()
# disparities[sim_flat != 0] = disparities_flat
# disparities = disparities.reshape((n_samples, n_samples))
# disparities *= np.sqrt((n_samples * (n_samples - 1) / 2) /
# (disparities ** 2).sum())
dis_flat = dis.ravel()
# similarities with 0 are considered as missing values
dis_flat_w = dis_flat[sim_flat != 0]
# Compute the disparities using a monotonic regression
disparities_flat = ir.fit_transform(sim_flat_w, dis_flat_w)
disparities = dis_flat.copy()
disparities[sim_flat != 0] = disparities_flat
disparities = disparities.reshape((n_samples, n_samples))
disparities *= np.sqrt((n_samples * (n_samples - 1) / 2) / (disparities ** 2).sum())
disparities[similarities==0] = 0
# Compute stress
# stress = ((dis.ravel() - disparities.ravel()) ** 2).sum() / 2
_stress = (W.ravel()*((dis.ravel() - disparities.ravel()) ** 2)).sum() / 2
# Update X using the Guttman transform
# dis[dis == 0] = 1e-5
# ratio = disparities / dis
# B = - ratio
# B[np.arange(len(B)), np.arange(len(B))] += ratio.sum(axis=1)
# X = 1. / n_samples * np.dot(B, X)
# print (1. / n_samples * np.dot(B, X))[:5].T
dis[dis == 0] = 1e-5
ratio = disparities / dis
_B = - W*ratio
_B[np.arange(len(_B)), np.arange(len(_B))] += (W*ratio).sum(axis=1)
X = np.dot(Vp, np.dot(_B, X))
# print X[:5].T
dis = np.sqrt((X ** 2).sum(axis=1)).sum()
if verbose >= 2:
print('it: %d, stress %s' % (it, _stress))
if old_stress is not None:
if(old_stress - _stress / dis) < eps:
if verbose:
print('breaking at iteration %d with stress %s' % (it,
_stress))
break
old_stress = _stress / dis
return X, _stress, it + 1
def run_nmds(directory):
print directory
if os.path.exists(os.path.join(directory,
"config.ini")):
config_file = os.path.join(directory, "config.ini")
else:
config_file = None
options = parse(config_file)
run_mds(directory)
for i in range(0, max_iter):
if i == 0:
try:
X = np.loadtxt(
os.path.join(directory,
"MDS." + options["output_name"] + ".txt"))
except IOError:
return
else:
X = np.loadtxt(
os.path.join(directory,
'%d.NMDS.' % (i) + options["output_name"] +
".txt"))
X = X.reshape((len(X) / 3, 3))
dis = euclidean_distances(X) * 1000
counts = np.load(
os.path.join(directory, options["counts"]))
counts[np.isnan(counts)] = 0
wish_distances = np.zeros(counts.shape)
print "Fitting isotonic regression..."
ir = IsotonicRegression()
wish_distances[counts != 0] = ir.fit_transform(
1. / counts[counts != 0],
dis[counts != 0])
print "writing wish distances"
lengths = np.loadtxt(
os.path.join(directory, options["organism_structure"]))
try:
len(lengths)
except TypeError:
lengths = np.array([lengths])
write(wish_distances,
os.path.join(directory,
'%d.NMDS.wish_distances.txt' % i),
lengths=lengths, resolution=options["resolution"])
if i == 0:
shutil.copy(
os.path.join(directory,
"MDS." + options["output_name"] + ".txt"),
os.path.join(directory,
'%d.NMDS.' % (i + 1) + options["output_name"] +
".temp.txt"))
else:
shutil.copy(
os.path.join(directory,
'%d.NMDS.' % i + options["output_name"] + ".txt"),
os.path.join(directory,
'%d.NMDS.' % (i + 1) + options["output_name"] +
".temp.txt"))
locus_coord = options["output_name"].replace(".pdb",".bed")
cmd = CMD_MDS % (options["binary_mds"],
os.path.join(directory,
"%d.NMDS." % (i + 1) +
options["output_name"]),
options["resolution"],
os.path.join(directory,
options["organism_structure"]),
os.path.join(directory,
"%d.NMDS.wish_distances.txt" % (i)),
os.path.join(directory,
locus_coord),
options["adjacent_beads"],
options["chromosomes"],
os.path.join(directory,
str(i + 1) + '.NMDS.log'))
filename = os.path.join(directory, str(i + 1) + '.NMDS.sh')
fileptr = open(filename, 'wb')
fileptr.write(cmd)
fileptr.close()
st = os.stat(filename)
os.chmod(filename, st.st_mode | stat.S_IXUSR)
p =subprocess.Popen(filename.split(), shell='True')
p.wait()
def _smacof_with_anchors_single(config, similarities, metric=True, n_components=2, init=None,
max_iter=300, verbose=0, eps=1e-3, random_state=None, estimated_dist_weights=None):
"""
Computes multidimensional scaling using SMACOF algorithm
Parameters
----------
config : Config object
configuration object for anchor-tag deployment parameters
similarities: symmetric ndarray, shape [n * n]
similarities between the points
metric: boolean, optional, default: True
compute metric or nonmetric SMACOF algorithm
n_components: int, optional, default: 2
number of dimension in which to immerse the similarities
overwritten if initial array is provided.
