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Merged
weikang9009 merged 28 commits into from
Jul 18, 2019
Merged

Gsoc19 - updates for Poisson and Binomial MGWR #60

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4ad7706
adding a univariate example for Poisson MGWR
mehak-sachdeva Jun 18, 2019
09ef414
adding important equations for reference
mehak-sachdeva Jun 18, 2019
3ed2f41
minor error update
mehak-sachdeva Jun 18, 2019
edf4bcf
cleaning
mehak-sachdeva Jun 18, 2019
f3c957b
adding the notebook for Binomial MGWR model
mehak-sachdeva Jun 18, 2019
e44555b
changes to accomodate Poisson and Binomial MGWR
mehak-sachdeva Jun 19, 2019
2c2edc3
changes to accomodate Poisson and Binomial MGWR
mehak-sachdeva Jun 19, 2019
48b9766
Merge remote-tracking branch 'upstream/master' into multi_bw_changes
mehak-sachdeva Jun 22, 2019
ac981d7
fixed merge conflicts
mehak-sachdeva Jun 22, 2019
279f518
fixing MGWR init error
mehak-sachdeva Jun 24, 2019
0dc24c3
moving binomial edits to other branch
mehak-sachdeva Jun 25, 2019
0167b26
binomial_mgwr_updates
mehak-sachdeva Jun 27, 2019
b487e6e
real data example notebook Poisson-MGWR
mehak-sachdeva Jun 27, 2019
f0cda34
copying simulated data example to this branch
mehak-sachdeva Jun 27, 2019
bdf6259
adding notebook for Binomial MGWR discussion
mehak-sachdeva Jun 27, 2019
fec7f95
updates to Poisson notebooks and adding Binomial notebooks for discus…
mehak-sachdeva Jul 4, 2019
6ee25bf
Poisson monte carlo script for reference
mehak-sachdeva Jul 4, 2019
0872fdc
adding Poisson Monte Carlo results notebook
mehak-sachdeva Jul 4, 2019
b92c1b5
adding result objects folder
mehak-sachdeva Jul 8, 2019
ff2eab5
changing inference calculations for Poisson MGWR
mehak-sachdeva Jul 16, 2019
db116e1
cleaning
mehak-sachdeva Jul 16, 2019
775d4ee
adding parameters to MC design for Poisson MGWR
mehak-sachdeva Jul 16, 2019
2614cb6
second try for inference - Poisson MGWR
mehak-sachdeva Jul 17, 2019
5d2a607
cleaning
mehak-sachdeva Jul 18, 2019
488783d
adding mega notebook for Poisson MGWR
mehak-sachdeva Jul 18, 2019
828efe3
Monte carlo results, code and notebook update
mehak-sachdeva Jul 18, 2019
eb7a4ba
adding structure to MC results ipynb
mehak-sachdeva Jul 18, 2019
9610e01
adding structure to all Poisson notebooks
mehak-sachdeva Jul 18, 2019
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13 changes: 8 additions & 5 deletions mgwr/diagnostics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -11,34 +11,37 @@
def get_AICc(gwr):
"""
Get AICc value

Gaussian: p61, (2.33), Fotheringham, Brunsdon and Charlton (2002)

GWGLM: AICc=AIC+2k(k+1)/(n-k-1), Nakaya et al. (2005): p2704, (36)

"""
n = gwr.n
k = gwr.tr_S
y = gwr.y
mu = gwr.mu
#sigma2 = gwr.sigma2
if isinstance(gwr.family, Gaussian):
aicc = -2.0 * gwr.llf + 2.0 * n * (k + 1.0) / (
n - k - 2.0) #equivalent to below but
#can't control denominator of sigma without altering GLM familt code
#can't control denominator of sigma without altering GLM family code
#aicc = n*np.log(sigma2) + n*np.log(2.0*np.pi) + n*(n+k)/(n-k-2.0)
elif isinstance(gwr.family, (Poisson, Binomial)):
aicc = get_AIC(gwr) + 2.0 * k * (k + 1.0) / (n - k - 1.0)
#aicc = np.sum(gwr.family.resid_dev(y, mu)**2) + 2.0 * n * (k + 1.0) / (n - k - 2.0)
return aicc


def get_AIC(gwr):
"""
Get AIC calue
Get AIC value

Gaussian: p96, (4.22), Fotheringham, Brunsdon and Charlton (2002)

GWGLM: AIC(G)=D(G) + 2K(G), where D and K denote the deviance and the effective
number of parameters in the model with bandwidth G, respectively.

