pymc-extras

Name: pymc-extras
Author: pymc-labs

28installs10forks

How to install pymc-extras?

pymc-labs/python-analytics-skills/pymc-extras

$npx -y skills add pymc-labs/python-analytics-skills --skill pymc-extras

Installs into the current project.

Summary

Load when the user is working with pymc-extras (pmx) features: splines / BSplineBasis, distributional regression / GAMLSS, R2D2M2CP or horseshoe priors, discrete variable marginalization, or Laplace approximation via fit_laplace. Triggers include: pymc_extras, pymc-extras, pmx, s

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SKILL.md

1	# PyMC-Extras (pmx) — Advanced Extensions
2
3	```python
4	import pymc_extras as pmx
5	```
6
7	## Splines
8
9	### BSplineBasis
10
11	Create B-spline basis matrices for nonlinear effects:
12
13	```python
14	import numpy as np
15	import pymc as pm
16	import pymc_extras as pmx
17
18	x = np.linspace(0, 1, 100)
19
20	# Create B-spline basis with 10 knots, degree 3 (cubic)
21	B = pmx.BSplineBasis(n_knots=10, degree=3)
22	basis_matrix = B.build(x) # shape: (100, n_basis)
23
24	with pm.Model() as spline_model:
25	# Coefficients for each basis function
26	w = pm.Normal("w", mu=0, sigma=1, shape=basis_matrix.shape[1])
27	mu = pm.math.dot(basis_matrix, w)
28	sigma = pm.HalfNormal("sigma", sigma=1)
29	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
30	```
31
32	### Penalized Splines with Smoothing Priors
33
34	Prevent overfitting by penalizing roughness via random walk priors on coefficients:
35
36	```python
37	with pm.Model() as penalized_spline:
38	# Smoothing parameter controls wiggliness
39	tau = pm.HalfCauchy("tau", beta=1)
40
41	# Random walk prior on spline coefficients (penalizes second differences)
42	w = pm.GaussianRandomWalk("w", sigma=tau, shape=basis_matrix.shape[1])
43
44	mu = pm.math.dot(basis_matrix, w)
45	sigma = pm.HalfNormal("sigma", sigma=1)
46	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
47	```
48
49	### ZeroSumNormalBasis
50
51	For identifiable models where basis coefficients must sum to zero:
52
53	```python
54	# Ensures sum-to-zero constraint on spline coefficients
55	B_zs = pmx.ZeroSumNormalBasis(n_knots=10, degree=3)
56	```
57
58	See `references/splines.md` for detailed spline reference.
59
60	## Distributional Regression (GAMLSS-style)
61
62	Model ALL distribution parameters as functions of covariates, not just the mean.
63
64	### Basic Pattern
65
66	```python
67	with pm.Model() as dist_reg:
68	# Model both mean AND variance as functions of covariates
69	# Location model
70	beta_mu = pm.Normal("beta_mu", 0, 1, shape=X.shape[1])
71	mu = pm.math.dot(X, beta_mu)
72
73	# Scale model (log link to ensure positivity)
