def fit(self, A, Y, weights, fit_init=None, refit=False, increasing=True): #fit isotonic regression model. model = IsotonicRegression(increasing=increasing,out_of_bounds="clip",y_min=0.0,y_max=1.0) model.fit(X=A,y=Y,sample_weight=weights) self.model_obj = model return(0)
def test_isotonic_copy_before_fit():
# https://github.com/scikit-learn/scikit-learn/issues/6628
ir = IsotonicRegression()
copy.copy(ir)
import numpy as np
from sklearn.isotonic import IsotonicRegression
ir = IsotonicRegression()
class TimeRetrieval:
"""
!! ONLY deal with small datasets, because the trainning step is slow
X: data features such as polar angle
Y: known time stamps
"""
def __init__(self, train_x=None, train_y=None):
self.train_x = train_x # {idx: feature(polar angle)}
self.train_y = train_y # {idx: stamps (mean,std)}
self.fit_x = None
self.fit_y = None
def train(self,
train_x=None,
train_y=None,
train_alg="fitting_1",
**kwargs):
"""
use data points to get labels in X axis
"""
if train_x is None: train_x = self.train_x.copy()
if train_y is None: train_y = self.train_y.copy()
return getattr(self, train_alg)(train_x=train_x,
train_y=train_y,
def known_iso(self, axis=1, unknowns=0):
# performs isotonic regression ONLY for known data values
# and ONLY on columns where there are non-increasing points
# row-wise (axis = 0) or column-wise (axis = 1)
# unknowns should be 0 or none
tonic = copy.deepcopy(self.array) # returns a new isotonic matrix
known_dict = self.known_for_iso(axis, unknowns)
if axis == 1:
increase_dict, non_increase_percent = self.is_col_inc()
else:
increase_dict = self.is_row_inc()
# dat dict tells me where things arent increasing (from is_row_inc() or is_col_inc())
if axis == 1:
for i in range(len(tonic[0])):
try:
# if i is a key in increase dict then this column needs regression
# else just pass to the next column
tester = increase_dict[i]
X = known_dict[i]
if X != []:
initial_vals = [tonic[j][i] for j in X]
# Use the initial values to fit the model and then predict what the decreasing ones should be
iso = IsotonicRegression(out_of_bounds='clip').fit(
X, initial_vals)
predictions = iso.predict(range(len(tonic)))
# put everything back:
for row in range(len(predictions)):
tonic[row][i] = predictions[row]
except:
pass
else:
# same thing but with rows
for i in range(len(tonic)):
try:
tester = increase_dict[i]
X = known_dict[i]
if X != []:
initial_vals = [tonic[i][j] for j in X]
# Use the initial values to fit the model and then predict what the decreasing ones should be
iso = IsotonicRegression(out_of_bounds='clip').fit(
X, initial_vals)
predictions = iso.predict(range(len(tonic[i])))
# put everything back:
tonic[i] = predictions
except:
pass
newframe = pd.DataFrame(tonic)
newframe.columns = self.dataframe.columns
newframe.index = self.dataframe.index
if unknowns == 0:
# Isotonic outputs NaN values, replace them with zeros
newframe = newframe.fillna(0)
return mat_opr(newframe)
forward = lambda X, thetas: simulate_posterior_predictive(X, thetas, noise=0.5)
# Construct the calibration dataset
predicted_quantiles, empirical_quantiles = make_cal_dataset(
y[:, np.newaxis], x, coefs, forward)
# -
plt.scatter(predicted_quantiles, empirical_quantiles)
plt.plot([0, 1], [0, 1], color='tab:grey', linestyle='--')
plt.xlabel('Predicted Cumulative Distribution')
plt.ylabel('Empirical Cumulative Distribution')
plt.title('Calibration Dataset')
# +
# Train isotonic regression in reverse mode
ir = IsotonicRegression(out_of_bounds='clip')
ir.fit(empirical_quantiles, predicted_quantiles)
# Find the values of calibrated quantiles
calibrated_quantiles = ir.predict([0.025, 0.5, 0.975])
# +
# Plot the posterior predictive
low, mid, high = np.percentile(posterior_predictive, [2.5, 50, 97.5], axis=1)
plt.fill_between(x_test, low, high, alpha=0.2, label='95% Predictive Interval')
plt.plot(x_test, mid, color='tab:red', label='Predicted Median')
low, mid, high = np.quantile(posterior_predictive,
calibrated_quantiles,
axis=1)
plt.fill_between(x_test, low, high, alpha=0.2, label='95% Calibrated Interval')
import matplotlib.pyplot as plt from matplotlib.collections import LineCollection 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, )) + 50.0 * np.log1p(np.arange(n)) # %% # Fit IsotonicRegression and LinearRegression models: ir = IsotonicRegression(out_of_bounds="clip") y_ = ir.fit_transform(x, y) lr = LinearRegression() lr.fit(x[:, np.newaxis], y) # x needs to be 2d for LinearRegression # %% # Plot results: 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(np.full(n, 0.5)) fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(12, 6))
def fit_Spline(mainDic,x,y,yerr,infilename,outfilename,biasDic,outliersline,outliersdist,observedIntraInRangeSum, possibleIntraInRangeCount, possibleInterAllCount, observedIntraAllSum, observedInterAllSum, resolution, passNo):
with open(logfile, 'a') as log:
log.write("\nFitting a univariate spline to the probability means\n"),
log.write("------------------------------------------------------------------------------------\n"),
splineX = None
newSplineY = None
residual = None
FDRx = None
FDRy = None
if not interOnly:
if outliersdist != None:
y = [f for _, f in sorted(zip(x,y), key=lambda pair: pair[0])]
x.sort()
for i in range(1,len(x)):
if x[i]<=x[i-1]:
print("ERROR in spline fitting. Distances do not decrease across bins. Ensure interaction file is correct.")
