|
| 1 | +import numpy as np |
| 2 | +import pytest |
| 3 | + |
| 4 | +import pytensor.tensor as pt |
| 5 | +from pytensor.graph.replace import graph_replace |
| 6 | +from pytensor.graph.rewriting import rewrite_graph |
| 7 | +from pytensor.graph.traversal import explicit_graph_inputs |
| 8 | + |
| 9 | + |
| 10 | +def create_radon_model( |
| 11 | + intercept_dist="normal", sigma_dist="halfnormal", centered=False |
| 12 | +): |
| 13 | + def halfnormal(name, *, sigma=1.0, model_logp): |
| 14 | + log_value = pt.scalar(f"{name}_log") |
| 15 | + value = pt.exp(log_value) |
| 16 | + |
| 17 | + logp = ( |
| 18 | + -0.5 * ((value / sigma) ** 2) + pt.log(pt.sqrt(2.0 / np.pi)) - pt.log(sigma) |
| 19 | + ) |
| 20 | + logp = pt.switch(value >= 0, logp, -np.inf) |
| 21 | + model_logp.append(logp + value) |
| 22 | + return value |
| 23 | + |
| 24 | + def normal(name, *, mu=0.0, sigma=1.0, model_logp, observed=None): |
| 25 | + value = pt.scalar(name) if observed is None else pt.as_tensor(observed) |
| 26 | + |
| 27 | + logp = ( |
| 28 | + -0.5 * (((value - mu) / sigma) ** 2) |
| 29 | + - pt.log(pt.sqrt(2.0 * np.pi)) |
| 30 | + - pt.log(sigma) |
| 31 | + ) |
| 32 | + model_logp.append(logp) |
| 33 | + return value |
| 34 | + |
| 35 | + def lognormal(name, *, mu=0.0, sigma=1.0, model_logp): |
| 36 | + value = normal(name, mu=mu, sigma=sigma, model_logp=model_logp) |
| 37 | + return pt.exp(value) |
| 38 | + |
| 39 | + def zerosumnormal(name, *, sigma=1.0, size, model_logp): |
| 40 | + raw_value = pt.vector(f"{name}_zerosum", shape=(size - 1,)) |
| 41 | + n = raw_value.shape[0] + 1 |
| 42 | + sum_vals = raw_value.sum(0, keepdims=True) |
| 43 | + norm = sum_vals / (pt.sqrt(n) + n) |
| 44 | + fill_value = norm - sum_vals / pt.sqrt(n) |
| 45 | + value = pt.concatenate([raw_value, fill_value]) - norm |
| 46 | + |
| 47 | + shape = value.shape |
| 48 | + _full_size = pt.prod(shape) |
| 49 | + _degrees_of_freedom = pt.prod(shape[-1:].inc(-1)) |
| 50 | + logp = pt.sum( |
| 51 | + -0.5 * ((value / sigma) ** 2) |
| 52 | + - (pt.log(pt.sqrt(2.0 * np.pi)) + pt.log(sigma)) |
| 53 | + * (_degrees_of_freedom / _full_size) |
| 54 | + ) |
| 55 | + model_logp.append(logp) |
| 56 | + return value |
| 57 | + |
| 58 | + dist_fn_map = { |
| 59 | + fn.__name__: fn for fn in (halfnormal, normal, lognormal, zerosumnormal) |
| 60 | + } |
| 61 | + |
| 62 | + rng = np.random.default_rng(1) |
| 63 | + n_counties = 85 |
| 64 | + county_idx = rng.integers(n_counties, size=919) |
| 65 | + county_idx.sort() |
| 66 | + floor = rng.binomial(n=1, p=0.5, size=919).astype(np.float64) |
| 67 | + log_radon = rng.normal(size=919) |
| 68 | + |
| 69 | + model_logp = [] |
| 70 | + intercept = dist_fn_map[intercept_dist]( |
| 71 | + "intercept", sigma=10, model_logp=model_logp |
| 72 | + ) |
| 73 | + |
| 74 | + # County effects |
| 75 | + county_sd = halfnormal("county_sd", model_logp=model_logp) |
| 76 | + if centered: |
| 77 | + county_effect = zerosumnormal( |
| 78 | + "county_raw", sigma=county_sd, size=n_counties, model_logp=model_logp |