init: {None or ndarray}, optional
if None, randomly chooses the initial configuration
if ndarray, initialize the SMACOF algorithm with this array
max_iter: int, optional, default: 300
Maximum number of iterations of the SMACOF algorithm for a single run
verbose: int, optional, default: 0
level of verbosity
eps: float, optional, default: 1e-6
relative tolerance w.r.t stress to declare converge
random_state: integer or numpy.RandomState, optional
The generator used to initialize the centers. If an integer is
given, it fixes the seed. Defaults to the global numpy random
number generator.
Returns
-------
X: ndarray (n_samples, n_components), float
coordinates of the n_samples points in a n_components-space
stress_: float
The final value of the stress (sum of squared distance of the
disparities and the distances for all constrained points)
n_iter : int
Number of iterations run
last_positions: ndarray [X1,...,Xn]
An array of computed Xs.
"""
NO_OF_TAGS, NO_OF_ANCHORS = config.no_of_tags, config.no_of_anchors
similarities = check_symmetric(similarities, raise_exception=True)
n_samples = similarities.shape[0]
random_state = check_random_state(random_state)
sim_flat = ((1 - np.tri(n_samples)) * similarities).ravel()
sim_flat_w = sim_flat[sim_flat != 0]
if init is None:
# Randomly choose initial configuration
X = random_state.rand(n_samples * n_components)
X = X.reshape((n_samples, n_components))
# uncomment the following if weight matrix W is not hollow
#X[:-2] = Xa
else:
# overrides the parameter p
n_components = init.shape[1]
if n_samples != init.shape[0]:
raise ValueError("init matrix should be of shape (%d, %d)" %
(n_samples, n_components))
X = init
old_stress = None
ir = IsotonicRegression()
# setup weight matrix
if getattr(config, 'weights', None) is not None:
weights = config.weights
else:
weights = np.ones((n_samples, n_samples))
if getattr(config, 'missingdata', None):
weights[-NO_OF_TAGS:, -NO_OF_TAGS:] = 0
if estimated_dist_weights is not None:
weights[-NO_OF_TAGS:, -NO_OF_TAGS:] = estimated_dist_weights
diag = np.arange(n_samples)
weights[diag, diag] = 0
last_n_configs = []
Xa = config.anchors
for it in range(max_iter):
# Compute distance and monotonic regression
dis = euclidean_distances(X)
if metric:
disparities = similarities
else:
dis_flat = dis.ravel()
# similarities with 0 are considered as missing values
dis_flat_w = dis_flat[sim_flat != 0]
# Compute the disparities using a monotonic regression
disparities_flat = ir.fit_transform(sim_flat_w, dis_flat_w)
disparities = dis_flat.copy()
disparities[sim_flat != 0] = disparities_flat
disparities = disparities.reshape((n_samples, n_samples))
disparities *= np.sqrt((n_samples * (n_samples - 1) / 2) /
(disparities ** 2).sum())
# Compute stress
stress = (weights.ravel()*(dis.ravel() - disparities.ravel()) ** 2).sum() / 2
#stress = ((dis[:-NO_OF_TAGS, -NO_OF_TAGS:].ravel() - disparities[:-NO_OF_TAGS, -NO_OF_TAGS:].ravel()) ** 2).sum()
# Update X using the Guttman transform
dis[dis == 0] = 1e5
ratio = weights*disparities / dis
B = - ratio
B[diag, diag] = 0
B[diag, diag] = -B.sum(axis=1)
# Apply update to only tag configuration since anchor config is already known
V = - weights
V[diag, diag] += weights.sum(axis=1)
# V_inv = np.linalg.pinv(V)
V12 = V[-NO_OF_TAGS:, :-NO_OF_TAGS]
B11 = B[-NO_OF_TAGS:, -NO_OF_TAGS:]
Zu = X[-NO_OF_TAGS:]
B12 = B[-NO_OF_TAGS:, :-NO_OF_TAGS]