"""
k = gwr.tr_S
#deviance = -2*log-likelihood
Expand Down
70 changes: 49 additions & 21 deletions mgwr/gwr.py
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Original file line number Diff line number Diff line change
Expand Up @@ -134,7 +134,7 @@ class GWR(GLM):
spherical : boolean
True for shperical coordinates (long-lat),
False for projected coordinates (defalut).

hat_matrix : boolean
True to store full n by n hat matrix,
False to not store full hat matrix to minimize memory footprint (defalut).
Expand Down Expand Up @@ -516,10 +516,10 @@ class GWRResults(GLMResults):

R2 : float
R-squared for the entire model (1- RSS/TSS)

adj_R2 : float
adjusted R-squared for the entire model

aic : float
Akaike information criterion

Expand Down Expand Up @@ -575,11 +575,11 @@ class GWRResults(GLMResults):
pDev : float
local percent of deviation accounted for; analogous to
r-squared for GLM's

D2 : float
percent deviance explained for GLM, equivaleng to R2 for
Gaussian.

adj_D2 : float
adjusted percent deviance explained, equivaleng to adjusted
R2 for Gaussian.
Expand Down Expand Up @@ -1438,8 +1438,8 @@ class MGWR(GWR):

"""

def __init__(self, coords, y, X, selector, sigma2_v1=True,
kernel='bisquare', fixed=False, constant=True,
def __init__(self, coords, y, X, selector, family, offset=None,
sigma2_v1=True, kernel='bisquare', fixed=False, constant=True,
spherical=False, hat_matrix=False):
"""
Initialize class
Expand All @@ -1448,17 +1448,18 @@ def __init__(self, coords, y, X, selector, sigma2_v1=True,
self.bws = self.selector.bw[0] #final set of bandwidth
self.bws_history = selector.bw[1] #bws history in backfitting
self.bw_init = self.selector.bw_init #initialization bandiwdth
self.family = Gaussian(
) # manually set since we only support Gassian MGWR for now
GWR.__init__(self, coords, y, X, self.bw_init, family=self.family,
sigma2_v1=sigma2_v1, kernel=kernel, fixed=fixed,
constant=constant, spherical=spherical,
self.family = family
self.offset = offset
# manually set since we only support Gassian MGWR for now
GWR.__init__(self, coords, y, X, self.bw_init, self.family,
self.offset,sigma2_v1=sigma2_v1, kernel=kernel,
fixed=fixed, constant=constant, spherical=spherical,
hat_matrix=hat_matrix)
self.selector = selector
self.sigma2_v1 = sigma2_v1
self.points = None
self.P = None
self.offset = None
self.family = family
self.exog_resid = None
self.exog_scale = None
self_fit_params = None
Expand All @@ -1483,7 +1484,14 @@ def _chunk_compute_R(self, chunk_id=0):

for i in range(n):
wi = self._build_wi(i, self.bw_init).reshape(-1, 1)
xT = (self.X * wi).T
if isinstance(self.family, Poisson):
wi=wi.reshape(-1,1)
rslt = iwls(self.y, self.X, self.family, self.offset, None, wi=wi)
inv_xtx_xt = rslt[5]
w = rslt[3]
xT = (self.X * w).T
else:
xT = (self.X * wi).T
P = np.linalg.solve(xT.dot(self.X), xT).dot(init_pR).T
pR[i, :, :] = P * self.X[i]

Expand All @@ -1502,8 +1510,16 @@ def _chunk_compute_R(self, chunk_id=0):
for i in range(len(chunk_index_Aj)):
index = chunk_index_Aj[i]
wi = self._build_wi(index, self.bws_history[iter_i, j])
xw = Xj * wi
pAj[i, :] = Xj[index] / np.sum(xw * Xj) * xw
if isinstance(self.family, Poisson):
Xj = Xj.reshape(-1,1)
wi = wi.reshape(-1,1)
rslt = iwls(self.y, Xj, self.family, self.offset, None, wi=wi)

w = rslt[3]
xw = Xj * w
else:
xw = Xj * wi
pAj[i, :] = (Xj[index] / np.sum(xw * Xj) * xw).reshape(-1)
pR[chunk_index_Aj, :, j] = pAj.dot(pRj_old)
err = pRj_old - pR[:, :, j]

Expand All @@ -1520,21 +1536,33 @@ def _chunk_compute_R(self, chunk_id=0):
def fit(self, n_chunks=1, pool=None):
"""
Compute MGWR inference by chunk to reduce memory footprint.