print("Avg. distance of bin(i-1)... %s" % x[i-1])
print("Avg. distance of bin(i)... %s" % x[i])
sys.exit(2)
# maximum residual allowed for spline is set to min(y)^2
splineError=min(y)*min(y)
# use fitpack2 method -fit on the real x and y from equal occupancy binning
ius = UnivariateSpline(x, y, s=splineError)
tempMaxX=max(x)
tempMinX=min(x)
tempList=sorted([dis for dis in mainDic])
splineX=[]
### The below for loop will make sure nothing is out of range of [min(x) max(x)]
### Therefore everything will be within the range where the spline is defined
for i in tempList:
if tempMinX<=i<=tempMaxX:
splineX.append(i)
splineY=ius(splineX)
#print(splineY)
#print(yerr)
ir = IsotonicRegression(increasing=False)
newSplineY = ir.fit_transform(splineX,splineY)
#print(newSplineY)
residual =sum([i*i for i in (y - ius(x))])
if visual==True:
xi = np.linspace(min(x),max(x),5*len(x))
yi = ius(xi)
print("Plotting %s" % (outfilename + ".png"))
plt.clf()
fig = plt.figure()
ax = fig.add_subplot(2,1,1)
plt.plot(myUtils.scale_a_list(splineX,toKb), myUtils.scale_a_list(newSplineY,toProb),'g-',label="spline-"+str(passNo),linewidth=2)
plt.errorbar(myUtils.scale_a_list(x,toKb),myUtils.scale_a_list(y,toProb),myUtils.scale_a_list(yerr,toProb),fmt='r.',label="Mean with std. error",linewidth=2)
#plt.ylabel('Contact probability (x10$^{-5}$)',fontsize='large')
#plt.xlabel('Genomic distance (kb)',fontsize='large')
plt.ylabel('Contact probability (x10$^{-5}$)')
plt.xlabel('Genomic distance (kb)')
if distLowThres>0 and distUpThres<float("inf"):
plt.xlim(myUtils.scale_a_list([distLowThres, distUpThres],toKb))
plt.gca().yaxis.set_major_locator( MaxNLocator(nbins = 3, prune=None))
ax.legend(loc="upper right")
ax = fig.add_subplot(2,1,2)
plt.loglog(splineX,newSplineY,'g-')
plt.errorbar(x, y, yerr=yerr, fmt='r.') # Data
if distLowThres>0 and distUpThres<float("inf"):
plt.xlim([distLowThres, distUpThres])
plt.ylabel('Contact probability (log-scale)')
plt.xlabel('Genomic distance (log-scale)')
plt.savefig(outfilename+'.png')
# NOW write the calculated pvalues and corrected pvalues in a file
infile = gzip.open(infilename, 'rt')
intraInRangeCount=0
intraOutOfRangeCount=0
intraVeryProximalCount=0
interCount=0
discardCount=0
p_vals=[]
q_vals=[]
biasl=[]
biasr=[]
for line in infile:
ch1,mid1,ch2,mid2,contactCount=line.rstrip().split()
contactCount = float(contactCount)
interxn=myUtils.Interaction([ch1, int(mid1), ch2, int(mid2)])
interxn.setCount(contactCount)
mid1 = int(mid1); mid2 = int(mid2)
interactionType = interxn.getType(distLowThres,distUpThres)
bias1=1.0; bias2=1.0; # assumes there is no bias to begin with
# if the biasDic is not null sets the real bias values
if biasDic:
if ch1 in biasDic and mid1 in biasDic[ch1]:
bias1=biasDic[ch1][mid1]
if ch2 in biasDic and mid2 in biasDic[ch2]:
bias2=biasDic[ch2][mid2]
biasl.append(bias1)
biasr.append(bias2)
if (bias1<0 or bias2<0) and interactionType !='inter':
prior_p=1.0
p_val=1.0
discardCount+=1
elif interactionType=='intraInRange' and not interOnly:
distToLookUp=max(interxn.getDistance(),min(x))
distToLookUp=min(distToLookUp,max(x))
i=min(bisect.bisect_left(splineX, distToLookUp),len(splineX)-1)
prior_p=newSplineY[i]*(bias1*bias2)
p_val=scsp.bdtrc(interxn.getCount()-1,observedIntraInRangeSum,prior_p)
intraInRangeCount +=1
elif interactionType =='intraShort' and not interOnly:
prior_p=1.0
p_val=1.0
intraVeryProximalCount += 1
elif interactionType =='intraLong' and not interOnly:
prior_p=1.0
#p_val=scsp.bdtrc(interxn.getCount()-1, observedIntraAllSum,prior_p) ##RUNBY
p_val=1.0
intraOutOfRangeCount += 1
else:
if allReg or interOnly:
prior_p=interChrProb*(bias1*bias2)
p_val=scsp.bdtrc(interxn.getCount()-1,observedInterAllSum,prior_p)
interCount += 1
else:
p_val=1.0
#p_vals.append(p_val)
p_vals.append(p_val)
infile.close()
outlierThres = 0
# Do the BH FDR correction
if allReg:
outlierThres=1.0/(possibleIntraInRangeCount+possibleInterAllCount)
q_vals=myStats.benjamini_hochberg_correction(p_vals, possibleInterAllCount+possibleIntraInRangeCount)
elif interOnly and not allReg:
outlierThres = 1.0/possibleInterAllCount
q_vals=myStats.benjamini_hochberg_correction(p_vals, possibleInterAllCount)
else:
outlierThres = 1.0/possibleIntraInRangeCount
q_vals=myStats.benjamini_hochberg_correction(p_vals, possibleIntraInRangeCount)
print("Outlier threshold is... %s" % (outlierThres))
#now we write the values back to the file
infile =gzip.open(infilename, 'rt')
if resolution:
outfile =gzip.open(outfilename+'.res'+str(resolution)+'.significances.txt.gz', 'wt')
else:
outfile =gzip.open(outfilename+'.significances.txt.gz', 'wt')
print("Writing p-values and q-values to file %s" % (outfilename + ".significances.txt"))
outfile.write("chr1\tfragmentMid1\tchr2\tfragmentMid2\tcontactCount\tp-value\tq-value\tbias1\tbias2\n")
count=0
for line in infile:
words=line.rstrip().split()
chr1=words[0]
midPoint1=int(words[1])
chr2=words[2]
midPoint2=int(words[3])
interactionCount=float(words[4])
p_val=p_vals[count]
q_val=q_vals[count]
bias1=biasl[count]
bias2=biasr[count]
if (allReg or interOnly) and chr1!=chr2:
outfile.write("%s\t%d\t%s\t%d\t%d\t%e\t%e\t%e\t%e\n" % (str(chr1), midPoint1, str(chr2), midPoint2, interactionCount, p_val, q_val, bias1, bias2))
if (allReg or not interOnly) and chr1==chr2:
interactionDistance = abs(midPoint1-midPoint2)
if myUtils.in_range_check(interactionDistance,distLowThres, distUpThres):
outfile.write("%s\t%d\t%s\t%d\t%d\t%e\t%e\t%e\t%e\n" % (str(chr1), midPoint1, str(chr2), midPoint2, interactionCount, p_val, q_val, bias1, bias2))
if p_val<outlierThres:
outliersline.add(count)
outliersdist.add(abs(midPoint1-midPoint2))
count+=1
outfile.close()
infile.close()
if visual == True:
print("Plotting q-values to file %s" % outfilename + ".qplot.png")
minFDR=0.0
maxFDR=0.05
increment=0.001
FDRx,FDRy=plot_qvalues(q_vals,minFDR,maxFDR,increment,outfilename+".qplot")
with open(logfile, 'a') as log:
