#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates.
# All rights reserved.
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
from collections.abc import Iterable
from configparser import NoOptionError
from typing import Any, Dict, List, Mapping, Optional, Tuple, Union
import numpy as np
import torch
from aepsych.config import Config
from botorch.models.gpytorch import GPyTorchModel
from scipy.stats import norm
from torch.quasirandom import SobolEngine
[docs]def make_scaled_sobol(
lb: torch.Tensor, ub: torch.Tensor, size: int, seed: Optional[int] = None
) -> torch.Tensor:
"""Create a scaled Sobol grid
Args:
lb (torch.Tensor): Lower bounds
ub (torch.Tensor): Upper bounds
size (int): Number of points to generate
seed (int, optional): Random seed. Defaults to None.
Returns:
torch.Tensor: Scaled Sobol grid
"""
lb, ub, ndim = _process_bounds(lb, ub, None)
grid = SobolEngine(dimension=ndim, scramble=True, seed=seed).draw(size).to(lb)
# rescale from [0,1] to [lb, ub]
grid = lb + (ub - lb) * grid
return grid
[docs]def dim_grid(
lower: torch.Tensor,
upper: torch.Tensor,
gridsize: int = 30,
slice_dims: Optional[Mapping[int, float]] = None,
) -> torch.Tensor:
"""Create a grid
Create a grid based on lower, upper, and dim.
Parameters
Args:
lower (int): lower bound.
upper (int): upper bound.
gridsize (int): size for grid. Defaults to 30.
slice_dims (Mapping[int, float], optional): values to use for slicing axes, as an {index:value} dict. Defaults to None.
Returns:
torch.Tensor: Tensor of grid points.
"""
slice_dims = slice_dims or {}
lower, upper, dim = _process_bounds(lower, upper, None)
mesh_vals = []
for i in range(dim):
if i in slice_dims.keys():
mesh_vals.append(slice(slice_dims[i] - 1e-10, slice_dims[i] + 1e-10, 1))
else:
mesh_vals.append(slice(lower[i].item(), upper[i].item(), gridsize * 1j)) # type: ignore
return torch.Tensor(np.mgrid[mesh_vals].reshape(dim, -1).T)
def _process_bounds(
lb: Union[np.ndarray, torch.Tensor, List],
ub: Union[np.ndarray, torch.Tensor, List],
dim: Optional[int],
) -> Tuple[torch.Tensor, torch.Tensor, int]:
"""Helper function for ensuring bounds are correct shape and type.
Args:
lb (Union[np.ndarray, torch.Tensor, List]): Lower bounds.
ub (Union[np.ndarray, torch.Tensor, List]): Upper bounds.
dim (int, optional): Dimension of the bounds.
Returns:
Tuple[torch.Tensor, torch.Tensor, int]: Tuple of lower bounds, upper bounds, and dimension.
"""
lb = promote_0d(lb)
ub = promote_0d(ub)
if not isinstance(lb, torch.Tensor):
lb = torch.tensor(lb)
if not isinstance(ub, torch.Tensor):
ub = torch.tensor(ub)
lb = lb.to(torch.float64)
ub = ub.to(torch.float64)
assert lb.shape[0] == ub.shape[0], "bounds should be of equal shape!"
if dim is not None:
if lb.shape[0] == 1:
lb = lb.repeat(dim)
ub = ub.repeat(dim)
else:
assert lb.shape[0] == dim, "dim does not match shape of bounds!"
else:
dim = lb.shape[0]
for i, (l, u) in enumerate(zip(lb, ub)):
assert (
l <= u
), f"Lower bound {l} is not less than or equal to upper bound {u} on dimension {i}!"
return lb, ub, dim
[docs]def interpolate_monotonic(
x: Union[torch.Tensor, np.ndarray],
y: Union[torch.Tensor, np.ndarray],
z: Union[torch.Tensor, np.ndarray, float],
min_x: Union[torch.Tensor, np.ndarray, float] = -np.inf,
max_x: Union[torch.Tensor, np.ndarray, float] = np.inf,
) -> Any:
"""Interpolate a monotonic function
Args:
x (Union[torch.Tensor, np.ndarray]): x values.
y (Union[torch.Tensor, np.ndarray]): y values.
z (Union[torch.Tensor, np.ndarray, float]): z values.
min_x (Union[torch.Tensor, np.ndarray, float]): Minimum x value. Defaults to -np.inf.
max_x (Union[torch.Tensor, np.ndarray, float]): Maximum x value. Defaults to np.inf.
Returns:
Any: Interpolated value.
