Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Neural Posterior Estimation with Autoregressive Tiling for Detecting Objects in Astronomical Images

Jeffrey Regier

TL;DR

This work addresses the challenge of probabilistic object catalogs in large, high-density astronomical images by introducing a spatially autoregressive tiling scheme with a $K$-color checkerboard that mirrors the posterior dependencies. The variational family is amortized through a CNN-based inference network and fitted using neural posterior estimation (NPE) to minimize the forward KL, enabling efficient, likelihood-free inference for transdimensional catalogs. The authors prove that their variational structure can be configured to be a minimal I-map of the true posterior under suitable choices of $K$, tile size $T$, and radii $r_{\mathcal{X}}$, $r_{\mathcal{N}}$, and demonstrate state-of-the-art performance on SDSS data with improved posterior calibration. Two case studies—typical SDSS fields and a crowded M2-like starfield—show substantial gains in log-likelihood, precision, recall, and F1 over independent tiling methods and established approaches, while also discussing exposure bias and model misspecification as practical considerations for probabilistic catalogs and downstream science.

Abstract

Upcoming astronomical surveys will produce petabytes of high-resolution images of the night sky, providing information about billions of stars and galaxies. Detecting and characterizing the astronomical objects in these images is a fundamental task in astronomy -- and a challenging one, as most of these objects are faint and many visually overlap with other objects. We propose an amortized variational inference procedure to solve this instance of small-object detection. Our key innovation is a family of spatially autoregressive variational distributions that partition and order the latent space according to a $K$-color checkerboard pattern. By construction, the conditional independencies of this variational family mirror those of the posterior distribution. We fit the variational distribution, which is parameterized by a convolutional neural network, using neural posterior estimation (NPE) to minimize an expectation of the forward KL divergence. Using images from the Sloan Digital Sky Survey, our method achieves state-of-the-art performance. We further demonstrate that the proposed autoregressive structure greatly improves posterior calibration.

Neural Posterior Estimation with Autoregressive Tiling for Detecting Objects in Astronomical Images

TL;DR

This work addresses the challenge of probabilistic object catalogs in large, high-density astronomical images by introducing a spatially autoregressive tiling scheme with a -color checkerboard that mirrors the posterior dependencies. The variational family is amortized through a CNN-based inference network and fitted using neural posterior estimation (NPE) to minimize the forward KL, enabling efficient, likelihood-free inference for transdimensional catalogs. The authors prove that their variational structure can be configured to be a minimal I-map of the true posterior under suitable choices of , tile size , and radii , , and demonstrate state-of-the-art performance on SDSS data with improved posterior calibration. Two case studies—typical SDSS fields and a crowded M2-like starfield—show substantial gains in log-likelihood, precision, recall, and F1 over independent tiling methods and established approaches, while also discussing exposure bias and model misspecification as practical considerations for probabilistic catalogs and downstream science.

Abstract

Upcoming astronomical surveys will produce petabytes of high-resolution images of the night sky, providing information about billions of stars and galaxies. Detecting and characterizing the astronomical objects in these images is a fundamental task in astronomy -- and a challenging one, as most of these objects are faint and many visually overlap with other objects. We propose an amortized variational inference procedure to solve this instance of small-object detection. Our key innovation is a family of spatially autoregressive variational distributions that partition and order the latent space according to a -color checkerboard pattern. By construction, the conditional independencies of this variational family mirror those of the posterior distribution. We fit the variational distribution, which is parameterized by a convolutional neural network, using neural posterior estimation (NPE) to minimize an expectation of the forward KL divergence. Using images from the Sloan Digital Sky Survey, our method achieves state-of-the-art performance. We further demonstrate that the proposed autoregressive structure greatly improves posterior calibration.

Paper Structure

This paper contains 46 sections, 2 theorems, 37 equations, 17 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Generative models of astronomical images
  3. Prior
  4. Conditional likelihood
  5. A new representation of catalogs
  6. Tiling
  7. Objects of interest
  8. A variational family with spatially autoregressive tiling
  9. A checkerboard-based factorization
  10. The within-rank variational distribution
  11. The inference network
  12. Stuctural equivalence between the posterior and the variational distribution
  13. Fitting the variational distribution
  14. Comparison of ELBO-based VI and NPE
  15. Efficient NPE for fitting the proposed variational distribution
  16. ...and 31 more sections

Key Result

Proposition 0

Let $A \subset \Omega$ and $C \subset \Omega$ be subsets of the tile indices such that for all $a \in A$ and $c \in C$, $\|a - c\|_\infty \ge 2R/T + 1$. Let $B \coloneqq \Omega \setminus (A \cup C)$. Then, in the posterior,

Figures (17)

  • Figure 1: $K$-color checkerboard patterns for $K=$ 4, 9, and 16 colors, with color-specific ranks assigned by $\Psi(h, w)$. Tiles of the same color are separated by 1, 2, and 3 tiles, respectively, in these checkerboards, and $\sqrt{K} - 1$ in general.
  • Figure 2: The inference network. Sampling from $q(z \mid x)$ or evaluating a likelihood under it involves a single forward pass of the image backbone, whereas the neighborhood network and detection head must be called iteratively, for each tile rank $k \in \{1,\ldots K\}$ and each potential object $i \in \{1,\ldots,M\}$.
  • Figure 3: Three simulated images of a star. The tiles, which are $4\times{}4$ pixels in size, are demarked by thin white lines. The red dot in each image indicates the star's position within that image. In the left image, the star is imaged at a tile boundary. In the center image, the star is imaged 0.27 pixels below the tile boundary. In the right image, the star is imaged 0.54 pixels below the tile boundary.
  • Figure 4: Analyzing a simulated image of a star centered on the border of two tiles. Left) the image. Center-left) the marginal probability of detection in each tile under the BLISS variational distribution. Center-right) the conditional probabilty of detection given no detections in the white tiles. Right) the conditional probability of detection given a single object was detected in tile (3, 3).
  • Figure 5: The probability under the variational distribution of correctly detecting exactly one star, for simulated images of one star in a variety of positions. The simulated stars are either bright with a magnitude of 20.47 (left) or faint with a magnitude of 22.21 (right). Tile boundaries are at positions that are multiples of four.
  • ...and 12 more figures

Theorems & Definitions (4)

  • Proposition 0
  • Definition 1
  • Definition 2
  • Theorem 3