log.write("Spline successfully fit\n"),
log.write("\n"),
log.write("\n"),
return [splineX, newSplineY, residual, outliersline, outliersdist, FDRx, FDRy] # from fit_Spline
if "Auto" in datasets:
build_auto(TransformedTargetRegressor(DecisionTreeRegressor(random_state = 13)), "TransformedDecisionTreeAuto")
build_auto(TransformedTargetRegressor(LinearRegression(), func = numpy.log, inverse_func = numpy.exp), "TransformedLinearRegressionAuto")
def build_auto_isotonic(regressor, auto_isotonic_X, name):
pipeline = PMMLPipeline([
("regressor", regressor)
])
pipeline.fit(auto_isotonic_X, auto_y)
pipeline.verify(auto_isotonic_X.sample(frac = 0.05, random_state = 13))
store_pkl(pipeline, name)
mpg = DataFrame(pipeline.predict(auto_isotonic_X), columns = ["mpg"])
store_csv(mpg, name)
if "Auto" in datasets:
build_auto_isotonic(IsotonicRegression(increasing = True, out_of_bounds = "nan"), auto_X["acceleration"], "IsotonicRegressionIncrAuto")
build_auto_isotonic(IsotonicRegression(increasing = False, y_min = 12, y_max = 36, out_of_bounds = "clip"), auto_X["weight"], "IsotonicRegressionDecrAuto")
auto_train_mask = numpy.random.choice([False, True], size = (392,), p = [0.5, 0.5])
auto_test_mask = ~auto_train_mask
def build_auto_opt(regressor, name, fit_params = {}, **pmml_options):
pipeline = PMMLPipeline([
("regressor", regressor)
])
pipeline.fit(auto_X[auto_train_mask], auto_y[auto_train_mask], **fit_params)
if isinstance(regressor, XGBRegressor):
pipeline.verify(auto_X.sample(frac = 0.05, random_state = 13), precision = 1e-5, zeroThreshold = 1e-5)
else:
pipeline.verify(auto_X.sample(frac = 0.05, random_state = 13))
store_pkl(pipeline, name)
def run_train_all_sklearn(file, fp_name, cv=5, verbose=0, seed=1):
np.random.seed(seed)
c = defaultdict(list)
for k in ProgIter([
'synergy_zip', 'synergy_bliss', 'synergy_loewe', 'synergy_hsa',
'css_ri', 'name'
],
verbose=verbose,
total=5):
v = file[k]
if k != 'name':
temp = dict(
) # for results storage. Assuming that "name" comes last
if 'drug_row_col' in v.columns:
v.drop(columns=['drug_row_col'], inplace=True)
cat_cols = ['cell_line_name']
categories = [
v[column].unique() for column in v[cat_cols]
] # manually find all available categories for one-hot
# pipelines
encode = Pipeline(steps=[('one-hot-encode',
OneHotEncoder(categories=categories))])
processor = ColumnTransformer(transformers=[
('cat_encoding', encode, cat_cols), ('dropping', 'drop', [k])
],
remainder='passthrough')
catbst = ColumnTransformer(transformers=[('dropping', 'drop', [k])
],
remainder='passthrough')
# regressions
lr = make_pipeline(processor, linear_model.LinearRegression())
ridge = make_pipeline(processor, linear_model.Ridge())
lasso = make_pipeline(processor, linear_model.Lasso())
elastic = make_pipeline(processor, linear_model.ElasticNet())
lassolars = make_pipeline(processor, linear_model.LassoLars())
b_ridge = make_pipeline(processor, linear_model.BayesianRidge())
kernel = DotProduct() + WhiteKernel()
gpr = make_pipeline(processor,
GaussianProcessRegressor(kernel=kernel))
linSVR = make_pipeline(processor, LinearSVR())
hist_gbr = make_pipeline(
processor,
HistGradientBoostingRegressor(warm_start=True, max_depth=6))
rfr = make_pipeline(
processor,
RandomForestRegressor(warm_start=True, max_depth=6, n_jobs=3))
iso = make_pipeline(processor,
IsotonicRegression(increasing='auto'))
xgb = make_pipeline(
processor, XGBRegressor(tree_method='gpu_hist', max_depth=6))
cbt = make_pipeline(
catbst,
CatBoostRegressor(task_type='GPU',
depth=6,
cat_features=np.array([0]),
verbose=False))
mls = [
cbt, rfr, gpr, hist_gbr, lr, ridge, lasso, elastic, lassolars,
b_ridge, gpr, linSVR, iso
]
mls_names = [
"cbt", "rfr", "gpr", "hist_gbr", "lr", "ridge", "lasso",
"elastic", "lassolars", "b_ridge", "gpr", "linSVR", "iso"
]
# results
start = time.time()
for MODEL, name in zip(mls, mls_names):
print(f'\n{name}')
if 'cbt' == name:
n_jobs = 1
else:
n_jobs = cv
cv_dict = cross_validate(
MODEL,
v,
v[k],
cv=cv,
scoring={
"pearsonr": pearson,
"rmse": rmse
},
return_train_score=False,
verbose=verbose,
n_jobs=n_jobs,
)
temp[name] = {
'test_pearsonr': np.nanmean(cv_dict['test_pearsonr']),
'test_rmse': abs(np.nanmean(cv_dict['test_rmse']))
}
print(temp[name])
print(f'{k} took {int(time.time()-start)/60} mins')
c[k] = temp
else:
nm = f'/tf/notebooks/code_for_pub/_logs_as_python_files/{fp_name}_13models_5foldCV_{time.ctime()}.pickle'
with open(nm, 'wb') as file:
pickle.dump(c, file)
print(f'saving complete to {nm}')
return c
def __init__(self):
self.ir = IsotonicRegression(out_of_bounds="clip")
# ===============================================
SGDClf = linear_model.SGDClassifier(loss='modified_huber',penalty='l1')
LogicReg = linear_model.LogisticRegression(penalty='l1', C=1.0, n_jobs=4)
RidgeReg = linear_model.Ridge(alpha=1.0)
KernelRidge = KernelRidge(alpha=1.0, kernel="linear", gamma=None)
RANSACReg = linear_model.RANSACRegressor(linear_model.LinearRegression())
BayesReg = linear_model.BayesianRidge(n_iter=300,alpha_1=1.e-6,alpha_2=1.e-6,
lambda_1=1.e-6, lambda_2=1.e-6)
IsotonicReg = IsotonicRegression(y_min=None, y_max=None, increasing=True,
out_of_bounds='nan')
linear_SVC = svm.SVC(C=1.0, kernel='linear', decision_function_shape='ovr')
def createCLF(model):
model_str = str(model)
paras = model.get_params()
if 'SVC' in model_str:
return svm.SVC(C=paras['C'], kernel='linear', decision_function_shape='ovr')
if 'Logistic' in model_str:
C = paras['C']
penalty = paras['penalty']
return linear_model.LogisticRegression(C=C, penalty=penalty)
def lseErr(X, y, leafType):
def calibration_comparison(base_estimator,
n_samples,
weights=None,
n_bins=10,
detail=False):
X, y = make_classification(n_samples=3 * n_samples,
n_features=6,
random_state=42,
weights=weights)
base_estimator_dict = {
"MultinomialNB": MultinomialNB(),
"GaussianNB": GaussianNB(),
"SVC": LinearSVC()
}
if (base_estimator == "MultinomialNB"):
X -= X.min()
