Photometry is all you need: supernova classification as a mixing problem

Technical Summary: Photometry is all you need: supernova classification as a mixing problem

Problem Statement
The advent of large-scale photometric surveys, such as the Zwicky Transient Facility (ZTF) and the upcoming Vera C. Rubin Observatory (LSST), has created a bottleneck in transient astronomy: the inability to spectroscopically follow up the millions of candidate supernovae (SNe) being detected. While spectroscopy remains the gold standard for classification, it is infeasible for the vast majority of transients (>90%). Current machine learning approaches for SN classification often rely on supervised learning, requiring large, labeled training sets that are specific to a particular survey's observational parameters. This creates significant challenges regarding "domain shift" (the inability to apply a model trained on one dataset to another) and class imbalance (where SNe Ia vastly outnumber SNe Ibc). Consequently, there is a need for scalable, robust classification methods that rely solely on photometric light curves without requiring labeled training data or spectroscopic follow-up for individual objects.

Methodology
The authors propose a novel framework that treats SN classification as a population-level mixing problem rather than an individual object classification task. The methodology proceeds in three main stages:

1. Light Curve Fitting: The authors utilize a semi-analytical "Arnett" model, which describes SN luminosity as being powered by the radioactive decay of $^{56}\text{Ni}$ and $^{56}\text{Co}$. They fit this model to photometric light curves (specifically $g$ and $r$ bands) from the ZTF Bright Transient Survey (BTS). The fitting process optimizes four parameters: ejecta velocity ($v_{ej}$), ejecta mass ($M_{ej}$), the fraction of initial $^{56}\text{Ni}$ ($f_{Ni}$), and the explosion time ($t_{exp}$). The authors found that using the full set of parameters in a Gaussian Mixture Model (GMM) was computationally challenging and less effective; instead, they selected a subset of two parameters—$\log_{10}(v_{ej})$ and $\log_{10}(f_{Ni})$—which provided the best discriminatory power between SNe Ia and SNe Ibc.

2. Gaussian Mixture Modeling (GMM): The distributions of the fitted parameters ($\log_{10}(v_{ej})$ and $\log_{10}(f_{Ni})$) are modeled as a mixture of two multivariate Gaussian distributions, representing the two SN populations. The model is parameterized by a mixing fraction $\alpha$ (the fraction of SNe Ibc) and the mean vectors and covariance matrices of the two components. The Expectation-Maximization (EM) algorithm is used to optimize these parameters. To avoid local minima, the authors initialize the GMM using 2D KMeans clustering and repeat the fit 30 times with different initializations, selecting the result with the highest log-likelihood.

3. Classification and Validation: Once the GMM is fitted, individual objects are classified based on the posterior probability ($\gamma$) of belonging to the SNe Ia component. Objects with $\gamma_{Ia} \geq 0.5$ are classified as SNe Ia. The method was tested under three redshift scenarios: (a) using ground-truth spectroscopic redshifts, (b) using simulated photometric redshifts (with broad bounds), and (c) assuming no redshift information. Additionally, the authors explored a "10% known" scenario where 10% of the population had known spectroscopic labels to test if partial supervision improved performance.

Key Results

• High Accuracy without Labels: The method achieves classification accuracy of $\geq 90\%$ for both SNe Ia and SNe Ibc across a range of population mixing fractions (0.1 to 0.5) without requiring any labeled training data.
• Redshift Sensitivity: Models utilizing spectroscopic redshifts and those utilizing simulated photometric redshifts perform nearly identically, both maintaining high accuracy ($\geq 90\%$). In contrast, the "no-redshift" case performs significantly worse, often heavily underestimating the mixing fraction and dropping accuracy to as low as 50%.
• Impact of Known Labels: The inclusion of 10% known spectroscopic labels provides negligible improvement for the spectroscopic and photometric redshift cases. However, for the "no-redshift" case, adding 10% known labels significantly improves performance, raising accuracy to $\geq 80\%$.
• Purity and Completeness: For the spectroscopic and photometric redshift cases, the model achieves $\sim90\%$ purity and completeness for SNe Ia and $\sim80\%$ for SNe Ibc. The model shows a slight bias toward over-classifying SNe as Ibc at low Ibc fractions, leading to slightly higher Ia purity than Ibc purity.
• Parameter Selection: The authors found that fitting all parameters from both the Arnett and SALT2 models simultaneously (using a diagonal covariance matrix) did not improve performance and, in some cases, diluted the signal of the most discriminatory features. The two-parameter subset ($\log_{10}(v_{ej})$ and $\log_{10}(f_{Ni})$) proved optimal.

Significance and Claims
The paper claims that "photometry is all you need" to reliably classify SNe Ia and Ibc, provided that redshift information (even rough photometric estimates) is available. The primary significance of this work lies in its ability to:

1. Eliminate the need for labeled training data: By framing the problem as a population mixing problem, the method avoids the domain shift issues inherent in supervised learning, allowing it to be applied to any survey dataset where the majority class is known but individual labels are not.
2. Enable population characterization: The method not only classifies individual objects but also constrains the mixing fraction of the population, which is critical for cosmological parameter estimation where SN Ibc contamination can bias distance modulus calculations.
3. Provide a scalable solution: The approach is robust to changes in survey parameters and mixing fractions, making it suitable for the massive datasets expected from the LSST era.

The authors note that while the method is robust, it requires fitting a light curve model for every object, which is computationally more intensive than a simple neural network forward pass. They suggest that this bottleneck could be mitigated in the future by using simulation-based inference to predict fit parameters directly, though this would reintroduce domain-specific training requirements. Furthermore, the authors caution that allowing fit parameters to reach non-physical values (e.g., $f_{Ni} > 1$) improves statistical discrimination but renders those specific parameter values physically meaningless for studying intrinsic physics.