def get_r2c_sim(coords):
dims = [
'est',
'sim',
'r2',
'sig2',
'snr',
'ms',
'ns',
]
res = xr.DataArray(np.zeros(tuple(len(c) for c in coords)),
coords=coords,
dims=dims)
res = res.stack(c=dims[2:])
for i in range(res.shape[-1]):
[r2, sig2, snr, m, n] = res[:, :, i].coords['c'].values.tolist()
mu2y = SNR_to_mu2(snr, sig2, m, n)
theta = [r2, sig2, mu2y, mu2y, m, n]
x, y = rc.pds_n2m_r2c(theta, n_exps, ddof=1)
x = x.squeeze()[np.newaxis, np.newaxis]
r2c, r2 = rc.r2c_n2m(x, y)
res[..., i] = np.array([r2, r2c]).squeeze()
res = res.unstack()
return res
def get_ci(x,
y,
n_r2c_eval=50,
n_r2c_sims=500,
r2c_range=[0, 1],
alpha_targ=0.1,
trunc_sig2=[0, np.inf],
trunc_d2=[0, np.inf]):
#get confidence intervals
r2c_hat_obs = rc.r2c_n2m(x.squeeze(), y)[0]
#r2c_hat_obs = trunc_ud(1, 0, r2c_hat_obs)
trace, p = sample_post_s2_d2(
y, n_samps=1000, trunc_sig2=trunc_sig2,
trunc_d2=trunc_d2) # get posterior dist of params
sig2_post = trace[1] #trial-to-trial variance
d2m_post = trace[0] * m #dynamic range
sample_inds = np.random.choice(
len(sig2_post), size=n_r2c_sims,
replace=True) #randomly sample from post-dist
#get distribution of r2er_hat
res = np.zeros([n_r2c_eval, n_r2c_sims])
r2cs = np.linspace(r2c_range[0], r2c_range[1], n_r2c_eval)
for i, r2c in (enumerate(r2cs)):
for j in range(n_r2c_sims):
k = sample_inds[j]
theta = [r2c, sig2_post[k], d2m_post[k], d2m_post[k], m, n]
x, y = pds_n2m_r2c(theta, 1, ddof=1)
res[i, j] = rc.r2c_n2m(x.squeeze(), y)[0]
alpha_obs = np.mean(res > r2c_hat_obs, 1)
ll_dif = np.abs(alpha_obs - alpha_targ / 2)
ll_ind = np.argmin(ll_dif)
if ll_dif[ll_ind] < alpha_targ:
ll = r2cs[ll_ind]
else:
ll = 0
ul_dif = np.abs(alpha_obs - (1 - alpha_targ / 2))
ul_ind = np.argmin(ul_dif)
if ul_dif[ul_ind] < alpha_targ:
ul = r2cs[ul_ind]
else:
ul = 1
return ll, ul, alpha_obs, r2c_hat_obs, res, trace
def r2c_n2m_ci_from_post(trace,
n,
m,
r2c_hat_obs,
alpha_targ=0.10,
nr2cs=50,
nr2c_hat=1000):
sig2s = trace[0]
mu2ys = trace[1] * m
sample_inds = np.random.choice(len(sig2s), size=nr2c_hat, replace=False)
n_exps = 1
ress = []
r2s = np.linspace(0, 1, nr2cs)
for r2 in r2s:
res = []
for i in range(nr2c_hat):
i = sample_inds[i]
theta = [r2, sig2s[i], mu2ys[i], mu2ys[i], m, n]
x, y = rc.pds_n2m_r2c(theta, n_exps, ddof=1)
res.append(rc.r2c_n2m(x.squeeze(), y)[0])
ress.append(np.array(res).squeeze())
ress = np.array(ress)
tol = alpha_targ
alpha_obs = np.mean(ress > r2c_hat_obs, 1)
ll_dif = np.abs(alpha_obs - alpha_targ / 2)
ll_ind = np.argmin(ll_dif)
if ll_dif[ll_ind] < tol:
ll = r2s[ll_ind]
else:
ll = 0
ul_dif = np.abs(alpha_obs - (1 - alpha_targ / 2))
ul_ind = np.argmin(ul_dif)
if ul_dif[ul_ind] < tol:
ul = r2s[ul_ind]
else:
ul = 1
return ll, ul, alpha_obs
def get_emp_dist_r2er(r2c_check,
r2c_hat_obs,
trace,
m,
n,
p_thresh=0.01,
n_r2c_sims=100):
sig2_post = trace[1] #trial-to-trial variance
d2m_post = trace[0] * m #dynamic range
sample_inds = np.random.choice(
len(sig2_post), size=n_r2c_sims,
replace=True) #randomly sample from post-dist
res = np.zeros(n_r2c_sims)
for j in range(n_r2c_sims):
k = sample_inds[j]