# Train data: train binary model.
X_train, y_train = X[:n_samples], y[:n_samples]
print("Positive Rate: {x}".format(x=y_train.mean()))
# calibrate data.
X_calib, y_calib = X[n_samples:2 * n_samples], y[n_samples:2 * n_samples]
# test data.
X_test, y_test = X[2 * n_samples:], y[2 * n_samples:]
# train the base estimator
clf = base_estimator_dict[base_estimator].fit(X_train, y_train)
if (base_estimator == "SVC"):
# y_calib_score: training in the calibration model.
y_calib_score = clf.decision_function(X_calib)
y_calib_score = (y_calib_score - y_calib_score.min()) /\
(y_calib_score.max() - y_calib_score.min())
# y_test_score: evaluation in the calibration model.
y_test_score = clf.decision_function(X_test)
y_test_score = (y_test_score - y_test_score.min()) /\
(y_test_score.max() - y_test_score.min())
else:
# y_calib_score: training in the calibration model.
y_calib_score = clf.predict_proba(X_calib)
y_calib_score = np.array([score[1] for score in y_calib_score])
# y_test_score: evaluation in the calibration model.
y_test_score = clf.predict_proba(X_test)
y_test_score = np.array([score[1] for score in y_test_score])
calibrate_model_dict = {
"mimic": _MimicCalibration(threshold_pos=5, record_history=False),
"isotonic": IsotonicRegression(y_min=0.0,
y_max=1.0,
out_of_bounds='clip'),
# "platt": LogisticRegression()
}
result = {}
result[base_estimator] = {}
for cal_name, cal_object in calibrate_model_dict.items():
# import pdb; pdb.set_trace()
print(cal_name)
cal_object.fit(copy(y_calib_score), copy(y_calib))
if cal_name in ["mimic", "isotonic"]:
y_output_score = cal_object.predict(copy(y_test_score))
else:
raise "Please specify probability prediction function."
frac_pos, predicted_value = calibration_curve(y_test,
y_output_score,
n_bins=n_bins)
b_score = brier_score_loss(y_test, y_output_score, pos_label=1)
# precsion = precision_score(y_test, y_output_score)
# recall = recall_score(y_test, y_output_score)
# f1 = f1_score(y_test, y_output_score)
result[base_estimator][cal_name] = {
"calibration_curve": [frac_pos, predicted_value],
# "eval_score" : [b_score, precsion, recall, f1]
"eval_score": [b_score]
}
if (detail):
result[base_estimator][cal_name]["detail"] = {
"y_test": y_test,
"y_test_calibrate_score": y_output_score
}
return result
y,
test_size=0.3,
random_state=42)
X_train, X_cv, y_train, y_cv = train_test_split(X_train,
y_train,
test_size=0.3,
random_state=42)
bins = 15
### fit naive bayes classifier
clf = GaussianNB()
clf.fit(X_train, y_train)
clf_proba = clf.predict_proba(X_cv)[:, 1]
### fit isotonic regression
isotonic_regression = IsotonicRegression(y_min=0, y_max=1, increasing=True)
isotonic_regression.fit(clf_proba, y_cv)
### predict probabilities
uncalibrated_prob = clf.predict_proba(X_test)[:, 1]
calibrated_prob = isotonic_regression.predict(uncalibrated_prob)
### compute score
logloss = log_loss(y_test, uncalibrated_prob)
roc = roc_auc_score(y_test, uncalibrated_prob)
calibrated_loss = log_loss(y_test, calibrated_prob)
calibrated_roc = roc_auc_score(y_test, calibrated_prob)
### plot calibration curve
plt.plot([0, 1], [0, 1], 'k:', label='Perfectly calibrated')
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
----------
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)
# ipdb.set_trace()
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 _smacof_with_anchors_single(config,
similarities,
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
----------
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
weights = np.ones((n_samples, n_samples))
if getattr(config, 'missingdata', None):
weights[-NO_OF_TAGS:, -NO_OF_TAGS:] = 0
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)
linear_regression.fit(visual_vector, conceptual_vector)
predictions = linear_regression.predict(visual_vector)
r2_linear = r2_score(conceptual_vector, predictions)
print("R² linear visual to conceptual:", r2_linear)
# compute least squares regression for R² metric: conceptual to visual
linear_regression = LinearRegression()
linear_regression.fit(conceptual_vector, visual_vector)
predictions = linear_regression.predict(conceptual_vector)
r2_linear = r2_score(visual_vector, predictions)
print("R² linear conceptual to visual:", r2_linear)
# compute isotonic regression for R² metric: visual to conceptual
x = np.reshape(visual_dissimilarities, (-1))
y = np.reshape(conceptual_dissimilarities, (-1))
isotonic_regression = IsotonicRegression()
predictions = isotonic_regression.fit_transform(x, y)
r2_isotonic = r2_score(y, predictions)
print("R² isotonic visual to conceptual:", r2_isotonic)
# compute isotonic regression for R² metric: visual to conceptual
x = np.reshape(conceptual_dissimilarities, (-1))
y = np.reshape(visual_dissimilarities, (-1))
isotonic_regression = IsotonicRegression()
predictions = isotonic_regression.fit_transform(x, y)
r2_isotonic = r2_score(y, predictions)
print("R² isotonic conceptual to visual:", r2_isotonic)
if args.plot:
# create scatter plot if user want us to
fig, ax = plt.subplots(figsize=(12, 12))
test_cases = [
(VotingClassifier([('logistic', LogisticRegression()),
('earth',
Pipeline([('earth', Earth()),
('logistic', LogisticRegression())]))],
'hard',
weights=[1.01, 1.01]), ['predict'],
create_weird_classification_problem_1()),
(GradientBoostingClassifier(max_depth=10,
n_estimators=10), ['predict_proba', 'predict'],
create_weird_classification_problem_1()),
(LogisticRegression(), ['predict_proba', 'predict'],
create_weird_classification_problem_1()),
(IsotonicRegression(out_of_bounds='clip'), ['predict'],
create_isotonic_regression_problem_1()),
(Earth(), ['predict', 'transform'], create_regression_problem_1()),
(Earth(allow_missing=True), ['predict', 'transform'],
create_regression_problem_with_missingness_1()),
(ElasticNet(), ['predict'], create_regression_problem_1()),
(ElasticNetCV(), ['predict'], create_regression_problem_1()),
(LassoCV(), ['predict'], create_regression_problem_1()),
(Ridge(), ['predict'], create_regression_problem_1()),
(RidgeCV(), ['predict'], create_regression_problem_1()),
(SGDRegressor(), ['predict'], create_regression_problem_1()),
(Lasso(), ['predict'], create_regression_problem_1()),
(Pipeline([('earth', Earth()), ('logistic', LogisticRegression())]),
['predict', 'predict_proba'], create_weird_classification_problem_1()),