"""
# Ben Letham's 1d interpolation code, assuming monotonicity.
# basic idea is find the nearest two points to the LSE and
# linearly interpolate between them (I think this is bisection
# root-finding)
idx = np.searchsorted(y, z)
if idx == len(y):
return float(max_x)
elif idx == 0:
return float(min_x)
x0 = x[idx - 1]
x1 = x[idx]
y0 = y[idx - 1]
y1 = y[idx]
x_star = x0 + (x1 - x0) * (z - y0) / (y1 - y0)
if isinstance(x_star, torch.Tensor):
return x_star.cpu().item()
else:
return x_star
[docs]def get_lse_interval(
model: GPyTorchModel,
mono_grid: Union[torch.Tensor, np.ndarray],
target_level: float,
grid_lb: torch.Tensor,
grid_ub: torch.Tensor,
cred_level: Optional[float] = None,
mono_dim: int = -1,
n_samps: int = 500,
lb: float = -float("inf"),
ub: float = float("inf"),
gridsize: int = 30,
**kwargs,
) -> Union[Tuple[torch.Tensor, torch.Tensor, torch.Tensor], torch.Tensor]:
"""Get the level set estimate interval
Args:
model (GPyTorchModel): Model to use for sampling.
mono_grid (Union[torch.Tensor, np.ndarray]): Monotonic grid.
target_level (float): Target level.
grid_lb (torch.Tensor): The lower bound of the grid to sample from to calculate
LSE.
grid_ub (torch.Tensor): The upper bound of the grid to sample from to calculate
LSE.
cred_level (float, optional): Credibility level. Defaults to None.
mono_dim (int): Monotonic dimension. Defaults to -1.
n_samps (int): Number of samples. Defaults to 500.
lb (float): Theoreticaly true lower bound for the parameter. Defaults to
-float("inf").
ub (float): Theoretical true uppper bound for the parameters. Defaults to
float("inf").
gridsize (int): Grid size. Defaults to 30.
Returns:
Union[Tuple[torch.Tensor, torch.Tensor, torch.Tensor], torch.Tensor]: Level set estimate interval.
"""
# Create a meshgrid using torch.linspace
xgrid = torch.stack(
torch.meshgrid(
[
torch.linspace(grid_lb[i].item(), grid_ub[i].item(), gridsize)
for i in range(model.dim)
]
),
dim=-1,
).reshape(-1, model.dim)
if model.transforms is not None:
xgrid = model.transforms.untransform(xgrid)
samps = model.sample(xgrid, num_samples=n_samps, **kwargs)
samps = [s.reshape((gridsize,) * model.dim) for s in samps]
# Define the normal distribution for the CDF
normal_dist = torch.distributions.Normal(0, 1)
# Calculate contours using torch.stack and the torch CDF for each sample
contours = torch.stack(
[
get_lse_contour(
normal_dist.cdf(s), mono_grid, target_level, mono_dim, lb, ub
)
for s in samps
]
)
if cred_level is None:
return torch.median(contours, dim=0).values
else:
alpha = 1 - cred_level
qlower = alpha / 2
qupper = 1 - alpha / 2
lower = torch.quantile(contours, qlower, dim=0)
upper = torch.quantile(contours, qupper, dim=0)
median = torch.quantile(contours, 0.5, dim=0)
return median, lower, upper
[docs]def get_lse_contour(
post_mean: torch.Tensor,
mono_grid: Union[torch.Tensor, np.ndarray],
level: float,
mono_dim: int = -1,
lb: Union[torch.Tensor, float] = -np.inf,
ub: Union[torch.Tensor, float] = np.inf,
) -> torch.Tensor:
"""Get the level set estimate contour
Args:
post_mean (torch.Tensor): Posterior mean.
mono_grid (Union[torch.Tensor, np.ndarray]): Monotonic grid.
level (float): Level.
mono_dim (int): Monotonic dimension. Defaults to -1.
lb (float): Lower bound. Defaults to -np.inf.
ub (float): Upper bound. Defaults to np.inf.
Returns:
torch.Tensor: Level set estimate contour.
"""
return torch.tensor(
np.apply_along_axis(
lambda p: interpolate_monotonic(mono_grid, p, level, lb, ub),
mono_dim,
post_mean,
)
)
[docs]def get_jnd_1d(
post_mean: torch.Tensor,
mono_grid: torch.Tensor,
df: int = 1,
mono_dim: int = -1,
lb: Union[torch.Tensor, float] = -float("inf"),
ub: Union[torch.Tensor, float] = float("inf"),
) -> torch.Tensor:
"""Get the just noticeable difference for a 1D function
Args:
post_mean (torch.Tensor): Posterior mean.
mono_grid (torch.Tensor): Monotonic grid.
df (int): Degrees of freedom. Defaults to 1.
mono_dim (int): Monotonic dimension. Defaults to -1.
lb (Union[torch.Tensor, float]): Lower bound. Defaults to -float("inf").
ub (Union[torch.Tensor, float]): Upper bound. Defaults to float("inf").