Parameters
----------

n_chunks : integer, optional
A number of chunks parameter to reduce memory usage.
A number of chunks parameter to reduce memory usage.
e.g. n_chunks=2 should reduce overall memory usage by 2.
pool : A multiprocessing Pool object to enable parallel fitting; default is None.

Returns
-------
: MGWRResults
"""
#self.fit_params['ini_params'] = ini_params
#self.fit_params['tol'] = tol
#self.fit_params['max_iter'] = max_iter

params = self.selector.params
predy = np.sum(self.X * params, axis=1).reshape(-1, 1)

if isinstance(self.family,Poisson):
predy = self.offset*(np.exp(np.sum(self.X * params, axis=1).reshape(-1, 1)))

elif isinstance(self.family,Binomial):
predy = 1/(1+np.exp(-1*np.sum(self.X * params, axis=1).reshape(-1, 1)))

else:
predy = np.sum(self.X * params, axis=1).reshape(-1, 1)

try:
from tqdm.autonotebook import tqdm #progress bar
Expand Down Expand Up @@ -1692,7 +1720,7 @@ class MGWRResults(GWRResults):

R2 : float
R-squared for the entire model (1- RSS/TSS)

adj_R2 : float
adjusted R-squared for the entire model

Expand Down
36 changes: 32 additions & 4 deletions mgwr/search.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,7 @@

import numpy as np
from copy import deepcopy
from spglm.family import Gaussian, Binomial, Poisson


def golden_section(a, c, delta, function, tol, max_iter, int_score=False,
Expand Down Expand Up @@ -164,8 +165,8 @@ def equal_interval(l_bound, u_bound, interval, function, int_score=False,
return opt_val, opt_score, output


def multi_bw(init, y, X, n, k, family, tol, max_iter, rss_score, gwr_func,
bw_func, sel_func, multi_bw_min, multi_bw_max, bws_same_times,
def multi_bw(init, y, X, n, k, family, offset, tol, max_iter, rss_score, gwr_func,
gwr_func_g, bw_func, bw_func_g, sel_func, multi_bw_min, multi_bw_max, bws_same_times,
verbose=False):
"""
Multiscale GWR bandwidth search procedure using iterative GAM backfitting
Expand All @@ -180,7 +181,17 @@ def multi_bw(init, y, X, n, k, family, tol, max_iter, rss_score, gwr_func,
err = optim_model.resid_response.reshape((-1, 1))
param = optim_model.params

XB = np.multiply(param, X)
if isinstance(family, Poisson):
XB = offset*np.exp(np.multiply(param,X))
elif isinstance(family, Binomial):
#v = np.multiply(X, param)
#XB = 1 / (1 + np.exp(-1 * v))
#XB = v + ((1 / (mu * (1 - mu))) * (y - mu))
XB = 1/(1+np.exp(-1*np.multiply(param,X)))
#XB=np.log(XB/(1-XB))
else:
XB = np.multiply(param, X)

if rss_score:
rss = np.sum((err)**2)
iters = 0
Expand All @@ -205,6 +216,10 @@ def tqdm(x, desc=''): #otherwise, just passthrough the range
temp_y = XB[:, j].reshape((-1, 1))
temp_y = temp_y + err
temp_X = X[:, j].reshape((-1, 1))

#if isinstance(family, Binomial):
#bw_class = bw_func_g(temp_y, temp_X)
#else:
bw_class = bw_func(temp_y, temp_X)

if np.all(bw_stable_counter == bws_same_times):
Expand All @@ -217,10 +232,16 @@ def tqdm(x, desc=''): #otherwise, just passthrough the range
else:
bw_stable_counter = np.ones(k)

#if isinstance(family, Binomial):
#optim_model = gwr_func_g(temp_y, temp_X, bw)