theta = [r2c_check, sig2_post[k], d2m_post[k], d2m_post[k], m, n]
x, y = pds_n2m_r2c(theta, 1, ddof=1)
res[j] = (rc.r2c_n2m(x.squeeze(), y)[0]).squeeze()
return res
def get_ci(x,
y,
n_r2c_sims=1000,
alpha_targ=0.1,
p_thresh=0.01,
n_splits=6,
trunc_sig2=[0, np.inf],
trunc_d2=[0, np.inf]):
#get confidence intervals
n, m = y.shape
r2c_hat_obs = rc.r2c_n2m(x.squeeze(), y)[0]
trace, p = sample_post_s2_d2(
y, n_samps=2000, trunc_sig2=trunc_sig2,
trunc_d2=trunc_d2) # get posterior dist of params
ul, ul_alpha = find_cdf_pos(r2c_hat_obs,
alpha_targ / 2,
trace,
m,
n,
n_splits=n_splits,
p_thresh=p_thresh,
n_r2c_sims=n_r2c_sims,
int_l=0,
int_h=1)
ll, ll_alpha = find_cdf_pos(r2c_hat_obs,
1 - alpha_targ / 2,
trace,
m,
n,
n_splits=n_splits,
p_thresh=p_thresh,
n_r2c_sims=n_r2c_sims,
int_l=0,
int_h=1)
return ll, ul, r2c_hat_obs, trace, ll_alpha, ul_alpha
[np.cos(theta), np.sin(theta),
np.ones((len(theta), 1))], -1)
pred_0 = np.dot(
a,
np.linalg.lstsq(a, s.mean('trial_tot').sel(unit=0).values.T,
rcond=None)[0])
pred_1 = np.dot(
a,
np.linalg.lstsq(a, s.mean('trial_tot').sel(unit=1).values.T,
rcond=None)[0])
pred_null = np.dot(
a,
np.linalg.lstsq(a, resp.mean('trial').values.T, rcond=None)[0])
pred_0_fit = np.squeeze([
rc.r2c_n2m(a_pred, aunit.values)[0]
for a_pred, aunit in zip(pred_0.T, s.sel(unit=0))
])
pred_1_fit = np.squeeze([
rc.r2c_n2m(a_pred, aunit.values)[0]
for a_pred, aunit in zip(pred_1.T, s.sel(unit=1))
])
pred_null_fit = np.squeeze([
rc.r2c_n2m(a_pred, aunit.values)[0]
for a_pred, aunit in zip(pred_null.T, resp)
])
snr = ((s.mean('trial_tot').var('dir') / s.var('trial_tot').mean('dir')))
snr_null = (resp.mean('trial').var('stim') / resp.var('trial').mean('stim'))
n_splits = 10
n_r2c_sims = 1000
p_thresh = 0.001
n_r2c_sims = 300
alpha_targ = 0.2
trunc_sig2 = [0.1, 2]
trunc_d2 = [0.1, 2]
n_exps = 200
r2 = 0.5
#%%
theta = [r2, sig2, 1, mu2y, m, n]
x, y = pds_n2m_r2c(theta, 1, ddof=1)
#get confidence intervals
n, m = y.shape
r2c_hat_obs = rc.r2c_n2m(x.squeeze(), y)[0].squeeze()
trace, p = sample_post_s2_d2(y,
n_samps=2000,
trunc_sig2=trunc_sig2,
trunc_d2=trunc_d2) # get posterior dist of params
#%%
r2c_check = r2c_hat_obs
res = get_emp_dist_r2er(r2c_check,
r2c_hat_obs,
trace,
m,
n,
p_thresh=0.01,
n_r2c_sims=1000)
r2_qs = np.quantile(res, [0, 0.33, 0.5, 0.66, 1])
r2cs = []
r2s = []
for l, m in enumerate(ms):
for j, r2 in enumerate(r2sims):
theta = [r2, sig2, mu2y, mu2y, m, n]
[x, y] = rc.pds_n2m_r2c(theta, n_exps, ddof=1)
res = []
for i in range(y.shape[0]):
a_y = y[i]
mod = np.zeros((len(x), 2))
mod[:,0] = 1
mod[:, 1] = x.squeeze()
beta = np.linalg.lstsq(mod, a_y.mean(0), rcond=-1)[0]
y_hat = np.dot(beta[np.newaxis], mod.T).squeeze()
r2c, r2 = rc.r2c_n2m(x.T, a_y)
r2_pc = rc.r2_SE_corrected(x.squeeze(), a_y)
r2_upsilon = rc.upsilon(y_hat, a_y)
r2_hsu = rc.cc_norm_split(x.squeeze(), a_y)**2
r2_yd = rc.r2_SB_normed(x.squeeze(), a_y)
r2_sl = rc.normalized_spe(y_hat, a_y)
r2_sc = rc.cc_norm(x.squeeze(), a_y)**2
r2_zyl = rc.cc_norm_bs(x.squeeze(), a_y)**2
res.append([np.double(r2.squeeze()),
np.double(r2c.squeeze()),