(FeatureUnion([('earth', Earth()), ('earth2', Earth(max_degree=2))],
transformer_weights={
def __init__(self):
self.clf = IsotonicRegression(y_min=0.0,
y_max=1.0,
out_of_bounds='clip')
def _smacof_single(dissimilarities1,
dissimilarities2,
p,
weights1=None,
weights2=None,
metric=True,
n_components=2,
init1=None,
init2=None,
max_iter=300,
verbose=0,
eps=1e-3,
random_state1=None,
random_state2=None):
"""
Computes multidimensional scaling using SMACOF algorithm
Parameters
----------
dissimilarities : ndarray, shape (n_samples, n_samples)
Pairwise dissimilarities between the points. Must be symmetric.
metric : boolean, optional, default: True
Compute metric or nonmetric SMACOF algorithm.
n_components : int, optional, default: 2
Number of dimensions in which to immerse the dissimilarities. If an
``init`` array is provided, this option is overridden and the shape of
``init`` is used to determine the dimensionality of the embedding
space.
init : ndarray, shape (n_samples, n_components), optional, default: None
Starting configuration of the embedding to initialize the algorithm. By
default, the algorithm is initialized with a randomly chosen 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-3
Relative tolerance with respect to stress at which to declare
convergence.
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, shape (n_samples, n_components)
Coordinates of the 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
The number of iterations corresponding to the best stress.
"""
dissimilarities1 = check_symmetric(dissimilarities1, raise_exception=True)
dissimilarities2 = check_symmetric(dissimilarities2, raise_exception=True)
if dissimilarities1.shape != dissimilarities2.shape:
print("Error. Distance matrices have different shapes.")
sys.exit("Error. Distance matrices have different shapes.")
n_samples = dissimilarities1.shape[0]
X1, sim_flat1, sim_flat_w1 = initialize(dissimilarities1, random_state1,
init1, n_samples, n_components)
X2, sim_flat2, sim_flat_w2 = initialize(dissimilarities2, random_state2,
init2, n_samples, n_components)
#Default: equal weights
if weights1 is None:
weights1 = np.ones((n_samples, n_samples))
if weights2 is None:
weights2 = np.ones(n_samples)
# Disparity-specific weights (V in Borg)
V1 = np.zeros((n_samples, n_samples))
for i in range(n_samples):
diagonal = 0
for j in range(n_samples):
V1[i, j] = -weights1[i, j]
diagonal += weights1[i, j]
V1[i, i] = diagonal
# Locus-specific weights
V2 = np.zeros((n_samples, n_samples))
for i, weight in enumerate(weights2):
V2[i, i] = weight * p * n_samples
inv_V = moore_penrose(V1 + V2)
old_stress = None
ir = IsotonicRegression()
for it in range(max_iter):
# Compute distance and monotonic regression
dis1 = euclidean_distances(X1)
dis2 = euclidean_distances(X2)
if metric:
disparities1 = dissimilarities1
disparities2 = dissimilarities2
else:
disparities1 = nonmetric_disparities1(dis1, sim_flat1, n_samples)
disparities2 = nonmetric_disparities2(dis2, sim_flat2, n_samples)
# Compute stress
stress = ((dis1.ravel() - disparities1.ravel())**2).sum() + (
(dis2.ravel() - disparities2.ravel())**2
).sum() + n_samples * p * ssd(
X1, X2
) #multiply by n_samples to make ssd term comparable in magnitude to embedding error terms
# Update X1 using the Guttman transform
X1 = guttman(X1, X2, disparities1, inv_V, V2, dis1)
# Update X2 using the Guttman transform
X2 = guttman(X2, X1, disparities2, inv_V, V2, dis2)
# Test stress
dis1 = np.sqrt((X1**2).sum(axis=1)).sum()
dis2 = np.sqrt((X2**2).sum(axis=1)).sum()
dis = np.mean((dis1, dis2))
if verbose >= 2:
print('it: %d, stress %s' % (it, stress))
if old_stress is not None:
if np.abs(old_stress - stress / dis) < eps:
if verbose:
print('breaking at iteration %d with stress %s' %
(it, stress))
break
old_stress = stress / dis
return X1, X2, stress, it + 1
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 iso(self, axis=1, unk='No'):
# performs isotonic regression row-wise (axis = 0) or column-wise (axis = 1)
tonic = copy.deepcopy(self.array) # returns a new isotonic matrix
# either use a value for unknowns or just do isotonic with all present values
if unk == 0 or unk is None:
known_dict = self.known_for_iso(axis, unk)
else:
known_dict = None
# dat dict tells me where things arent increasing (from is_row_inc() or is_col_inc())
if axis == 1:
if known_dict is None:
for i in range(len(tonic[0])):
initial_vals = [tonic[j][i] for j in range(len(tonic))]
X = list(range(len(initial_vals)))
# Use the initial values to fit the model and then predict what the decreasing ones should be
iso = IsotonicRegression(out_of_bounds='clip').fit(
X, initial_vals)
predictions = iso.predict(range(len(tonic)))
# put everything back:
for row in range(len(predictions)):
tonic[row][i] = predictions[row]
else:
for i in range(len(tonic[0])):
X = known_dict[i]
initial_vals = [tonic[j][i] for j in X]
# Use the initial values to fit the model and then predict what the decreasing ones should be
iso = IsotonicRegression(out_of_bounds='clip').fit(
X, initial_vals)
predictions = iso.predict(range(len(tonic)))
# put everything back:
for row in range(len(predictions)):
tonic[row][i] = predictions[row]
else:
if known_dict is None:
for i in range(len(tonic)):
initial_vals = [tonic[i][j] for j in range(len(tonic[0]))]
X = list(range(len(initial_vals)))
# Use the initial values to fit the model and then predict what the decreasing ones should be
iso = IsotonicRegression(out_of_bounds='clip').fit(
X, initial_vals)
predictions = iso.predict(range(len(tonic)))
# put everything back:
tonic[i] = predictions
else:
for i in range(len(tonic)):
X = known_dict[i]
initial_vals = [tonic[i][j] for j in X]
# Use the initial values to fit the model and then predict what the decreasing ones should be
iso = IsotonicRegression(out_of_bounds='clip').fit(
X, initial_vals)
predictions = iso.predict(range(len(tonic)))
# put everything back:
tonic[i] = predictions
newframe = pd.DataFrame(tonic)
newframe.columns = self.dataframe.columns
newframe.index = self.dataframe.index
return mat_opr(newframe)
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
def find_regions(t,
x,
minimum_datapoints=10,
mu_factor=0.7,
low_density_factor=0.01):
"""Finds clean regions of gradual growth between jump events.
