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add: calculate AIC when solving the model fitting problem

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This commit is contained in:
Yves Biener
2026-01-17 13:46:37 +01:00
parent 79a460dea0
commit 64844e860c
3 changed files with 68 additions and 83 deletions
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133
example.py
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@@ -42,6 +42,46 @@ def random_graph(n=5000, seed=None):
return rng.random((n, 2)), seed
def random_graph_favor_border(n=3000, seed = None):
if seed is None:
import secrets
seed = secrets.randbits(128)
rng = np.random.default_rng(seed=seed)
vps = np.zeros((n, 2))
for i in range(0, n):
r_x = rng.random()
if rng.random() > 0.5:
while (r_x > 0.3 and r_x < 0.7):
r_x = rng.random()
r_y = rng.random()
if rng.random() > 0.5:
while (r_y > 0.3 and r_y < 0.7):
r_y = rng.random()
vps[i][0] = r_x
vps[i][1] = r_y
return vps, seed
def random_graph_favor_center(n=3000, seed = None):
if seed is None:
import secrets
seed = secrets.randbits(128)
rng = np.random.default_rng(seed=seed)
vps = np.zeros((n, 2))
for i in range(0, n):
r_x = rng.random()
if rng.random() > 0.7:
while (r_x < 0.4 or r_x > 0.6):
r_x = rng.random()
r_y = rng.random()
if rng.random() > 0.7:
while (r_y < 0.4 or r_y > 0.6):
r_y = rng.random()
vps[i][0] = r_x
vps[i][1] = r_y
return vps, seed
def spatial_graph(adata):
"""
Generate the spatial graph using delaunay for the given `adata`.
@@ -87,16 +127,7 @@ def merfish_example():
# optimize model's piece-wise linear function
d = quantification[:, 0]
C = quantification[:, 1]
m_opt, c0_opt, b_opt = fitting.fit_piece_wise_linear(d, C)
# AIC
# AIC = 2 * k (= 2) - 2 * ln(L^~)
# with L^~ = sum(f(x_i)) where x_i describes a data point
# - f is *not normalized*
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_opt* b_opt + c0_opt if x_i >= b_opt else m_opt * x_i + c0_opt)
aic_model = 6. - 2. * sum_log # three parameters: b_opt, m_opt, c0_opt
m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)
# TODO
# should this be part of the plotting function itself, it should not be necessary for me to do this
@@ -107,25 +138,18 @@ def merfish_example():
[lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
)
# plot model containing modeled piece-wise linear function
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_model)
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_opt)
# linear regression model
m_reg, c_reg = fitting.fit_linear_regression(d, C)
# AIC
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_reg * x_i + c_reg)
aic_regression = 4. - 2. * sum_log # two parameter: m_reg, c_reg
m_reg, c_reg, aic_reg = fitting.fit_linear_regression(d, C)
x = np.linspace(min(d), max(d), 500)
y = m_reg * x + c_reg
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_regression}")
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_reg}")
ax1.legend()
fig.savefig(f"Merfish_closeness.svg", format='svg')
for i in range(1, 6):
points, seed = random_graph()
g, weight = spatial_graph(points)
@@ -158,16 +182,7 @@ for i in range(1, 6):
# optimize model's piece-wise linear function
d = quantification[:, 0]
C = quantification[:, 1]
m_opt, c0_opt, b_opt = fitting.fit_piece_wise_linear(d, C)
# AIC
# AIC = 2 * k (= 2) - 2 * ln(L^~)
# with L^~ = sum(f(x_i)) where x_i describes a data point
# - f is *not normalized*
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_opt* b_opt + c0_opt if x_i >= b_opt else m_opt * x_i + c0_opt)
aic_model = 6. - 2. * sum_log # three parameters: b_opt, m_opt, c0_opt
m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)
# TODO
# should this be part of the plotting function itself, it should not be necessary for me to do this
@@ -178,20 +193,14 @@ for i in range(1, 6):
[lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
)
# plot model containing modeled piece-wise linear function
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_model)
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_opt)
# linear regression model
m_reg, c_reg = fitting.fit_linear_regression(d, C)
# AIC
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_reg * x_i + c_reg)
aic_regression = 4. - 2. * sum_log # two parameter: m_reg, c_reg
