import particles
from particles import state_space_models as ssm
# Data and parameter values from Pitt & Shephard
raw_data = np.loadtxt('../../datasets/GBP_vs_USD_9798.txt',
skiprows=2,
usecols=(3, ),
comments='(C)')
T = 201
data = 100. * np.diff(np.log(raw_data[:(T + 1)]))
my_ssm = ssm.StochVol(mu=2 * np.log(.5992), sigma=0.178, rho=0.9702)
# FK models
models = OrderedDict()
models['bootstrap'] = ssm.Bootstrap(ssm=my_ssm, data=data)
models['guided'] = ssm.GuidedPF(ssm=my_ssm, data=data)
models['apf'] = ssm.AuxiliaryPF(ssm=my_ssm, data=data)
# Get results
results = particles.multiSMC(fk=models, N=10**3, nruns=250, moments=True)
# Golden standard
bigN = 10**5
bigpf = particles.SMC(fk=models['bootstrap'], N=bigN, qmc=True, moments=True)
print('One SQMC run with N=%i' % bigN)
bigpf.run()
# PLOTS
# =====
plt.style.use('ggplot')
savefig = False # True if you want to save figs as pdfs
sigmaY = .2
rho = 0.9
T = 1000
N = 200
# define ss model, simulate data
ssm = kalman.LinearGauss(sigmaX=sigmaX, sigmaY=sigmaY, rho=rho)
true_states, data = ssm.simulate(T)
# computes true log-likelihood
kf = kalman.Kalman(ssm=ssm, data=data)
kf.filter()
true_loglik = np.sum(kf.logpyt)
# FK model
fk_model = state_space_models.GuidedPF(ssm=ssm, data=data)
# Run SMC algorithm for different values of ESS_min
alphas = list(np.linspace(0., .1, 11)) + list(np.linspace(0.15, 1., 18))
results = particles.multiSMC(fk=fk_model,
N=N,
ESSrmin=alphas,
nruns=200,
nprocs=1)
# PLOTS
#======
plt.style.use('ggplot')
savefigs = True # False if you don't want to save plots as pdfs
# inter-quartile range of log-likelihood estimate as a function of ESSmin
def fkmod(**kwargs):
return ssms.GuidedPF(ssm=ssms.ThetaLogistic(**kwargs), data=data)
alpha0 = 0.3
T = 50
dims = range(5, 21, 5)
# instantiate models
models = OrderedDict()
true_loglik, true_filt_means = {}, {}
for d in dims:
ssm = kalman.MVLinearGauss_Guarniero_etal(alpha=alpha0, dx=d)
_, data = ssm.simulate(T)
kf = kalman.Kalman(ssm=ssm, data=data)
kf.filter()
true_loglik[d] = np.cumsum(kf.logpyt)
true_filt_means[d] = [f.mean for f in kf.filt]
models['boot_%i' % d] = ssms.Bootstrap(ssm=ssm, data=data)
models['guided_%i' % d] = ssms.GuidedPF(ssm=ssm, data=data)
# Get results
N = 10**4
results = particles.multiSMC(fk=models, qmc=[False, True], N=N, moments=True,
nruns=100, nprocs=1)
# Format results
results_mse = []
for d in dims:
for t in range(T):
# this returns the estimate of E[X_t(1)|Y_{0:t}]
estimate = lambda r: r['output'].summaries.moments[t]['mean'][0]
for type_fk in ['guided', 'boot']:
for qmc in [False, True]:
est = np.array( [estimate(r) for r in results
dy = 80 # number of neurons
dx = 6 # 3 for position, 3 for velocity
T = 25
a0 = random.normal(loc=2.5, size=dy) # from Koyama et al
# the b's are generated uniformly on the unit sphere in R^6 (see Koyama et al)
b0 = random.normal(size=(dy, dx))
b0 = b0 / (linalg.norm(b0, axis=1)[:, np.newaxis])
delta0 = 0.03; tau0 = 1.
x0 = np.zeros(dx)
# models
chosen_ssm = NeuralDecoding(a=a0, b=b0, x0=x0, delta=delta0, tau=tau0)
_, data = chosen_ssm.simulate(T)
models = OrderedDict()
models['boot'] = ssms.Bootstrap(ssm=chosen_ssm, data=data)
models['guided'] = ssms.GuidedPF(ssm=chosen_ssm, data=data)
# models['apf'] = ssms.AuxiliaryPF(ssm=chosen_ssm, data=data)
# Uncomment this if you want to include the APF in the comparison
N = 10**4; nruns = 50
results = particles.multiSMC(fk=models, N=N, nruns=nruns, nprocs=1,
collect=[Moments], store_history=True)
## PLOTS
#########
savefigs = True # False if you don't want to save plots as pdfs
plt.style.use('ggplot')
# arbitrary time
t0 = 9
dx = 6 # 3 for position, 3 for velocity
T = 25
a0 = random.normal(loc=2.5, size=dy) # from Kass' paper
# the b's are generated uniformly on the unit sphere in R^6 (see Kass' paper)
b0 = random.normal(size=(dy, dx))
b0 = b0 / (linalg.norm(b0, axis=1)[:, np.newaxis])
delta0 = 0.03
tau0 = 1.