Args:
t (1D numpy.array): clean time points
x (1D numpy.array): cleaned log-OD series (same shape as `t`)
minimum_datapoints (int): regions must have at least this many data points
mu_factor (float): the linear fit is tempered by this factor before isotonic regression
Low values (0.0..0.5) can result in missing jump events.
High values (0.8..1.0) can result in oversegmentation, i.e. false jump events
Returns:
numpy.array: list of start indexes for the regions
numpy.array: list of end indexes (inclusive) for the regions
"""
# find gaps in the data
avg_dt = (t[-1] - t[0]) / (len(t) - 1)
gap_start_idexes = np.where(np.diff(t) > avg_dt / low_density_factor)[0]
# build initial set of regions from these gaps
s_raw = [0]
e_raw = []
for gap_idx in gap_start_idexes:
e_raw.append(gap_idx)
s_raw.append(gap_idx + 1)
e_raw.append(len(t) - 1)
regions_to_investigate = list(zip(s_raw, e_raw))
s = []
e = []
while len(regions_to_investigate) > 0:
# pick a new region
start_idx, end_idx = regions_to_investigate.pop()
# check that there are at least a minimum number of datapoints
if end_idx - start_idx + 1 < minimum_datapoints:
continue
# find optimal drift
t_region = t[start_idx:end_idx + 1]
x_region = x[start_idx:end_idx + 1]
mu_min = LinearRegression(fit_intercept=True) \
.fit(t_region.reshape([-1, 1]),
x_region) \
.coef_
# fit monotonic function
x_drifting = x_region - t_region * mu_min * mu_factor
iso_reg = IsotonicRegression(increasing=False) \
.fit(t_region, x_drifting)
x_segmented = iso_reg.predict(t_region)
# find jumps
jump_indexes = np.where(np.diff(x_segmented) < 0)[0] + start_idx
if len(jump_indexes) > 0:
# if found, add the sub-regions to the list of new regions
start_indexes = [start_idx]
end_indexes = []
for jump_idx in jump_indexes:
end_indexes.append(jump_idx)
start_indexes.append(jump_idx + 1)
end_indexes.append(end_idx)
for start_idx, end_idx in zip(start_indexes, end_indexes):
regions_to_investigate.append((start_idx, end_idx))
else:
# if no subregions are found, add regions to final set
s.append(start_idx)
e.append(end_idx)
s.sort()
e.sort()
return np.array(s), np.array(e)
def train_models(orig_vector_prediction_matrix,
orig_scalar_prediction_matrix,
vector_target_matrix,
scalar_target_matrix,
separate_by_height=True):
"""Trains isotonic-regression models.
E = number of examples
H = number of heights
T_v = number of vector target variables
T_s = number of scalar target variables
:param orig_vector_prediction_matrix: numpy array (E x H x T_v) of predicted
values for vector target variables.
:param orig_scalar_prediction_matrix: numpy array (E x T_s) of predicted
values for scalar target variables.
:param vector_target_matrix: numpy array (E x H x T_v) of actual values
for vector target variables.
:param scalar_target_matrix: numpy array (E x T_s) of actual values for
scalar target variables.
:param separate_by_height: Boolean flag. If True, will train one model for
each target variable (channel). If False, will train one model for each
pair of target variable and height.
:return: scalar_model_objects: List (length T_s) of models (instances of
`sklearn.isotonic.IsotonicRegression`) for scalar target variables.
:return: vector_model_object_matrix: numpy array (H x T_v) of models
(instances of `sklearn.isotonic.IsotonicRegression`) for vector target
variables. If `separate_by_height == True`, this array is H x T_v.
If `separate_by_height == False`, this array has length T_v.
"""
# Check input args.
num_examples = None
num_heights = 0
num_vector_targets = 0
num_scalar_targets = 0
have_vectors = (orig_vector_prediction_matrix is not None
or vector_target_matrix is not None)
if have_vectors:
error_checking.assert_is_numpy_array(orig_vector_prediction_matrix,
num_dimensions=3)
error_checking.assert_is_numpy_array_without_nan(
orig_vector_prediction_matrix)
error_checking.assert_is_numpy_array(
vector_target_matrix,
exact_dimensions=numpy.array(orig_vector_prediction_matrix.shape,
dtype=int))
error_checking.assert_is_numpy_array_without_nan(vector_target_matrix)
num_examples = vector_target_matrix.shape[0]
num_heights = vector_target_matrix.shape[1]
num_vector_targets = vector_target_matrix.shape[2]
have_scalars = (orig_scalar_prediction_matrix is not None
or scalar_target_matrix is not None)
if have_scalars:
error_checking.assert_is_numpy_array(orig_scalar_prediction_matrix,
num_dimensions=2)
if num_examples is None:
num_examples = orig_scalar_prediction_matrix.shape[0]
expected_dim = numpy.array(
[num_examples, orig_scalar_prediction_matrix.shape[1]], dtype=int)
error_checking.assert_is_numpy_array(orig_scalar_prediction_matrix,
exact_dimensions=expected_dim)
error_checking.assert_is_numpy_array_without_nan(
orig_scalar_prediction_matrix)
error_checking.assert_is_numpy_array(
scalar_target_matrix,
exact_dimensions=numpy.array(orig_scalar_prediction_matrix.shape,
dtype=int))
error_checking.assert_is_numpy_array_without_nan(scalar_target_matrix)
num_scalar_targets = scalar_target_matrix.shape[1]
error_checking.assert_is_boolean(separate_by_height)