| 79 | + ) |
| 80 | + else: |
| 81 | + county_raw = zerosumnormal("county_raw", size=n_counties, model_logp=model_logp) |
| 82 | + county_effect = county_raw * county_sd |
| 83 | + |
| 84 | + # Global floor effect |
| 85 | + floor_effect = normal("floor_effect", sigma=2, model_logp=model_logp) |
| 86 | + |
| 87 | + county_floor_sd = halfnormal("county_floor_sd", model_logp=model_logp) |
| 88 | + if centered: |
| 89 | + county_floor_effect = zerosumnormal( |
| 90 | + "county_floor_raw", |
| 91 | + sigma=county_floor_sd, |
| 92 | + size=n_counties, |
| 93 | + model_logp=model_logp, |
| 94 | + ) |
| 95 | + else: |
| 96 | + county_floor_raw = zerosumnormal( |
| 97 | + "county_floor_raw", size=n_counties, model_logp=model_logp |
| 98 | + ) |
| 99 | + county_floor_effect = county_floor_raw * county_floor_sd |
| 100 | + |
| 101 | + mu = ( |
| 102 | + intercept |
| 103 | + + county_effect[county_idx] |
| 104 | + + floor_effect * floor |
| 105 | + + county_floor_effect[county_idx] * floor |
| 106 | + ) |
| 107 | + |
| 108 | + sigma = dist_fn_map[sigma_dist]("sigma", model_logp=model_logp) |
| 109 | + _ = normal( |
| 110 | + "log_radon", |
| 111 | + mu=mu, |
| 112 | + sigma=sigma, |
| 113 | + observed=log_radon, |
| 114 | + model_logp=model_logp, |
| 115 | + ) |
| 116 | + |
| 117 | + model_logp = pt.sum([logp.sum() for logp in model_logp]) |
| 118 | + model_logp = rewrite_graph( |
| 119 | + model_logp, include=("canonicalize", "stabilize"), clone=False |
| 120 | + ) |
| 121 | + params = list(explicit_graph_inputs(model_logp)) |
| 122 | + model_dlogp = pt.concatenate([term.ravel() for term in pt.grad(model_logp, params)]) |
| 123 | + |
| 124 | + size = sum(int(np.prod(p.type.shape)) for p in params) |
| 125 | + joined_inputs = pt.vector("joined_inputs", shape=(size,)) |
| 126 | + idx = 0 |
| 127 | + replacement = {} |
| 128 | + for param in params: |
| 129 | + param_shape = param.type.shape |
| 130 | + param_size = int(np.prod(param_shape)) |
| 131 | + replacement[param] = joined_inputs[idx : idx + param_size].reshape(param_shape) |
| 132 | + idx += param_size |
| 133 | + assert idx == joined_inputs.type.shape[0] |
| 134 | + |
| 135 | + model_logp, model_dlogp = graph_replace([model_logp, model_dlogp], replacement) |
| 136 | + return joined_inputs, [model_logp, model_dlogp] |
| 137 | + |
| 138 | + |
| 139 | +@pytest.fixture(scope="session") |
| 140 | +def radon_model(): |
| 141 | + return create_radon_model() |
| 142 | + |
| 143 | + |
| 144 | +@pytest.fixture(scope="session") |
| 145 | +def radon_model_variants(): |
| 146 | + # Convert to list comp |
| 147 | + return [ |
| 148 | + create_radon_model( |
| 149 | + intercept_dist=intercept_dist, |
| 150 | + sigma_dist=sigma_dist, |
| 151 | + centered=centered, |
| 152 | + ) |
| 153 | + for centered in (True, False) |
| 154 | + for intercept_dist in ("normal", "lognormal") |
| 155 | + for sigma_dist in ("halfnormal", "lognormal") |
| 156 | + ] |
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