x0 = np.zeros(dx) # TODO
# models
chosen_ssm = NeuralDecoding(a=a0, b=b0, x0=x0, delta=delta0, tau=tau0)
_, data = chosen_ssm.simulate(T)
models = OrderedDict()
models['boot'] = state_space_models.Bootstrap(ssm=chosen_ssm, data=data)
models['guided'] = state_space_models.GuidedPF(ssm=chosen_ssm, data=data)
# models['apf'] = state_space_models.AuxiliaryPF(ssm=chosen_ssm, data=data)
# Uncomment this if you want to include the APF in the comparison
N = 10**4
nruns = 50
results = particles.multiSMC(fk=models,
N=N,
nruns=nruns,
nprocs=1,
moments=True,
store_history=True)
## PLOTS
#########
savefigs = True # False if you don't want to save plots as pdfs
evaluate.dist_cmp({
'px': cir.PX(dist_args['t'], dist_args['xp']),
'norm': cir.proposal_normal(**dist_args),
't': cir.proposal_t(**dist_args) # model.distributions.t_nn(df=30, loc=dist_norm.mu, scale=dist_norm.sigma)
# 'tq': cir.proposal_t_quantile(**dist_args)
}, title=f"Transition density and proposals at t={t}", ax=ax)
fig, ax = plt.subplots()
with np.errstate(divide='ignore', invalid='ignore'):
anim = FuncAnimation(fig, update, frames=np.arange(1, 100), interval=300)
# anim.save('compare_densities2.gif', dpi=80, writer='imagemagick')
plt.show()
# Trajectories of means of PX and proposals ===========================================================================
cir = CIR.CIR(tau=tau, H=H, **cir_args) # CIR with normal proposal
alg = particles.SMC(fk=ssm.GuidedPF(ssm=cir, data=real_y), **default_args)
alg.run()
xh = alg.summaries.moments # Estimated posterior mean
dists = pd.DataFrame({'px': np.array([cir.PX(t, xp).stats[0] for t, xp in enumerate(real_x[:99], start=1)]).reshape((99,)),
'norm': np.array([cir.proposal_normal(t, xp, real_y).mu for t, xp in enumerate(real_x[:99], start=1)]).reshape((99,)),
't': np.array([cir.proposal_t(t, xp, real_y).stats[0] for t, xp in enumerate(real_x[:99], start=1)]).reshape((99,))
})
dists.plot()
# Proposals and their tails ===========================================================================================
# Cross-sectional analysis
importlib.reload(CIR)
cir = CIR.CIR(tau=tau, H=H, **cir_args) # CIR with normal proposal
alg = particles.SMC(fk=ssm.GuidedPF(ssm=cir, data=real_y), **default_args)
alg.run()
# %% Settings parameters
N = 100 # 5000
T = 1 * 10**2 # 5 * 10 ** 4
R = 100 # Number of independent replications
my_seed = 3035802483
# Use same random seeds in R independent replications
MAX_INT_32 = np.iinfo(np.int32).max
seeds = [np.random.randint(MAX_INT_32) for i in range(R)]
tau = [0.25, 0.5, 1, 3, 5, 10]
#%% Define model and generate real data
# Run this cell to generate data or run the second cell below to load data generated and saved before.
cir = CIR()
real_x, real_y = cir.simulate(T)
fk_PF = ssm.GuidedPF(ssm=CIR(), data=real_y)
CIR_plot(real_x)
#%% Save the generated data
# Run this cell to save the newly generated data into the Records/CIRYYYYmmdd-HHMMSS folder.
name = datetime.datetime.now().strftime("%Y%m%d-%H%M%S")
os.mkdir(f"./Records/CIR{name}") # Create folder
# Save the real_states plot
plt.savefig(f"./Records/CIR{name}/real_states.png")
# Save the generated data
np.savez(file=f"./Records/CIR{name}/data", real_x=real_x, real_y=real_y)
# Save parameters of the model where data from.
config = configparser.ConfigParser()
config["PARAMETERS"] = {**cir.default_params, "Delta": cir.Delta, "H": cir.H}
#parameter values
alpha0 = 0.4
T = 50
dims = range(5, 21, 5)
# instantiate models
models = OrderedDict()
true_loglik, true_filt_means = {}, {}
for d in dims:
my_ssm = ssm.MVLinearGauss_Guarniero_etal(alpha=alpha0, dx=d)
_, data = my_ssm.simulate(T)
truth = my_ssm.kalman_filter(data)
true_loglik[d] = truth.logpyts.cumsum()
true_filt_means[d] = truth.filt.means
models['boot_%i' % d] = ssm.Bootstrap(ssm=my_ssm, data=data)
models['guided_%i' % d] = ssm.GuidedPF(ssm=my_ssm, data=data)
# Get results
N = 10**4
results = particles.multiSMC(fk=models,
qmc=[False, True],
N=N,
moments=True,
nruns=100,
nprocs=0)
# Format results
results_mse = []
for d in dims:
for t in range(T):
# this returns the estimate of E[X_t(1)|Y_{0:t}]
