We present GenJAX, a new language and compiler for vectorized programmable probabilistic inference. GenJAX integrates the vectorizing map (vmap) operation from array programming frameworks such as JAX into the programmable inference paradigm, enabling compositional vectorization of features such as probabilistic program traces, stochastic branching (for expressing mixture models), and programmable inference interfaces for writing custom probabilistic inference algorithms. We formalize vectorization as a source-to-source program transformation on a core calculus for probabilistic programming ( λ GEN ), and prove that it correctly vectorizes both modeling and inference operations. We have implemented our approach in the GenJAX language and compiler, and have empirically evaluated this implementation on several benchmarks and case studies. Our results show that our implementation supports a wide and expressive set of programmable inference patterns and delivers performance comparable to hand-optimized JAX code.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today’s PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented inJAX), and evaluate our automation on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.