V11_inv = np.linalg.inv(V[-NO_OF_TAGS:, -NO_OF_TAGS:])
Xu = V11_inv.dot(B11.dot(Zu) + (B12 - V12).dot(Xa))
# merge known anchors config with new tags config
X = np.concatenate((Xa, Xu))
last_n_configs.append(X)
#X = (1/n_samples)*B.dot(X)
#dis = np.sqrt((X ** 2).sum(axis=1)).sum()
dis = (weights*dis**2).sum() / 2
if verbose >= 2:
print('it: %d, stress %s' % (it, stress))
if old_stress is not None:
if(old_stress - stress / dis) < eps:
if verbose:
print('breaking at iteration %d with stress %s' % (it,
stress))
break
old_stress = stress / dis
return X, stress, it + 1, np.array(last_n_configs)
from sklearn.linear_model import LinearRegression from sklearn.isotonic import IsotonicRegression from sklearn.utils import check_random_state n = 100 x = np.arange(n) rs = check_random_state(0) y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n)) ############################################################################### # Fit IsotonicRegression and LinearRegression models ir = IsotonicRegression() y_ = ir.fit_transform(x, y) lr = LinearRegression() lr.fit(x[:, np.newaxis], y) # x needs to be 2d for LinearRegression ############################################################################### # plot result segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)] lc = LineCollection(segments, zorder=0) lc.set_array(np.ones(len(y))) lc.set_linewidths(0.5 * np.ones(n)) fig = plt.figure() plt.plot(x, y, 'r.', markersize=12) plt.plot(x, y_, 'g.-', markersize=12)
test = pd.read_csv(r'csvs\\submit_xB.csv')
testId = test.id.values
test = test.drop('id', axis=1)
##one vs all
ir1 = IsotonicRegression()
ir2 = IsotonicRegression()
ir3 = IsotonicRegression()
ir4 = IsotonicRegression()
ir5 = IsotonicRegression()
ir6 = IsotonicRegression()
ir7 = IsotonicRegression()
ir8 = IsotonicRegression()
ir9 = IsotonicRegression()
y_1 = ir1.fit_transform(cv10fold.ix[:,0], y_train.ix[:,0])
y_2 = ir2.fit_transform(cv10fold.ix[:,1], y_train.ix[:,1])
y_3 = ir3.fit_transform(cv10fold.ix[:,2], y_train.ix[:,2])
y_4 = ir4.fit_transform(cv10fold.ix[:,3], y_train.ix[:,3])
y_5 = ir5.fit_transform(cv10fold.ix[:,4], y_train.ix[:,4])
y_6 = ir6.fit_transform(cv10fold.ix[:,5], y_train.ix[:,5])
y_7 = ir7.fit_transform(cv10fold.ix[:,6], y_train.ix[:,6])
y_8 = ir8.fit_transform(cv10fold.ix[:,7], y_train.ix[:,7])
y_9 = ir9.fit_transform(cv10fold.ix[:,8], y_train.ix[:,8])
#container
cv10fold.calibrated = pd.DataFrame({'id' : id
, 'Class_1' : y_1
, 'Class_2' : y_2
, 'Class_3' : y_3
, 'Class_4' : y_4
def IsotonicRegression_pred(y_train, predictions_train, test_preds, bin_step, y_test):
# Y Training Target sort the y_test
# X Training Data use the indexes of sorted(y_test)
# y_train_len=len(y_train)
# if bin_step<1:
# step_count = 1/bin_step
# else:
# step_count = int(math.floor(y_train_len/bin_step))
# step_element_count = int(math.floor(y_train_len/step_count))
# bin_start_indexes=np.array(range(0,step_count))*step_element_count
predictions_np = np.array(predictions_train, float)
predictions_sorted = np.sort(predictions_np)
predictions_sorted_indexes = predictions_np.argsort()
y_train_arranged = np.array(y_train, float)[predictions_sorted_indexes].ravel()
# not_binned_y_train_arranged = y_train_arranged[:]
# for index in range(len(bin_start_indexes)-1):
# pin = bin_start_indexes[index]
# pend = bin_start_indexes[index+1]
# y_train_arranged[pin:pend] = np.average(y_train_arranged[pin:pend])
# if bin_start_indexes[-1]<y_train_len:
# pin = bin_start_indexes[-1]
# pend = y_train_len
# y_train_arranged[pin:pend] = np.average(y_train_arranged[pin:pend])
ir = IsotonicRegression()
