[FEAT]: Sensitivity score ranking chart

[liunelson]

Is your feature request related to a problem? Please describe.
Currently, the parameters are listed not in a particular order (alphabetical?).

Below, I propose that we compute a score per parameter and rank them.

Describe the solution you'd like

I do this in this "Transform dataset" operator.

1. Start with a "Simulate" result dataframe d1
2. Define a regular grid over the parameter space
3. Linearly interpolate the outcome of interest (e.g. cases_observable_state) over this grid
4. Calculate the directional gradient of the outcome of interest along each parameter
5. Calculate the median and standard deviation of the directional gradient of each parameter
6. Make a bar chart where each parameter gets a bar (height = median, error bar = +/- 0.5 * std), sorted by height.

# Parameter sensitivity score

# Get relevant values from simulation result
n = d1["sample_id"].max()
b = np.array([d1[d1["sample_id"] == i]["persistent_b_param"].iloc[0]for i in range(n)])
rHR = np.array([d1[d1["sample_id"] == i]["persistent_rHR_param"].iloc[0] for i in range(n)])
outcomes = np.array([d1[d1["sample_id"] == i]["cases_observable_state"].max() for i in range(n)])

# Interpolate to a uniform grid
m = 100
x = np.linspace(b.min(), b.max(), m)
y = np.linspace(rHR.min(), rHR.max(), m)
xx, yy = np.meshgrid(x, y)

from scipy.interpolate import LinearNDInterpolator
xy = np.c_[b, rHR]
lut2 = LinearNDInterpolator(xy, outcomes)
zz = lut2(xx, yy)

# Derivative of "outcome of interest" with respect to each parameter
gx_all = []
for i in range(zz.shape[0]):
    gx = np.gradient(zz[i, :], 1.0 / m)
    gx_all.extend(list(gx))

gy_all = []
for j in range(zz.shape[1]):
    gy = np.gradient(zz[:, j], 1.0 / m)
    gy_all.extend(list(gy))

# Take absolute value

gx_all = np.abs(gx_all)
gy_all = np.abs(gy_all)

# Score = median of the derivatives
sensitivity_score_b = np.nanmedian(gx_all)
sensitivity_score_rHR = np.nanmedian(gy_all)

# Uncertainty
# sensitivity_score_b_unc = np.nanstd(gx_all) / np.sqrt(len(gx_all))
# sensitivity_score_rHR_unc = np.nanstd(gy_all) / np.sqrt(len(gy_all))
sensitivity_score_b_unc = np.nanstd(gx_all)
sensitivity_score_rHR_unc = np.nanstd(gy_all)

fig, ax = plt.subplots(1, 1, figsize = (8, 6))
__ = ax.plot([0.5, 2.5], [0, 0], color = 'k', linewidth = 0.5)
__ = ax.bar([1, 2], [sensitivity_score_b, sensitivity_score_rHR], width = 0.95, align = 'center')
__ = ax.errorbar(x = [1, 2], y = [sensitivity_score_b, sensitivity_score_rHR], yerr = [0.5 * sensitivity_score_b_unc, 0.5 * sensitivity_score_rHR_unc], color = 'k', capsize = 10)
__ = plt.setp(ax, xlabel = 'Model Parameters', ylabel = 'Gradient-based sensitivity score', xlim = [0.5, 2.5])
__ = ax.set_xticks([1, 2], labels = ['b', 'rHR'])

[liunelson]

I updated the above with np.abs to enforce positive value for the scores so the sorting works.