def piecewiseexp_diffevol(x, y, breaks=1, minwindow=14):
#prepare the bounds and guess vectors, and the other constants that will be used in the inner optimizer
guess = [1, 1 / 7] #initial count and initial growth rate
bounds = [(1e-1, 1e3), (-10 / 7, 10 / 7)
] #bounds for initial count and initial growth rate
alpha = 1
for i in range(breaks):
guess.append(1 / 7) #growth rate after breakpoint
bounds.append((-10 / 7, 10 / 7))
constants = {
'minwindow': minwindow,
'x': x,
'y': y,
'guess': guess,
'bounds': bounds,
'alpha': alpha
}
#bounds for the auxiliary variables that will be used to set the breakpoints
#these auxiliary variables are optimized by differential_evolution()
auxBounds = [(0, 1)] * breaks
#find the optimal breakpoints
res = differential_evolution(func=piecewiseexp_diffevol_inner,
bounds=auxBounds,
args=[constants])
#print(res)
#do the regression for the optimum breakpoints
aux = res.x
breakpoints = aux_to_breakpoints(aux, x[0], x[-1], minwindow)
params, likelihood, fit = fit_model(x,
y,
model_func=piecewiseexp,
constants={'breakpoints': breakpoints},
loglik_func=loglik_negbin,
guess=guess,
bounds=bounds,
alpha=alpha)
return params, breakpoints, likelihood, fit
def piecewiseexp_diffevol_inner(aux, constants):
x = constants['x']
y = constants['y']
bounds = constants['bounds']
guess = constants['guess']
alpha = constants['alpha']
breakpoints = aux_to_breakpoints(aux, x[0], x[-1], constants['minwindow'])
params, likelihood, fit = fit_model(x,
y,
model_func=piecewiseexp,
constants={'breakpoints': breakpoints},
loglik_func=loglik_negbin,
guess=guess,
bounds=bounds,
alpha=alpha)
return likelihood
def test_piecewiseexp():
x = np.arange(100)
guess = [1, 3 / 7, -1 / 7, 1.5 / 7]
bounds = [(1e-2, 1e3), (-2, 2), (-2, 2), (-2, 2)]
breakpoints = [20, 70]
#create some data
y = piecewiseexp(x, guess, {'breakpoints': breakpoints})
y = np.random.poisson(y)
plt.plot(x, y, "x")
plt.yscale('log')
#regression knowing the breakpoints
alpha = 0.1
params, likelihood, fit = fit_model(x,
y,
model_func=piecewiseexp,
constants={'breakpoints': breakpoints},
loglik_func=loglik_negbin,
guess=guess,
bounds=bounds,
alpha=alpha)
plt.plot(x, fit, "r:")
#grid search regression to find the breakpoints
#min_params, min_likelihood, min_fit, min_breakpoints, res = piecewiseexp_gridsearch(x,y,breaks=2,minwindow=14)
#plt.plot(x, min_fit, "g-")
#differential evolution search regression to find the breakpoints
min_params, min_breakpoints, min_likelihood, min_fit = piecewiseexp_diffevol(
x, y, breaks=2, minwindow=14)
plt.plot(x, min_fit, "g-")
plt.show()
def piecewiseexp_gridsearch(x, y, breaks=1, minwindow=14):
alpha = 0.1
breakpoints = [(i + 1) * minwindow for i in range(breaks)]
guess = [1, 1 / 7] #initial count and initial growth rate
bounds = [(1e-1, 1e3), (-10 / 7, 10 / 7)
] #bounds for initial count and initial growth rate
for i in range(breaks):
guess.append(1 / 7) #growth rate after breakpoint
bounds.append((-10 / 7, 10 / 7))
def reset_breakpoints(i):
if i <= breaks - 1:
breakpoints[i] = breakpoints[i - 1] + minwindow
reset_breakpoints(i + 1)
def next_breakpoint(i):
breakpoints[i] = breakpoints[i] + 1
reset_breakpoints(i + 1)
if i >= 1 and breakpoints[-1] > x[-1] - minwindow:
next_breakpoint(i - 1)
res = []
isFirst = True
min_params = None
min_likelihood = None
min_fit = None
min_breakpoints = None
while (True):
params, likelihood, fit = fit_model(
x,
y,
model_func=piecewiseexp,
constants={'breakpoints': breakpoints},
loglik_func=loglik_negbin,
guess=guess,
bounds=bounds,
alpha=alpha)
res.append({
'params': params,
'breakpoints': breakpoints,
'likelihood': likelihood,
'fit': fit
})
if isFirst:
isFirst = False
min_params = params
min_likelihood = likelihood
min_fit = fit
min_breakpoints = breakpoints.copy()
else:
if likelihood < min_likelihood:
min_params = params
min_likelihood = likelihood
min_fit = fit
min_breakpoints = breakpoints.copy()
next_breakpoint(breaks - 1)
if breakpoints[-1] > x[-1] - minwindow:
break
return min_params, min_likelihood, min_fit, min_breakpoints, res