y_ir = ir.fit_transform(predictions_sorted, y_train_arranged)
y_ir_pred = ir.predict(predictions_sorted)
# print "min(y_train_arranged) :", min(y_train_arranged)
# print "max(y_train_arranged) :", max(y_train_arranged)
# print "min(predictions_sorted) :", min(predictions_sorted)
# print "max(predictions_sorted) :", max(predictions_sorted)
# print "min(test_preds) :", min(test_preds)
# print "max(test_preds) :", max(test_preds)
# if max(test_preds)>=max(y_train_arranged):
# np.arrya(test_preds>max(y_train_arranged))==True
max_indexes = np.array((np.where(test_preds > max(y_train_arranged))), int).ravel()
if len(max_indexes) != 0:
for m_i in max_indexes:
test_preds[m_i] = max(y_train_arranged)
test_preds_sorted = np.sort(np.array(test_preds))
predictions_ir = ir.predict(test_preds)
ind = np.where(np.isnan(predictions_ir))[0]
preds_test_min = np.nanmin(predictions_ir)
if len(ind) != 0:
for i in ind:
predictions_ir[i] = preds_test_min
# ==============WRITING TO CSV================
# d_train={'y_train' :np.array(y_train,float)[predictions_sorted_indexes].ravel(),
# 'y_train_bin' :np.array(y_train_arranged).ravel(),
# 'train_preds' :np.array(predictions_sorted).ravel(),
# 'train_preds_ir' :y_ir}
# df_train=pd.DataFrame(d_train)
# df_train.to_csv("train_IR.csv")
# d_test={'y_test' :np.array(y_test).ravel(),
# 'test_preds' :np.array(test_preds).ravel(),
# 'test_preds_ir' :predictions_ir}
# df_test=pd.DataFrame(d_test)
# df_test.to_csv("test_IR.csv")
# score_test_ir=ir.score(test_preds,y_test)
score_test_ir = 0
return predictions_ir, y_ir_pred, ir.get_params(deep=True), score_test_ir
def interpolation_estimate(Z, Z_constraint,
lower=0.5,
upper=4,
npts=30,
ndraw=5000,
burnin=1000,
estimator='truncated'):
"""
Estimate the parameter $\sigma$ in $Z \sim N(0, \sigma^2 I) | Z \in C$
where $C$ is the convex set encoded by `Z_constraint`
.. math::
C = \left\{z: Az+b \geq 0 \right\}
with $(A,b)$ being `(Z_constraints.inequality,
Z_constraints.inequality_offset)`.
The algorithm proceeds by estimating $\|Z\|^2_2$
by Monte Carlo for a range of `npts` values starting from
`lower*np.linalg.norm(Z)/np.sqrt(n)` to
`upper*np.linalg.norm(Z)/np.sqrt(n)` with `n=Z.shape[0]`.
These values are then used to compute the GCM
(Greated Convex Minorant) which is interpolated and solved
for an arguments such that the expected value matches the observed
value `(Z**2).sum()`.
Parameters
----------
Z : `np.float`
Observed data to be used to estimate $\sigma$. Should be in
the cone specified by `Z_constraints`.
Z_constraint : `constraints`
Constraints under which we observe $Z$.
lower : float
Multiple of naive estimate to use as lower endpoint.
upper : float
Multiple of naive estimate to use as upper endpoint.
npts : int
Number of points in interpolation grid.
ndraw : int
Number of Gibbs steps to use for estimating
each expectation.
burnin : int
How many Gibbs steps to use for burning in.
Returns
-------
sigma_hat : float
The root of the interpolant derived from GCM values.
interpolant : `interp1d`
The interpolant, to be used for plotting or other
diagnostics.
WARNING
-------
* It is assumed that `Z_constraints.equality` is `None`.
* Uses `rpy2` and `fdrtool` library to compute the GCM.