r2_pc,
r2_upsilon,
r2_yd,
r2_hsu,
r2_sl,
r2_sc,
os.chdir('../../')
import r2c_common as r2c
os.chdir(cwd)
import pandas as pd
s = xr.open_dataarray('./mt_sqrt_spkcnt.nc')
snr = ((s.mean('trial_tot').var('dir')/
s.var('trial_tot').mean('dir')))
theta = np.deg2rad(s.coords['dir'].values)[:,np.newaxis]
sin_mod = np.concatenate([np.cos(theta), np.sin(theta),np.ones((len(theta), 1))], -1)
coefs = np.linalg.lstsq(sin_mod, s.mean('trial_tot').values.T)[0]
pred = np.dot(sin_mod, coefs)
r2er = np.squeeze([r2c.r2c_n2m(a_pred, aunit.values)[0]
for a_pred, aunit in zip(pred.T, s)])
theta_fine = np.deg2rad(np.linspace(0,s.coords['dir'].values[-1]))[:,np.newaxis]
sin_mod_fine = np.concatenate([np.cos(theta_fine),
np.sin(theta_fine),
np.ones((len(theta_fine), 1))], -1)
pred_fine = np.dot(sin_mod_fine,coefs)
os.chdir(cwd)
#os.chdir('../../')
p = pd.read_csv('./fits.csv', index_col=0)
p['ciw'] = p['ul'] - p['ll']
ss.to_netcdf('./mt_sqrt_spkcnt.nc')
#%%
os.chdir(cwd)
s = xr.open_dataarray('./mt_sqrt_spkcnt.nc')
snr = ((s.mean('trial_tot').var('dir') / s.var('trial_tot').mean('dir')))
theta = np.deg2rad(s.coords['dir'].values)[:, np.newaxis]
sin_mod = np.concatenate(
[np.cos(theta), np.sin(theta),
np.ones((len(theta), 1))], -1)
coefs = np.linalg.lstsq(sin_mod, s.mean('trial_tot').values.T, rcond=None)[0]
pred = np.dot(sin_mod, coefs)
r2er = np.squeeze(
[r2c.r2c_n2m(a_pred, aunit.values)[0] for a_pred, aunit in zip(pred.T, s)])
dat = np.zeros((len(s.coords['rec']), 4))
p = pd.DataFrame(dat, columns=['r2er', 'r2', 'll', 'ul'])
for i in range(dat.shape[0]):
x = pred[:, i]
y = s[i].values
ll, ul, r2c_hat_obs, alpha_obs = r2c.r2c_n2m_ci(x,
y,
alpha_targ=0.10,
nr2cs=100)
r2 = np.corrcoef(y.mean(0), x)[0, 1]**2
sig2 = 0.25
snr = 2
m = 30
n = 5
n_exps = 100
n_bs_samples = 500
ncps = snr * m
mu2y = mu2x = ncps * sig2
theta = [r2, sig2, mu2y, mu2y, m, n]
x, ys = pds_n2m_r2c(theta, n_exps, ddof=1)
res = []
for exp in tqdm(range(n_exps)):
y = ys[exp]
r2_er_obs = rc.r2c_n2m(x.squeeze(), y)[0]
y_news = []
for k in range(n_bs_samples):
y_new = np.array([np.random.choice(y_obs, size=n) for y_obs in y.T]).T
y_news.append(y_new)
y_news = np.array(y_news)
r2c_bs = rc.r2c_n2m(x.squeeze(), y_news)[0].squeeze()
res.append([r2c_bs, r2_er_obs])
#%%
r2c_bs = np.array([a_res[0] for a_res in res])
cis = np.quantile(r2c_bs, [0.1, 0.9], 1).T
in_ci = (cis[:, 0] <= r2) * (cis[:, 1] >= r2) * (cis[:, 0] != cis[:, 1])
#%%
cis = np.array([r[:2] for r in res])
snr = 0.5
m = 40
n = 4
ncps = snr * m
mu2y = mu2x = ncps * sig2
r2c_range = [0, 1]
alpha_targ = 0.2
n_r2c_eval = 30
n_r2c_sims = 500
r2s = np.linspace(0, 1, 5)
n_exps = 1000
r2 = 1
theta = [r2, sig2, mu2x, mu2y, m, n]
x, y = pds_n2m_r2c(theta, n_exps, ddof=1) # simulate experiment
r2c_hat_obs = np.squeeze(rc.r2c_n2m(x.squeeze(), y)[0])
plt.subplot(212)
plt.hist(r2c_hat_obs,
cumulative=True,
histtype='step',
bins=10000,
density=True,
range=[-1, 2],
color='b')
plt.xlabel(r'$\hat{r}^2_{ER}$')
#plt.title(np.round(np.median(r2c_hat_obs),4))
q = np.quantile(r2c_hat_obs, 0.9)
plt.plot([q, q], [0, 1], c='b')