m_reg, c_reg, aic_reg = fitting.fit_linear_regression(d, C)
x = np.linspace(min(d), max(d), 500)
y = m_reg * x + c_reg
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_regression}")
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_reg}")
ax1.legend()
fig.savefig(f"uniform_random_point_clouds/{i}_closeness.svg", format='svg')
@@ -221,16 +230,7 @@ for i in range(1, 6):
# optimize model's piece-wise linear function
d = quantification[:, 0]
C = quantification[:, 1]
m_opt, c0_opt, b_opt = fitting.fit_piece_wise_linear(d, C)
# AIC
# AIC = 2 * k (= 2) - 2 * ln(L^~)
# with L^~ = sum(f(x_i)) where x_i describes a data point
# - f is *not normalized*
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_opt* b_opt + c0_opt if x_i >= b_opt else m_opt * x_i + c0_opt)
aic_model = 6. - 2. * sum_log # three parameters: b_opt, m_opt, c0_opt
m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)
# TODO
# should this be part of the plotting function itself, it should not be necessary for me to do this
@@ -241,20 +241,14 @@ for i in range(1, 6):
[lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
)
# plot model containing modeled piece-wise linear function
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_model)
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_opt)
# linear regression model
m_reg, c_reg = fitting.fit_linear_regression(d, C)
# AIC
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_reg * x_i + c_reg)
aic_regression = 4. - 2. * sum_log # two parameter: m_reg, c_reg
m_reg, c_reg, aic_reg = fitting.fit_linear_regression(d, C)
x = np.linspace(min(d), max(d), 500)
y = m_reg * x + c_reg
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_regression}")
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_reg}")
ax1.legend()
fig.savefig(f"uniform_random_point_clouds/{i}_betweenness.svg", format='svg')
@@ -284,16 +278,7 @@ for i in range(1, 6):
# optimize model's piece-wise linear function
d = quantification[:, 0]
C = quantification[:, 1]
m_opt, c0_opt, b_opt = fitting.fit_piece_wise_linear(d, C)
# AIC
# AIC = 2 * k (= 2) - 2 * ln(L^~)
# with L^~ = sum(f(x_i)) where x_i describes a data point
# - f is *not normalized*
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_opt* b_opt + c0_opt if x_i >= b_opt else m_opt * x_i + c0_opt)
aic_model = 6. - 2. * sum_log # three parameters: b_opt, m_opt, c0_opt
m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)
# TODO
# should this be part of the plotting function itself, it should not be necessary for me to do this
@@ -304,20 +289,14 @@ for i in range(1, 6):
[lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
)
# plot model containing modeled piece-wise linear function
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_model)
plot.quantification_plot(ax1, quantification, d_curve, C_curve, 'Models', aic_opt)
# linear regression model
m_reg, c_reg = fitting.fit_linear_regression(d, C)
# AIC
sum_log = 0.0
for x_i in x_spatial:
sum_log += math.log(m_reg * x_i + c_reg)
aic_regression = 4. - 2. * sum_log # two parameter: m_reg, c_reg
m_reg, c_reg, aic_reg = fitting.fit_linear_regression(d, C)
x = np.linspace(min(d), max(d), 500)
y = m_reg * x + c_reg
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_regression}")
ax1.plot(x, y, color='k', linewidth=1, label=f"Simple Linear Regression | AIC: {aic_reg}")
ax1.legend()
fig.savefig(f"uniform_random_point_clouds/{i}_pagerank.svg", format='svg')

2
requirements.txt
View File

@@ -1,4 +1,4 @@
gurobipy
gurobi
graph-tools
numpy
matplotlib

16
src/fitting.py
View File

@@ -1,3 +1,5 @@
import math
import gurobipy as gp
from gurobipy import GRB
import numpy as np
@@ -49,7 +51,11 @@ def fit_piece_wise_linear(d, C, M=1000):
model.addConstr((1 - z[i]) * M >= d[i] - b)
model.optimize()
return m.X, c0.X, b.X
# AIC
k = 4
aic = 2. * k + n * math.log(model.ObjVal)
return m.X, c0.X, b.X, aic
def fit_linear_regression(d, C):
@@ -71,11 +77,11 @@ def fit_linear_regression(d, C):
model.setObjective(gp.quicksum((C[i] - alpha - beta * d[i])**2 for i in range(n)), GRB.MINIMIZE)
model.optimize()
# AIC
k = 2
aic = 2. * k + n * math.log(model.ObjVal)
for v in model.getVars():
print(f"{v.VarName} {v.X:g}")
return beta.X, alpha.X
return beta.X, alpha.X, aic
def plot_piece_wise_linear(d, C, m_opt, c0_opt, b_opt, measure, n, t, path):