def plot_regression(F, Ybreaks=None):
assert F.d == 2
X = F.marginals[0]
Y = F.marginals[1]
if Ybreaks is None:
Ybreaks = Y.get_piecewise_pdf().getBreaks()
def cond_pdf(F, Xpdf, x, y):
if not isscalar(y):
x = zeros_like(y) + x
return F.pdf(x, y) / Xpdf
def regfun(type, x):
# value of regression functions at point x
if isscalar(x):
Xpdf = float(X.pdf(x))
if Xpdf == 0:
y = NaN
else:
distr = FunDistr(fun=partial(cond_pdf, F, Xpdf, x),
breakPoints=Ybreaks)
if type == 1: y = distr.mean()
if type == 2: y = distr.median()
if type == 3: y = distr.mode()
if y is None:
y = NaN
else:
y = zeros_like(x)
for i in range(len(x)):
y[i] = regfun(type, x[i])
return y
F.contour()
Xbreaks = X.get_piecewise_pdf().getBreaks()
Xbreaks = concatenate([Xbreaks, [F.a[0], F.b[0]]])
Xbreaks.sort()
Xbreaks = epsunique(Xbreaks)
mreg = PiecewiseFunction(fun=partial(regfun, 1),
breakPoints=Xbreaks).toInterpolated()
mreg.plot(label="mean")
mreg = PiecewiseFunction(fun=partial(regfun, 2),
breakPoints=Xbreaks).toInterpolated()
mreg.plot(label="median", color="g")
mreg = PiecewiseFunction(fun=partial(regfun, 3),
breakPoints=Xbreaks).toInterpolated()
mreg.plot(label="mode", color="r")
legend()
def plot_regression(F, Ybreaks = None):
assert F.d == 2
X = F.marginals[0]
Y = F.marginals[1]
if Ybreaks is None:
Ybreaks = Y.get_piecewise_pdf().getBreaks()
def cond_pdf(F, Xpdf, x, y):
if not isscalar(y):
x = zeros_like(y) + x
return F.pdf(x, y) / Xpdf
def regfun(type, x):
# value of regression functions at point x
if isscalar(x):
Xpdf = float(X.pdf(x))
if Xpdf == 0:
y = NaN
else:
distr = FunDistr(fun = partial(cond_pdf, F, Xpdf, x),
breakPoints = Ybreaks)
if type==1: y = distr.mean()
if type==2: y = distr.median()
if type==3: y = distr.mode()
if y is None:
y = NaN
else:
y = zeros_like(x)
for i in range(len(x)):
y[i] = regfun(type, x[i])
return y
F.contour()
Xbreaks = X.get_piecewise_pdf().getBreaks()
Xbreaks = concatenate([Xbreaks, [F.a[0], F.b[0]]])
Xbreaks.sort()
Xbreaks = epsunique(Xbreaks)
mreg = PiecewiseFunction(fun=partial(regfun, 1), breakPoints=Xbreaks).toInterpolated()
mreg.plot(label = "mean")
mreg = PiecewiseFunction(fun=partial(regfun, 2), breakPoints=Xbreaks).toInterpolated()
mreg.plot(label = "median", color = "g")
mreg = PiecewiseFunction(fun=partial(regfun, 3), breakPoints=Xbreaks).toInterpolated()
mreg.plot(label = "mode", color = "r")
legend()
def convmean(F, G, p=0.5, q=0.5, theta=1.0):
"""Probabilistic weighted mean of f and g
"""
f = F.get_piecewise_pdf()
g = G.get_piecewise_pdf()
if p + q <> 1.0:
p1 = abs(p) / (abs(p) + abs(q))
q = abs(q) / (abs(p) + abs(q))
p = p1
if q == 0:
return f
bf = f.getBreaks()
bg = g.getBreaks()
b = add.outer(bf * p, bg * q)
fun = lambda x: convmeanx(F, G, segList, x, p, q, theta=theta)
ub = epsunique(b)
fg = PiecewiseDistribution([])
op = lambda x, y: p * x + q * y
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] - 1, op)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, op)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[0:-1]
for i in range(len(ub) - 1):
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, op)
seg = Segment(ub[i], ub[i + 1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
fg_discr = convdiracs(f, g, fun=lambda x, y: x * p + y * q)
for seg in fg_discr.getDiracs():
fg.addSegment(seg)
return fg
def convmean(F, G, p=0.5, q=0.5, theta=1.0):
"""Probabilistic weighted mean of f and g
"""
f = F.get_piecewise_pdf()
g = G.get_piecewise_pdf()
if p + q != 1.0 :
p1 = abs(p) / (abs(p) + abs(q))
q = abs(q) / (abs(p) + abs(q))
p = p1;
if q == 0:
return f;
bf = f.getBreaks()
bg = g.getBreaks()
b = add.outer(bf * p, bg * q)
fun = lambda x : convmeanx(F, G, segList, x, p, q, theta=theta)
ub = epsunique(b)
fg = PiecewiseDistribution([]);
op = lambda x, y : p * x + q * y;
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] - 1, op)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, op)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[0:-1]
for i in range(len(ub) - 1) :
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, op)
seg = Segment(ub[i], ub[i + 1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
fg_discr = convdiracs(f, g, fun=lambda x, y : x * p + y * q)
for seg in fg_discr.getDiracs():
fg.addSegment(seg)
return fg