Returns:
torch.Tensor: Just noticeable difference.
"""
interpolate_to = post_mean + df
return torch.tensor(
(
np.array(
[
interpolate_monotonic(mono_grid, post_mean, ito)
for ito in interpolate_to
]
)
- mono_grid.numpy()
)
)
[docs]def get_jnd_multid(
post_mean: torch.Tensor,
mono_grid: torch.Tensor,
df: int = 1,
mono_dim: int = -1,
lb: Union[torch.Tensor, float] = -float("inf"),
ub: Union[torch.Tensor, float] = float("inf"),
) -> torch.Tensor:
"""Get the just noticeable difference for a multidimensional function
Args:
post_mean (torch.Tensor): Posterior mean.
mono_grid (torch.Tensor): Monotonic grid.
df (int): Degrees of freedom. Defaults to 1.
mono_dim (int): Monotonic dimension. Defaults to -1.
lb (Union[torch.Tensor, float]): Lower bound. Defaults to -float("inf").
ub (Union[torch.Tensor, float]): Upper bound. Defaults to float("inf").
Returns:
torch.Tensor: Just noticeable difference.
"""
# Move mono_dim to the last dimension if it isn't already
if mono_dim != -1:
post_mean = post_mean.transpose(mono_dim, -1)
# Apply get_jnd_1d in a vectorized way
result = get_jnd_1d(post_mean, mono_grid, df=df, mono_dim=-1, lb=lb, ub=ub)
# Transpose back if necessary
if mono_dim != -1:
result = result.transpose(-1, mono_dim)
return result
[docs]def get_bounds(config: Config) -> torch.Tensor:
r"""Return the bounds for all parameters in config. Note that these bounds are
likely to be in the raw parameter space and any transformations that may affect
these bounds are unaccounted for. If the transformed bounds are needed, use the
transforms.transform_options() function to first transform the config and manually
get the transformed bounds from the ub/lb options in the common section.
Args:
config (Config): The config to find the bounds from.
Returns:
torch.Tensor: A `[2, d]` tensor with the lower and upper bounds for each
parameter.
"""
parnames = config.getlist("common", "parnames", element_type=str)
# Try to build a full array of bounds based on parameter-specific bounds
try:
_lower_bounds = torch.tensor(
[config.getfloat(par, "lower_bound") for par in parnames]
)
_upper_bounds = torch.tensor(
[config.getfloat(par, "upper_bound") for par in parnames]
)
bounds = torch.stack((_lower_bounds, _upper_bounds))
except NoOptionError: # Look for general lb/ub array
_lb = config.gettensor("common", "lb")
_ub = config.gettensor("common", "ub")
bounds = torch.stack((_lb, _ub))
return bounds
[docs]def get_optimizer_options(config: Config, name: str) -> Dict[str, Any]:
"""Return the optimizer options for the model to pass to the SciPy L-BFGS-B
optimizer. Only the somewhat useful ones for AEPsych are searched for: maxcor,
ftol, gtol, maxfun, maxiter, maxls. See docs for details:
https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html#optimize-minimize-lbfgsb
Args:
config (Config): Config to search for options.
name (str): Model name to look for options for.
Return:
Dict[str, Any]: Dictionary of options to pass to SciPy's minimize, assuming the
method is L-BFGS-B.
"""
options: Dict[str, Optional[Union[float, int]]] = {}
options["maxcor"] = config.getint(name, "maxcor", fallback=None)
options["ftol"] = config.getfloat(name, "ftol", fallback=None)
options["gtol"] = config.getfloat(name, "gtol", fallback=None)
options["maxfun"] = config.getint(name, "maxfun", fallback=None)
options["maxiter"] = config.getint(name, "maxiter", fallback=None)
options["maxls"] = config.getint(name, "maxls", fallback=None)
# Filter all the nones out, which could just come back as an empty dict
options = {key: value for key, value in options.items() if value is not None}
return options
[docs]def get_dims(config: Config) -> int:
"""Return the number of dimensions in the parameter space. This accounts for any
transforms that may modify the the parameter space for the model (e.g., Fixed
parameters will not be included).
Args:
config (Config): The config to look for the number of dimensions.
Return:
int: The number of dimensions in the search space.
"""
parnames = config.getlist("common", "parnames", element_type=str)
# This is pretty weak but fixed is currently the only thing that will changed the
# search space dims, when categorial transforms go in, this function needs to be
# smarter.
try:
valid_pars = [
parname for parname in parnames if config[parname]["par_type"] != "fixed"
]
return len(valid_pars)
except KeyError:
# Likely old style of parameter definition, fallback to looking at a bound
return len(config.getlist("common", "lb", element_type=float))