#else:
optim_model = gwr_func(temp_y, temp_X, bw)
err = optim_model.resid_response.reshape((-1, 1))
param = optim_model.params.reshape((-1, ))
#new_XB[:,j] = 1/(1+np.exp(-1*np.sum(temp_X * param, axis=1).reshape(-1)))
new_XB[:, j] = optim_model.predy.reshape(-1)
#new_XB[:, j] = np.log(new_XB[:,j]/(1-new_XB[:,j]))
params[:, j] = param
bws[j] = bw

Expand All @@ -230,7 +251,14 @@ def tqdm(x, desc=''): #otherwise, just passthrough the range
XB = new_XB

if rss_score:
predy = np.sum(np.multiply(params, X), axis=1).reshape((-1, 1))
if isinstance(family, Poisson):
predy = offset*(np.exp(np.sum(X * params, axis=1).reshape(-1, 1)))

elif isinstance(family,Binomial):
predy = 1/(1+np.exp(-1*np.sum(X * params, axis=1).reshape(-1, 1)))

else:
predy = np.sum(np.multiply(params, X), axis=1).reshape((-1, 1))
new_rss = np.sum((y - predy)**2)
score = np.abs((new_rss - rss) / new_rss)
rss = new_rss
Expand Down
32 changes: 27 additions & 5 deletions mgwr/sel_bw.py
View file
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Original file line number Diff line number Diff line change
Expand Up @@ -136,7 +136,7 @@ class Sel_BW(object):
>>> pov = np.array(data.by_col('PctPov')).reshape((-1,1))
>>> african_amer = np.array(data.by_col('PctBlack')).reshape((-1,1))
>>> X = np.hstack([rural, pov, african_amer])

Golden section search AICc - adaptive bisquare

>>> bw = Sel_BW(coords, y, X).search(criterion='AICc')
Expand Down Expand Up @@ -213,7 +213,7 @@ def search(self, search_method='golden_section', criterion='AICc',
min value used in bandwidth search
bw_max : float
max value used in bandwidth search
multi_bw_min : list
multi_bw_min : list
min values used for each covariate in mgwr bandwidth search.
Must be either a single value or have one value for
each covariate including the intercept
Expand Down Expand Up @@ -374,12 +374,34 @@ def _mbw(self):
bws_same_times = self.bws_same_times

def gwr_func(y, X, bw):
family = self.family
#if isinstance(family, Binomial):
#family = Gaussian()
return GWR(coords, y, X, bw, family=family, kernel=kernel,
fixed=fixed, offset=offset, constant=False,
spherical=self.spherical, hat_matrix=False).fit(
lite=True, pool=self.pool)

def gwr_func_g(y, X, bw):
family = self.family
family = Gaussian()
return GWR(coords, y, X, bw, family=family, kernel=kernel,
fixed=fixed, offset=offset, constant=False,
spherical=self.spherical, hat_matrix=False).fit(
lite=True, pool=self.pool)

def bw_func(y, X):
family = self.family
#if isinstance(family, Binomial):
#family = Gaussian()
selector = Sel_BW(coords, y, X, X_glob=[], family=family,
kernel=kernel, fixed=fixed, offset=offset,
constant=False, spherical=self.spherical)
return selector

def bw_func_g(y, X):
family = self.family
family = Gaussian()
selector = Sel_BW(coords, y, X, X_glob=[], family=family,
kernel=kernel, fixed=fixed, offset=offset,
constant=False, spherical=self.spherical)
Expand All @@ -391,9 +413,9 @@ def sel_func(bw_func, bw_min=None, bw_max=None):
bw_min=bw_min, bw_max=bw_max, interval=interval, tol=tol,
max_iter=max_iter, pool=self.pool, verbose=False)

self.bw = multi_bw(self.init_multi, y, X, n, k, family, self.tol_multi,
self.max_iter_multi, self.rss_score, gwr_func,
bw_func, sel_func, multi_bw_min, multi_bw_max,
self.bw = multi_bw(self.init_multi, y, X, n, k, family, offset, self.tol_multi,
self.max_iter_multi, self.rss_score, gwr_func,gwr_func_g,
bw_func,bw_func_g,sel_func, multi_bw_min, multi_bw_max,
bws_same_times, verbose=self.verbose)

def _init_section(self, X_glob, X_loc, coords, constant):
Expand Down
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