HALOSCOPE - Halo PropertieS having Covariance Preserved with Environment

Citation

If you use this code, please cite the following paper:

The multi-dimensional halo assembly bias can be preserved when enhancing halo properties with HALOSCOPE, Ramakrishnan et al., 2024

ConditionalMultiVariateGaussian

This repository contains the ConditionalMultiVariateGaussian class, a model for predicting high-resolution dark matter halo properties conditioned on their local density environments. The model leverages conditional multivariate Gaussian modeling and supports customizable linear constraints on predictions.

Features

• Conditional Multivariate Gaussian Modeling: Models conditional dependencies between multivariate input and output data.
• Quantile Transformation: Transforms input and output data to approximate Gaussian distributions, which improves prediction accuracy.
• Linear Constraints: Ensures generated predictions meet specified linear constraints.
• Random Sampling: Supports probabilistic predictions by drawing samples from the conditional distribution.

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Installation

To use the ConditionalMultiVariateGaussian class, clone this repository and import it into your project as follows:

from haloscope import ConditionalMultiVariateGaussian

Ensure that you have the necessary dependencies installed:

pip install numpy
pip intall sklearn

Usage Example (for enhancing dark matter halo resolution in simulations)

Here’s an example script demonstrating how to use the ConditionalMultiVariateGaussian class to predict high-resolution properties of dark matter halos based on their local density environments. In this setup:

• x_train and y_train represent the local density environment and high-resolution halo properties from a high-resolution simulation.
• x_test represents the local density environment from a low-resolution simulation.

import numpy as np
from haloscope import ConditionalMultiVariateGaussian 

# Initialize the ConditionalMultiVariateGaussian model without constraints
cg = ConditionalMultiVariateGaussian(A=A, b=b)

# Generate synthetic data for training and testing as an example

# High-resolution simulation data (for training)
# x_train represents the local density environment of dark matter halos in the high-res simulation
x_train = np.random.randn(100000, 2)  # Example: 100,000 halos with 2 environmental properties
# y_train represents high-resolution properties of dark matter halos in the high-res simulation
y_train = np.random.randn(100000, 3)  # Example: 100,000 halos with 3 detailed properties

# Low-resolution simulation data (for testing/prediction)
# x_test represents the local density environment of dark matter halos in the low-res simulation
x_test = np.random.randn(20000, 2)  # Example: 20,000 halos with 2 environmental properties

# Fit the model on the high-resolution simulation data
cg.fit(x_train, y_train)

# Make predictions for the low-resolution simulation data
# The model will predict high-resolution halo properties for the low-res environment
y_pred = cg.predict(x_test)

# Example usage: y_pred now contains the predicted high-resolution properties of the halos in the low-res simulation
print("Predicted high-resolution properties for low-resolution halos:", y_pred)

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Class Documentation

ConditionalMultiVariateGaussian(A=A, b=b)

Parameters

• A (np.array, optional): Matrix defining linear constraints on predictions.
• b (np.array, optional): Vector for constraints that predictions should meet.

Default for A and b is a set of constraints for the dark matter halo properties described by equation 10 in Ramakrishnan et al., 2024 .

Methods

fit(x, y)

Fits the model to the training data.

• x (np.array): Input data matrix of shape (n_samples, n_features).
• y (np.array): Output data matrix of shape (n_samples, n_targets).

predict(xP)

Makes predictions based on new input data.

• xP (np.array): New input data matrix for predictions of shape (n_samples, n_features).
• Returns: Predicted values for y of shape (n_samples, n_targets).

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