# Do actual stuff.
scalar_model_objects = [None] * num_scalar_targets
num_modeling_heights = num_heights if separate_by_height else 1
vector_model_object_matrix = numpy.full(
(num_modeling_heights, num_vector_targets), '', dtype=object)
for k in range(num_scalar_targets):
print(
('Training isotonic-regression model for {0:d}th of {1:d} scalar '
'target variables...').format(k + 1, num_scalar_targets))
scalar_model_objects[k] = IsotonicRegression(increasing=True,
out_of_bounds='clip')
scalar_model_objects[k].fit(X=orig_scalar_prediction_matrix[:, k],
y=scalar_target_matrix[:, k])
if num_scalar_targets > 0:
print('\n')
for k in range(num_vector_targets):
for j in range(num_modeling_heights):
print((
'Training isotonic-regression model for {0:d}th of {1:d} vector'
' target variables at {2:d}th of {3:d} modeling heights...'
).format(k + 1, num_vector_targets, j + 1, num_modeling_heights))
vector_model_object_matrix[j, k] = IsotonicRegression(
increasing=True, out_of_bounds='clip')
if separate_by_height:
vector_model_object_matrix[j, k].fit(
X=orig_vector_prediction_matrix[:, j, k],
y=vector_target_matrix[:, j, k])
else:
vector_model_object_matrix[j, k].fit(
X=numpy.ravel(orig_vector_prediction_matrix[..., k]),
y=numpy.ravel(vector_target_matrix[..., k]))
if k != num_vector_targets - 1:
print('\n')
return scalar_model_objects, vector_model_object_matrix
def test_isotonic_regression_reversed():
y = np.array([10, 9, 10, 7, 6, 6.1, 5])
y_ = IsotonicRegression(increasing=False).fit_transform(
np.arange(len(y)), y)
assert_array_equal(np.ones(y_[:-1].shape), ((y_[:-1] - y_[1:]) >= 0))
def __init__(self, add_one=False):
self.add_one = add_one
self._ir = IsotonicRegression()
def distance_law(matrix,
detectable_bins=None,
max_dist=None,
smooth=True,
fun=np.nanmean):
"""
Computes genomic distance law by averaging over each diagonal in the upper
triangle matrix. If a list of detectable bins is provided, pixels in
missing bins will be excluded from the averages. A maximum distance can be
specified to define how many diagonals should be computed.
parameters
----------
matrix: scipy.sparse.csr_matrix
the input matrix to compute distance law from.
detectable_bins : numpy.ndarray of ints
An array of detectable bins indices to consider when computing
distance law.
max_dist : int
Maximum distance from diagonal, in number of bins in which to compute
distance law
smooth : bool
Whether to use isotonic regression to smooth the distance law.
fun : callable
A function to apply on each diagonal. Defaults to mean.
Returns
-------
dist: np.ndarray
the output genomic distance law.
example
-------
>>> m = np.ones((3,3))
>>> m += np.array([1,2,3])
>>> m
array([[2., 3., 4.],
[2., 3., 4.],
[2., 3., 4.]])
>>> distance_law(csr_matrix(m))
array([3. , 3.5, 4. ])
"""
mat_n = matrix.shape[0]
if max_dist is None:
max_dist = mat_n
n_diags = min(mat_n, max_dist + 1)
dist = np.zeros(mat_n)
if detectable_bins is None:
detectable_bins = np.array(range(mat_n))
for diag in range(n_diags):
# Find detectable which fall in diagonal
detect_mask = np.zeros(mat_n, dtype=bool)
detect_mask[detectable_bins] = 1
# Find bins which are detectable in the diagonal (intersect of
# hori and verti)
detect_mask_h = detect_mask[:(mat_n - diag)]
detect_mask_v = detect_mask[mat_n - (mat_n - diag):]
detect_mask_diag = detect_mask_h & detect_mask_v
detect_diag = matrix.diagonal(diag)[detect_mask_diag]
dist[diag] = fun(detect_diag[detect_diag > 0])