74	beta_sigma = pm.Normal("beta_sigma", 0, 0.5, shape=Z.shape[1])
75	log_sigma = pm.math.dot(Z, beta_sigma)
76	sigma = pm.math.exp(log_sigma)
77
78	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
79	```
80
81	### Common Distributional Patterns
82
83	```python
84	# Beta regression: both mu and phi vary with covariates
85	with pm.Model() as beta_reg:
86	# Mean model (logit link)
87	beta_mu = pm.Normal("beta_mu", 0, 1, shape=X.shape[1])
88	mu = pm.math.sigmoid(pm.math.dot(X, beta_mu))
89
90	# Precision model (log link)
91	beta_phi = pm.Normal("beta_phi", 0, 0.5, shape=Z.shape[1])
92	phi = pm.math.exp(pm.math.dot(Z, beta_phi))
93
94	# Reparameterize: alpha = mu * phi, beta = (1-mu) * phi
95	y = pm.Beta("y", alpha=mu * phi, beta=(1 - mu) * phi, observed=y_obs)
96	```
97
98	```python
99	# Negative binomial: mu and alpha both depend on covariates
100	with pm.Model() as nb_dist:
101	beta_mu = pm.Normal("beta_mu", 0, 1, shape=X.shape[1])
102	mu = pm.math.exp(pm.math.dot(X, beta_mu))
103
104	beta_alpha = pm.Normal("beta_alpha", 0, 0.5, shape=Z.shape[1])
105	alpha = pm.math.exp(pm.math.dot(Z, beta_alpha))
106
107	y = pm.NegativeBinomial("y", mu=mu, alpha=alpha, observed=y_obs)
108	```
109
110	See `references/distributional.md` for more patterns.
111
112	## R2D2M2CP Prior
113
114	A prior for regression coefficients that reasons about the proportion of variance explained (R2) and decomposes it across predictors.
115
116	```python
117	with pm.Model() as r2d2_model:
118	# R2D2M2CP: specify expected R2 and concentration
119	beta, r2 = pmx.R2D2M2CP(
120	"beta",
121	X, # Design matrix
122	y_obs, # Observed response
123	r2=0.5, # Prior mean for R2
124	variance_concentration=None, # Equal concentration (default)
125	)
126	mu = pm.math.dot(X, beta)
127	sigma = pm.HalfNormal("sigma", sigma=1)
128	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
129	```
130
131	### When to Use R2D2M2CP vs Horseshoe
132
133	\| Aspect \| R2D2M2CP \| Horseshoe \|
134	\|---\|---\|---\|
135	\| Interpretability \| Reasons about R2 directly \| Reasons about shrinkage \|
136	\| Sparsity \| Soft shrinkage \| Strong sparsity (near-zero coefficients) \|
137	\| Best for \| Dense signals, moderate p \| Sparse signals, large p \|
138	\| Tuning \| Prior on R2 + concentration \| Global/local shrinkage scales \|
139	\| Implementation \| `pmx.R2D2M2CP()` \| Manual or pmx helper \|
140
141	For general prior specification guidance and elicitation workflows, see the [prior-elicitation skill](../prior-elicitation/SKILL.md).
142
143	## Regularized Horseshoe Prior
144
145	For sparse regression where most coefficients are expected to be near zero:
146
147	```pytho

