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Update pymc/logprob/transforms.py
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Co-authored-by: Ricardo Vieira <[email protected]>
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@LukeLB @ricardoV94
2 people authored and Luke LB committed Sep 4, 2023
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pymc as pm\n",
"import numpy as np\n",
"import pytensor.tensor as pt\n",
"import pytensor\n",
"from pymc.logprob.basic import logp"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"x_rv = pt.expm1(pt.random.normal())\n",
"\n",
"x_vv = x_rv.clone()\n",
"\n",
"x_logp_fn = pytensor.function([x_vv], pt.sum(logp(x_rv, x_vv)))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import pytensor.tensor as pt\n",
"import pytensor"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Elemwise(scalar_op=scalar_softplus,inplace_pattern=<frozendict {}>)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pt.log1pexp"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.6931471805599453"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def log(p = None):\n",
" return np.log(1+p)\n",
"log(True)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.6931471805599453"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(2)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.030929803620161386"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(np.cosh(0.25))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"y = np.exp(x)-1\n",
"y + 1 = np.exp(x)\n",
"np.log()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.993222846126381"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.arccosh(10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/yw/hvmlf6sd7yv3040wn8str6540000gn/T/ipykernel_5322/294505405.py:1: RuntimeWarning: invalid value encountered in log\n",
" np.log(-2)\n"
]
},
{
"data": {
"text/plain": [
"nan"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"# get assertion error because we are caulting jac det directly therefore skipping this line\n",
"# return pt.switch(pt.isnan(jacobian), -np.inf, input_logprob + jacobian)\n",
"# so is returned as nan rather than -inf as is expected\n",
"# hence switch statement in the test\n",
"\n",
"# also in have changed line 416 to \n",
"# return pt.switch(pt.isnan(input_logprob + jacobian), -np.inf, input_logprob + jacobian)\n",
"# as cosh transform was returtuning nan due to input_logprob being nan\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"import scipy.stats as stats\n",
"\n",
"def test_cosh_transform(test_val):\n",
" x_rv = pt.abs(pt.random.normal())\n",
" y_rv = pt.random.lognormal(sigma=1)\n",
"\n",
" x_vv = x_rv.clone()\n",
" y_vv = y_rv.clone()\n",
" x_transformed = pm.math.cosh(x_vv)\n",
" y_transformed = pm.math.cosh(y_vv)\n",
"\n",
" x_logp_fn = pytensor.function([x_vv], joint_logprob({x_rv: x_transformed}, sum=False))\n",
" y_logp_fn = pytensor.function([y_vv], joint_logprob({y_rv: y_transformed}, sum=False))\n",
"\n",
" # Calculate the log probability using SciPy's lognorm distribution\n",
" scipy_logp = stats.lognorm.logpdf(test_val, 1)\n",
"\n",
" assert np.allclose(x_logp_fn(test_val), y_logp_fn(test_val))\n",
" assert np.allclose(y_logp_fn(test_val), scipy_logp)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import pytensor\n",
"import pytensor.tensor as at\n",
"\n",
"k = at.iscalar(\"k\")\n",
"A = at.vector(\"A\")\n",
"\n",
"# Symbolic description of the result\n",
"result, updates = pytensor.scan(fn=lambda prior_result, A: prior_result * A,\n",
" outputs_info=at.ones_like(A),\n",
" non_sequences=A,\n",
" n_steps=k)\n",
"\n",
"# We only care about A**k, but scan has provided us with A**1 through A**k.\n",
"# Discard the values that we don't care about. Scan is smart enough to\n",
"# notice this and not waste memory saving them.\n",
"final_result = result[-1]\n",
"\n",
"# compiled function that returns A**k\n",
"power = pytensor.function(inputs=[A,k], outputs=final_result, updates=updates)\n",
"\n",
"print(power(range(10),2))\n",
"print(power(range(10),4))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def erfcxinv(y, tol = 1e-10, max_iter=100):\n",
" # Compute x using the appropriate formula for each value of y\n",
" x = at.switch(y <= 1, 1. / (y * at.sqrt(np.pi)), -at.sqrt(at.log(y)))\n",
" # for n in range(1, 8):\n",
" # x = x - (at.erfcx(x) - y) / (2 * x * at.erfcx(x) - 2 / at.sqrt(np.pi))\n",
" iter_count = 0\n",
" while iter_count < max_iter:\n",
" iter_count += 1\n",
" fx = at.erfcx(x) - y\n",
" fpx = 2 * x * at.erfcx(x) - 2 / at.sqrt(np.pi)\n",
" delta_x = fx / fpx\n",
" x = x - delta_x\n",
" if (at.abs(delta_x) < tol).all():\n",
" break\n",
" return x \n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Elemwise{sub,no_inplace}.0"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"erfcxinv(np.array([0.5, 0.5]))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "pymc-dev-py39",
"language": "python",
"name": "python3"
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"language_info": {
"codemirror_mode": {
"name": "ipython",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.0"
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"vscode": {
"interpreter": {
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}

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