# Smooth the curve using isotonic regression: Find closest approximation
# with the condition that point n+1 cannot be higher than point n.
# (i.e. contacts can only decrease when increasing distance)
if smooth and mat_n > 2:
ir = IsotonicRegression(increasing=False)
dist[~np.isfinite(dist)] = 0
dist = ir.fit_transform(range(len(dist)), dist)
return dist
def fit_spline(mainDic, x, y, yerr, infilename, outfilename, biasDic,
resolution, min_dist, max_dist, verbose):
if verbose:
print("\nFit a univariate spline to the probability means\n"),
print(
"------------------------------------------------------------------------------------\n"
),
# maximum residual allowed for spline is set to min(y)^2
splineError = min(y)**2
# use fitpack2 method -fit on the real x and y from equal occupancy binning
ius = UnivariateSpline(x, y, s=splineError)
#### POST-PROCESS THE SPLINE TO MAKE SURE IT'S NON-INCREASING
### NOW I DO THIS BY CALLING A SKLEARN ISOTONIC REGRESSION
### This does the isotonic regression using option antitonic to make sure
### I get monotonically decreasing probabilites with increasion genomic distance
min_x, max_x = min(x), max(x)
tempList = sorted([dis for dis in mainDic])
splineX = []
### The below for loop will make sure nothing is out of range of [min(x) max(x)]
### Therefore everything will be within the range where the spline is defined
for i in tempList:
if min_x <= i <= max_x:
splineX.append(i)
splineY = ius(splineX)
ir = IsotonicRegression(increasing=False)
rNewSplineY = ir.fit_transform(splineX, splineY)
newSplineY = []
diff = []
diffX = []
for i in range(len(rNewSplineY)):
newSplineY.append(rNewSplineY[i])
if (splineY[i] - newSplineY[i]) > 0:
diff.append(splineY[i] - newSplineY[i])
diffX.append(splineX[i])
### Now newSplineY holds the monotonic contact probabilities
residual = sum([i * i for i in (y - ius(x))])
### Now plot the results
plt.clf()
fig = plt.figure()
ax = fig.add_subplot(2, 1, 1)
plt.title(
'Univariate spline fit to the output of equal occupancy binning. \n Residual= %e'
% (residual),
size='small')
plt.plot([i / 1000.0 for i in x], [i * 100000 for i in y],
'ro',
label="Means")
plt.plot([i / 1000.0 for i in splineX], [i * 100000 for i in newSplineY],
'g-',
label="Spline fit")
plt.ylabel('Probability (1e-5)')
plt.xlabel('Genomic distance (kb)')
plt.xlim([min_x / 1000.0, max_x / 1000.0])
ax.legend(loc="upper right")
ax = fig.add_subplot(2, 1, 2)
plt.loglog(splineX, newSplineY, 'g-')
plt.loglog(x, y, 'r.') # Data
plt.ylabel('Probability (log scale)')
plt.xlabel('Genomic distance (log scale)')
plt.xlim([min_x, max_x])
plt.savefig(outfilename + '.res' + str(resolution) + '.png')
sys.stderr.write("Plotting %s" % outfilename + ".png\n")
# NOW write the calculated pvalues and corrected pvalues in a file
intraInRangeCount = 0
intraOutOfRangeCount = 0
intraVeryProximalCount = 0
interCount = 0
discardCount = 0
if verbose:
print("lower bound on mid-range distances " + repr(min_dist) +
", upper bound on mid-range distances " + repr(max_dist) +
"\n"),
with gzip.open(infilename, 'r') as infile:
with gzip.open(
'{}.res{}.significances.txt.gz'.format(outfilename,
resolution),
'w') as outfile:
outfile.write(
"chr1\tfragmentMid1\tchr2\tfragmentMid2\tcontactCount\tp-value\tq-value\n"
)
for line in infile:
chr1, mid1, chr2, mid2, contactCount = line.rstrip().split()
mid1, mid2, contactCount = int(mid1), int(mid2), int(
contactCount)
distance = mid2 - mid1
bias1 = 1.0
bias2 = 1.0
# assumes there is no bias to begin with
# if the biasDic is not null sets the real bias values
if len(biasDic) > 0:
if chr1 in biasDic and mid1 in biasDic[chr1]:
bias1 = biasDic[chr1][mid1]
if chr2 in biasDic and mid2 in biasDic[chr2]:
bias2 = biasDic[chr2][mid2]
if min_dist <= distance <= max_dist:
# make sure the interaction distance is covered by the probability bins
distToLookUp = min(max(distance, min_x), max_x)
i = min(bisect.bisect_left(splineX, distToLookUp),
len(splineX) - 1)
prior_p = newSplineY[i] * (bias1 * bias2
) # biases added in the picture
p_val = scsp.bdtrc(contactCount - 1,
observedIntraInRangeSum, prior_p)
if p_val <= 1:
outfile.write("{}\t{}\t{}\t{}\t{}\t{}\t{}\n".format(
chr1, mid1, chr2, mid2, contactCount, p_val, -1))
return splineX, newSplineY, residual
def fit_curve(x, y):
curve = IsotonicRegression(increasing=False)
curve.fit(x, y)
return curve
def compute(self) -> float:
"""
This method allows to compute multiple stress functions:
* Kruskal stress https://www.researchgate.net/publication/24061688_Nonmetric_multidimensional_scaling_A_numerical_method
* S stress http://gifi.stat.ucla.edu/janspubs/1977/articles/takane_young_deleeuw_A_77.pdf
* Sammon stress http://ieeexplore.ieee.org/document/1671271/?reload=true
* Quadratic Loss
Source: https://github.com/flowersteam/Unsupervised_Goal_Space_Learning/blob/master/src/embqual.py.
:return: Stress measure.
"""
# We retrieve dimensions of the data
n, m = self._low_dimensional_data.shape
# We compute distance matrices in both spaces
if self._use_geodesic_distances:
k: int = 2
is_connex: bool = False
while is_connex is False:
knn = sklearn.neighbors.NearestNeighbors(n_neighbors=k)
knn.fit(self._low_dimensional_data)
M = knn.kneighbors_graph(self._low_dimensional_data,
mode='distance')
graph = networkx.from_scipy_sparse_matrix(M)
is_connex = networkx.is_connected(graph)
k += 1
s_uni_distances = networkx.all_pairs_dijkstra_path_length(
graph, cutoff=None, weight='weight')
s_all_distances = np.array([
np.array(a.items())[:, 1]
for a in np.array(s_uni_distances.items())[:, 1]
])
s_all_distances = (s_all_distances + s_all_distances.T) / 2
s_uni_distances = scipy.spatial.distance.squareform(
s_all_distances)
s_all_distances = s_all_distances.ravel()
else:
s_uni_distances = scipy.spatial.distance.pdist(
self._low_dimensional_data)
s_all_distances = scipy.spatial.distance.squareform(
s_uni_distances).ravel()
l_uni_distances = scipy.spatial.distance.pdist(self._target_data)
l_all_distances = scipy.spatial.distance.squareform(
l_uni_distances).ravel()
# We set up the measure dict
measures = dict()
# 1. Quadratic Loss
# measures['quadratic_loss'] = numpy.square(s_uni_distances - l_uni_distances).sum()
# 2. Sammon stress
# measures['sammon_stress'] = (1 / s_uni_distances.sum()) * (
# numpy.square(s_uni_distances - l_uni_distances) / s_uni_distances
# ).sum()
# 3. S stress
# measures['s_stress'] = numpy.sqrt((1 / n) * (
# numpy.square(
# (numpy.square(s_uni_distances) - numpy.square(l_uni_distances)).sum()
# ) / numpy.power(s_uni_distances, 4)
# )).sum()
# 4. Kruskal stress
# We reorder the distances under the order of distances in latent space
s_all_distances: np.ndarray = s_all_distances[
l_all_distances.argsort()]
l_all_distances: np.ndarray = l_all_distances[
l_all_distances.argsort()]
# We perform the isotonic regression
iso: IsotonicRegression = IsotonicRegression()
s_iso_distances: np.ndarray = iso.fit_transform(
s_all_distances, l_all_distances)
# We compute the kruskal stress.
measures['kruskal_stress'] = np.sqrt(
np.square(s_iso_distances - l_all_distances).sum() /
np.square(l_all_distances).sum())
# Pick Kruskal's stress here. Best choices amongst Sammon, S, Kruskal, quadratic loss?
return measures['kruskal_stress']
