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np_tools.py
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np_tools.py
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import numpy as np
import KernelFunctions as kf
import scipy.optimize as opt
from scipy.integrate import *
kernel_func = dict(wangryzin=kf.WangRyzin, aitchisonaitken=kf.AitchisonAitken,
epanechnikov=kf.Epanechnikov, gaussian=kf.Gaussian,
gauss_convolution=kf.Gaussian_Convolution,
wangryzin_convolution=kf.WangRyzin_Convolution,
aitchisonaitken_convolution=kf.AitchisonAitken_Convolution)
Convolution_Kernels = dict(gauss_convolution=kf.Gaussian_Convolution,
wangryzin_convolution=kf.WangRyzin_Convolution)
def IntegrateSingle(val, pdf):
f1 = lambda x: pdf(edat=np.asarray(x))
return quad(f1, -np.Inf, val)[0]
def IntegrateDbl(val, pdf):
f2 = lambda x, y: pdf(edat=np.asarray([y, x]))
return dblquad(f2, -np.Inf, val[0], lambda x: -np.Inf, lambda x: val[1])[0]
class LeaveOneOut(object):
# Written by Skipper
"""
Generator to give leave one out views on X
Parameters
----------
X : array-like
2d array
Examples
--------
>>> X = np.random.normal(0,1,[10,2])
>>> loo = LeaveOneOut(X)
>>> for x in loo:
... print x
Notes
-----
A little lighter weight than sklearn LOO. We don't need test index.
Also passes views on X, not the index.
"""
def __init__(self, X):
self.X = np.asarray(X)
def __iter__(self):
X = self.X
N, K = np.shape(X)
for i in xrange(N):
index = np.ones(N, dtype=np.bool)
index[i] = False
yield X[index, :]
def GPKE(bw, tdat, edat, var_type, ckertype='gaussian',
okertype='wangryzin', ukertype='aitchisonaitken'):
"""
Returns the non-normalized Generalized Product Kernel Estimator
Parameters
----------
bw: array-like
The user-specified bandwdith parameters
tdat: 1D or 2d array
The training data
edat: 1d array
The evaluation points at which the kernel estimation is performed
var_type: str
The variable type (continuous, ordered, unordered)
ckertype: str
The kernel used for the continuous variables
okertype: str
The kernel used for the ordered discrete variables
ukertype: str
The kernel used for the unordered discrete variables
"""
var_type = np.asarray(list(var_type))
iscontinuous = np.where(var_type == 'c')[0]
isordered = np.where(var_type == 'o')[0]
isunordered = np.where(var_type == 'u')[0]
K = len(var_type)
edat = np.asarray(edat)
edat = np.squeeze(edat)
## if tdat.ndim > 1:
## N, K = np.shape(tdat)
## else:
## K = 1
## N = np.shape(tdat)[0]
## tdat = tdat.reshape([N, K])
if tdat.ndim == 1 and K == 1: # one variable many observations
N = np.size(tdat)
#N_edat = np.size(edat)
elif tdat.ndim == 1 and K > 1:
N = 1
else:
N, K = np.shape(tdat)
tdat = tdat.reshape([N, K])
## if edat.ndim > 1:
## N_edat = np.shape(edat)[0]
## else:
## N_edat = 1
## edat = edat.reshape([N_edat, K])
if edat.ndim == 1 and K > 1: # one obs many vars
N_edat = 1
elif edat.ndim == 1 and K == 1: # one obs one var
N_edat = np.size(edat)
else:
N_edat = np.shape(edat)[0] # ndim >1 so many obs many vars
assert np.shape(edat)[1] == K
edat = edat.reshape([N_edat, K])
bw = np.reshape(np.asarray(bw), (K,)) # must remain 1-D for indexing to work
dens = np.empty([N_edat, 1])
for i in xrange(N_edat):
Kval = np.concatenate((
kernel_func[ckertype](bw[iscontinuous], tdat[:, iscontinuous], edat[i, iscontinuous]),
