NILC-Inference-Pipeline

This repository contains pipelines for calculating parameter posteriors obtained via needlet internal linear combination (NILC) power spectrum based inference (needlet_ILC_pipeline), harmonic internal linear combination (HILC) power spectrum based inference (harmonic_ILC_pipeline), and multifrequency power spectrum based inference (multifrequency_pipeline). The shared folder contains utilities and functions that are shared across various pipelines, including files for likelihood-free inference, hyperparameter tuning, symbolic regression, and map simulation. The code allows for an arbitrary number of frequency channels and components, but currently only the SEDs of the CMB, tSZ effect, and CIB are implemented. This can easily be modified by implementing other SEDs in the function spectral_response in shared/utils.py. In particular, the code computes posteriors on amplitude parameters that uniformly scale component power spectra over the entire multipole range.

For each pipeline, there are options for two types of inference: inference based on a Gaussian likelihood, and likelihood-free inference. When using the Gaussian likelihood, to ensure reliability of results with a given number of simulations, posteriors are computed using three methods: maximum likelihood estimation (MLE), Fisher matrix forecasting, and Markov chain Monte Carlo (MCMC). For likelihood-free inference, the default network used is a masked autoregressive flow, but this network can be changed, tuned, or custom-designed in sbi_utils.py.

Requirements and Set-up

• Requires a clone of the pyilc repository (https://github.com/jcolinhill/pyilc).
• Requires map files for all the components being included in the problem. See the yaml files for details on required files and naming conventions. For the CMB map, a .fits file in Kelvin is required (lensed alm can be downloaded from WebSky at https://mocks.cita.utoronto.ca/data/websky/v0.0/). tSZ maps in .fits file format in dimensionless Compton-y units can be generated via halosky (https://github.com/marcelo-alvarez/halosky) on NERSC.

Running

To run any of the main pipelines, one first needs to modify the appropriate yaml files. There are several examples for various set-ups. See the subsections below for details. For all variants of the needlet ILC pipeline and for some variants of the harmonic ILC pipeline (specifically, when using symbolic regression to estimate parameter dependence in likelihood-based inference), there is a large amount of I/O from running the program. This is handled by the python tempfile module. Temporary files and directories will be created in the directory specificed as "output_dir" in the yaml files. It is highly recommended to run on an HPC cluster and to set the output_dir parameter in the yaml files to be a directory in a SCRATCH space.

When using likelihood-free inference, one has the option to tune hyperparameters with wandb using yaml files containing "with_tuning", or one can manually set hyperparemters (or use default ones that have been optimized for specific problem set-ups) using yaml files containing "no_tuning". If using "with_tuning", one first needs to create a wandb account and optionally create a new project (otherwise a new uncategorized project will be created). See details here (steps 1 and 2): https://docs.wandb.ai/quickstart. The project name can then be entered in the yaml file. To log into wandb, one can either configure the log in before running the program or specify the account API key in the wandb_api_key input in the yaml file.

Instructions for running each of the pipelines are below. After running the pipelines, you can use tutorial_plotting_notebook.ipynb to plot the results.

To run the parameter inference pipeline using needlet ILC power spectra:

Modify gaussian_likelihood.yaml, lfi_no_tuning.yaml, lfi_with_tuning.yaml in needlet_ILC_pipeline/example_yaml_files before running the needlet ILC pipeline to use an explicit Gaussian likelihood (with parameter dependence determined via symbolic regression), likelihood-free inference (LFI) with fixed hyperparameters, or LFI with hyperparameter tuning, respectively. Then,
cd needlet_ILC_pipeline
python main.py --config=example_yaml_files/[FILENAME]

To run the parameter inference pipeline using multifrequency power spectra:

Modify gaussian_likelihood.yaml, lfi_no_tuning.yaml, or lfi_with_tuning.yaml in multifrequency_pipeline/example_yaml_files before running the multifrequency pipeline to use an explicit Gaussian likelihood, likelihood-free inference with fixed hyperparameters, or likelihood-free inference with hyperparameter tuning, respectively. Then,
cd multifrequency_pipeline
python main.py --config=example_yaml_files/[FILENAME]

To run the parameter inference pipeline using harmonic ILC power spectra:

Modify a yaml file in harmonic_ILC_pipeline/example_yaml_files before running the harmonic ILC pipeline. There are several variants. To compute the harmonic ILC weights once from some template power spectra and apply those same weights to every realization, use a file with "weights_once", and to compute weights separately for every realization, use a file with "weights_vary". Use weights_once_analytic.yaml, weights_once_SR.yaml, weights_once_LFI_no_tuning.yaml, or weights_once_LFI_with_tuning.yaml to compute the weights once and then use a Gaussian likelihood with analytic parameter dependence, a Gaussian likelihood with parameter dependence determined via symbolic regression (SR), likelihood-free inference (LFI) with fixed hyperparameters, or LFI with hyperparameter tuning, respectively. Similarly, use weights_vary_SR.yaml, weights_vary_LFI_no_tuning.yaml, or weights_vary_LFI_with_tuning.yaml to compute the weights separately for each simulation and then use a Gaussian likelihood (with parameter dependence determined via symbolic regression), likelihood-free inference (LFI) with fixed hyperparameters, or LFI with hyperparameter tuning, respectively. (Note that there is no option for analytic parameter dependence when the weights are varied for each simulation since the weights become nontrivial functions of the parameters in that case.) Then,
cd harmonic_ILC_pipeline
python main.py --config=example_yaml_files/[FILENAME]

Other Tools

The plotting_notebooks folder contains example Jupyter notebooks for producing plots after running the above pipelines. The mathematica_notebooks folder contains Mathematica notebooks demonstrating analytic comparisons of the HILC and multifrequency power spectrum approaches in a Gaussian likelihood. The toy_model folder runs inference using various methods (numerical and analytic MLE, Fisher matrix, MCMC, and likelihood-free inference) to verify that the results are the same on a simple toy model $A \cos(x) + Bx$, where $A$ and $B$ are free parameters to fit, and Gaussian noise is added to each realization. There are also various tests in the individual subdirectories.

Dependencies

python >= 3.7
pytorch
sbi
pyyaml
healpy
pysr
getdist
emcee
tqdm
wandb

Acknowledgments

Portions of this code are adapted from pyilc and sbi.