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pymc-extras

28installs10forks

View on GitHub

How to install pymc-extras?

pymc-labs/python-analytics-skills/pymc-extras

$npx -y skills add pymc-labs/python-analytics-skills --skill pymc-extras

Installs into the current project.

Summary

Files · 1

View on GitHub

SKILL.md

1	# PyMC-Extras (pmx) — Advanced Extensions
2
3	```python
4	import pymc_extras as pmx
5	```
6
7	## Splines
8
9	### BSplineBasis
10
11	Create B-spline basis matrices for nonlinear effects:
12
13	```python
14	import numpy as np
15	import pymc as pm
16	import pymc_extras as pmx
17
18	x = np.linspace(0, 1, 100)
19
20	# Create B-spline basis with 10 knots, degree 3 (cubic)
21	B = pmx.BSplineBasis(n_knots=10, degree=3)
22	basis_matrix = B.build(x) # shape: (100, n_basis)
23
24	with pm.Model() as spline_model:
25	# Coefficients for each basis function
26	w = pm.Normal("w", mu=0, sigma=1, shape=basis_matrix.shape[1])
27	mu = pm.math.dot(basis_matrix, w)
28	sigma = pm.HalfNormal("sigma", sigma=1)
29	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
30	```
31
32	### Penalized Splines with Smoothing Priors
33
34	Prevent overfitting by penalizing roughness via random walk priors on coefficients:
35
36	```python
37	with pm.Model() as penalized_spline:
38	# Smoothing parameter controls wiggliness
39	tau = pm.HalfCauchy("tau", beta=1)
40
41	# Random walk prior on spline coefficients (penalizes second differences)
42	w = pm.GaussianRandomWalk("w", sigma=tau, shape=basis_matrix.shape[1])
43
44	mu = pm.math.dot(basis_matrix, w)
45	sigma = pm.HalfNormal("sigma", sigma=1)
46	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
47	```
48
49	### ZeroSumNormalBasis
50
51	For identifiable models where basis coefficients must sum to zero:
52
53	```python
54	# Ensures sum-to-zero constraint on spline coefficients
55	B_zs = pmx.ZeroSumNormalBasis(n_knots=10, degree=3)
56	```
57
58	See `references/splines.md` for detailed spline reference.
59
60	## Distributional Regression (GAMLSS-style)
61
62	Model ALL distribution parameters as functions of covariates, not just the mean.
63
64	### Basic Pattern
65
66	```python
67	with pm.Model() as dist_reg:
68	# Model both mean AND variance as functions of covariates
69	# Location model
70	beta_mu = pm.Normal("beta_mu", 0, 1, shape=X.shape[1])
71	mu = pm.math.dot(X, beta_mu)
72
73	# Scale model (log link to ensure positivity)
74	beta_sigma = pm.Normal("beta_sigma", 0, 0.5, shape=Z.shape[1])
75	log_sigma = pm.math.dot(Z, beta_sigma)
76	sigma = pm.math.exp(log_sigma)
77
78	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
79	```
80
81	### Common Distributional Patterns
82
83	```python
84	# Beta regression: both mu and phi vary with covariates
85	with pm.Model() as beta_reg:
86	# Mean model (logit link)
87	beta_mu = pm.Normal("beta_mu", 0, 1, shape=X.shape[1])
88	mu = pm.math.sigmoid(pm.math.dot(X, beta_mu))
89
90	# Precision model (log link)
91	beta_phi = pm.Normal("beta_phi", 0, 0.5, shape=Z.shape[1])
92	phi = pm.math.exp(pm.math.dot(Z, beta_phi))
93
94	# Reparameterize: alpha = mu * phi, beta = (1-mu) * phi
95	y = pm.Beta("y", alpha=mu * phi, beta=(1 - mu) * phi, observed=y_obs)
96	```
97
98	```python
99	# Negative binomial: mu and alpha both depend on covariates
100	with pm.Model() as nb_dist:
101	beta_mu = pm.Normal("beta_mu", 0, 1, shape=X.shape[1])
102	mu = pm.math.exp(pm.math.dot(X, beta_mu))
103
104	beta_alpha = pm.Normal("beta_alpha", 0, 0.5, shape=Z.shape[1])
105	alpha = pm.math.exp(pm.math.dot(Z, beta_alpha))
106
107	y = pm.NegativeBinomial("y", mu=mu, alpha=alpha, observed=y_obs)
108	```
109
110	See `references/distributional.md` for more patterns.
111
112	## R2D2M2CP Prior
113
114	A prior for regression coefficients that reasons about the proportion of variance explained (R2) and decomposes it across predictors.
115
116	```python
117	with pm.Model() as r2d2_model:
118	# R2D2M2CP: specify expected R2 and concentration
119	beta, r2 = pmx.R2D2M2CP(
120	"beta",
121	X, # Design matrix
122	y_obs, # Observed response
123	r2=0.5, # Prior mean for R2
124	variance_concentration=None, # Equal concentration (default)
125	)
126	mu = pm.math.dot(X, beta)
127	sigma = pm.HalfNormal("sigma", sigma=1)
128	y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
129	```
130
131	### When to Use R2D2M2CP vs Horseshoe
132
133	\| Aspect \| R2D2M2CP \| Horseshoe \|
134	\|---\|---\|---\|
135	\| Interpretability \| Reasons about R2 directly \| Reasons about shrinkage \|
136	\| Sparsity \| Soft shrinkage \| Strong sparsity (near-zero coefficients) \|
137	\| Best for \| Dense signals, moderate p \| Sparse signals, large p \|
138	\| Tuning \| Prior on R2 + concentration \| Global/local shrinkage scales \|
139	\| Implementation \| `pmx.R2D2M2CP()` \| Manual or pmx helper \|
140
141	For general prior specification guidance and elicitation workflows, see the [prior-elicitation skill](../prior-elicitation/SKILL.md).
142
143	## Regularized Horseshoe Prior
144
145	For sparse regression where most coefficients are expected to be near zero:
146
147	```pytho

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