kernel_func[okertype](bw[isordered], tdat[:, isordered], edat[i, isordered]),
kernel_func[ukertype](bw[isunordered], tdat[:, isunordered], edat[i, isunordered])
), axis=1)
dens[i] = np.sum(np.prod(Kval, axis=1)) * 1. / (np.prod(bw[iscontinuous]))
return dens
def GPKE2(bw, tdat, edat, var_type, ckertype='gaussian',
okertype='wangryzin', ukertype='aitchisonaitken'):
"""
Returns the non-normalized Generalized Product Kernel Estimator
Parameters
----------
bw: array-like
The user-specified bandwdith parameters
tdat: 1D or 2d array
The training data
edat: 1d array
The evaluation points at which the kernel estimation is performed
var_type: str
The variable type (continuous, ordered, unordered)
ckertype: str
The kernel used for the continuous variables
okertype: str
The kernel used for the ordered discrete variables
ukertype: str
The kernel used for the unordered discrete variables
"""
var_type = np.asarray(list(var_type))
iscontinuous = np.where(var_type == 'c')[0]
isordered = np.where(var_type == 'o')[0]
isunordered = np.where(var_type == 'u')[0]
K = len(var_type)
edat = np.asarray(edat)
edat = np.squeeze(edat)
if tdat.ndim == 1 and K == 1: # one variable many observations
N = np.size(tdat)
#N_edat = np.size(edat)
elif tdat.ndim == 1 and K > 1:
N = 1
else:
N, K = np.shape(tdat)
tdat = tdat.reshape([N, K])
if edat.ndim == 1 and K > 1: # one obs many vars
N_edat = 1
elif edat.ndim == 1 and K == 1: # one obs one var
N_edat = np.size(edat)
else:
N_edat = np.shape(edat)[0] # ndim >1 so many obs many vars
assert np.shape(edat)[1] == K
edat = edat.reshape([N_edat, K])
bw = np.reshape(np.asarray(bw), (K, )) # must remain 1-D for indexing to work
# dens = np.empty([N, 1])
for i in xrange(N_edat):
Kval = np.concatenate((
kernel_func[ckertype](bw[iscontinuous], tdat[:, iscontinuous], edat[i, iscontinuous]),
kernel_func[okertype](bw[isordered], tdat[:, isordered], edat[i, isordered]),
kernel_func[ukertype](bw[isunordered], tdat[:, isunordered], edat[i, isunordered])
), axis=1)
dens = np.prod(Kval, axis=1) * 1. / (np.prod(bw[iscontinuous]))
return dens
def GPKE3(bw, tdat, edat, var_type, ckertype='gaussian',
okertype='wangryzin', ukertype='aitchisonaitken'):
# Rename !
var_type = np.asarray(list(var_type))
iscontinuous = np.where(var_type == 'c')[0]
isordered = np.where(var_type == 'o')[0]
isunordered = np.where(var_type == 'u')[0]
K = len(var_type)
edat = np.asarray(edat)
edat = np.squeeze(edat)
if tdat.ndim == 1 and K == 1: # one variable many observations
N = np.size(tdat)
#N_edat = np.size(edat)
elif tdat.ndim == 1 and K > 1:
N = 1
else:
N, K = np.shape(tdat)
tdat = tdat.reshape([N, K])
if edat.ndim == 1 and K > 1: # one obs many vars
N_edat = 1
elif edat.ndim == 1 and K == 1: # one obs one var
N_edat = np.size(edat)
else:
N_edat = np.shape(edat)[0] # ndim >1 so many obs many vars
assert np.shape(edat)[1] == K
edat = edat.reshape([N_edat, K])
bw = np.reshape(np.asarray(bw), (K, )) # must remain 1-D for indexing to work
# dens = np.empty([N, 1])
Kval = np.concatenate((
kernel_func[ckertype](bw[iscontinuous], tdat[:, iscontinuous], edat[:, iscontinuous]),
kernel_func[okertype](bw[isordered], tdat[:, isordered], edat[:, isordered]),
kernel_func[ukertype](bw[isunordered], tdat[:, isunordered], edat[:, isunordered])
), axis=1)
dens = np.prod(Kval, axis=1) * 1. / (np.prod(bw[iscontinuous]))
return dens