"""
initial = np.linalg.norm(Z) / np.sqrt(Z.shape[0])
Svalues = np.linspace(lower*initial,upper*initial, npts)
Evalues = []
n = Z.shape[0]
L, V, U, S = quadratic_bounds(Z, np.identity(n), Z_constraint)
if estimator == 'truncated':
def _estimator(S, Z, Z_constraint):
L, V, U, _ = quadratic_bounds(Z, np.identity(n), Z_constraint)
num = mpquad(lambda x: mpexp(-x**2/(2*S**2) -L*x / S**2 + (n-1) * mplog((x+L)/S) + 2 * mplog(x+L)),
[0, U-L])
den = mpquad(lambda x: mpexp(-x**2/(2*S**2) -L*x / S**2 + (n-1) * mplog((x+L)/S)),
[0, U-L])
print num / den, V**2, S, (L, U)
return num / den
elif estimator == 'simulate':
state = Z.copy()
rpy.r.assign('state', state)
def _estimator(S, state, Z_constraint):
Z_constraint.covariance = S**2 * np.identity(Z.shape[0])
e, v, _state = expected_norm_squared(state,
Z_constraint, ndraw=ndraw,
burnin=burnin)
state[:] = _state
return e
state = Z.copy()
for S in Svalues:
Evalues.append(_estimator(S, state, Z_constraint))
ir = IsotonicRegression()
if DEBUG:
print Svalues, Evalues
Eiso = ir.fit_transform(Svalues, Evalues)
Sinterp, Einterp = Svalues, Eiso
# rpy.r.assign('S', Svalues)
# rpy.r.assign('E', np.array(Evalues))
# rpy.r('''
# library(fdrtool);
# G = gcmlcm(S, E, 'gcm');
# Sgcm = G$x.knots;
# Egcm = G$y.knots;
# ''')
# Sgcm = np.asarray(rpy.r('Sgcm'))
# Egcm = np.asarray(rpy.r('Egcm'))
# interpolant = interp1d(Sgcm, Egcm - (Z**2).sum())
interpolant = interp1d(Sinterp, Einterp - (Z**2).sum())
try:
sigma_hat = bisect(interpolant, Sinterp.min(), Sinterp.max())
except:
raise ValueError('''Bisection failed -- check (lower, upper). Observed = %0.1e, Range = (%0.1e,%0.1e)''' % ((Z**2).sum(), Einterp.min(), Einterp.max()))
return sigma_hat, interpolant
def truncated_estimate(Z, Z_constraint,
lower=0.5,
upper=2,
npts=15):
"""
Estimate the parameter $\sigma$ in $Z \sim N(0, \sigma^2 I) | Z \in C$
where $C$ is the convex set encoded by `Z_constraints`
.. math::
C = \left\{z: Az+b \geq 0 \right\}
with $(A,b)$ being `(Z_constraints.inequality,
Z_constraints.inequality_offset)`.
The algorithm proceeds by estimating $\|Z\|^2_2$
by Monte Carlo for a range of `npts` values starting from
`lower*np.linalg.norm(Z)/np.sqrt(n)` to
`upper*np.linalg.norm(Z)/np.sqrt(n)` with `n=Z.shape[0]`.
These values are then used to compute the GCM
(Greated Convex Minorant) which is interpolated and solved
for an arguments such that the expected value matches the observed
value `(Z**2).sum()`.
Parameters
----------
Z : `np.float`
Observed data to be used to estimate $\sigma$. Should be in
the cone specified by `Z_constraints`.
Z_constraint : `constraints`
Constraints under which we observe $Z$.
lower : float
Multiple of naive estimate to use as lower endpoint.
upper : float
Multiple of naive estimate to use as upper endpoint.
npts : int
Number of points in interpolation grid.
Returns
-------
sigma_hat : float
The root of the interpolant derived from GCM values.
interpolant : `interp1d`
The interpolant, to be used for plotting or other
diagnostics.
WARNING
-------
* It is assumed that `Z_constraints.equality` is `None`.
* Uses `rpy2` and `fdrtool` library to compute the GCM.
"""
initial = np.linalg.norm(Z) / np.sqrt(Z.shape[0])
Svalues = np.linspace(lower*initial,upper*initial, npts)
Evalues = []
# use truncated chi to estimate integral
# with scipy.integrate.quad
n = Z.shape[0]
operator = np.identity(n)
L, V, U, S = quadratic_bounds(Z, operator, Z_constraint)
for S in Svalues:
num = quad(lambda x: np.exp(-x**2/(2*S**2) + (n+1) * np.log(x)),
L, U)
den = quad(lambda x: np.exp(-x**2/(2*S**2) + (n-1) * np.log(x)),
L, U)
Evalues.append(num[0] / den[0])
print num, den
ir = IsotonicRegression()
if DEBUG:
print Svalues, Evalues
Eiso = ir.fit_transform(Svalues, Evalues)
Sinterp, Einterp = Svalues, Eiso
interpolant = interp1d(Sinterp, Einterp - (Z**2).sum())
try:
sigma_hat = bisect(interpolant, Sinterp.min(), Sinterp.max())
except:
raise ValueError('''Bisection failed -- check (lower, upper). Observed = %0.1e, Range = (%0.1e,%0.1e)''' % ((Z**2).sum(), Einterp.min(), Einterp.max()))
return sigma_hat, interpolant
print L, V, U, S
