Research map / Probabilistic and scientific modeling / Variational and generative sampling
Latent variable marginalization and estimators
Estimates marginal likelihood and marginalizes discrete latent variables with unbiased estimators.
91 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Variational and generative sampling, keyword cluster “estimation · probabilistic · variables”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
14 papers in 2023–24 and 10 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 3.4% to 2.0%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Multi-view Anomaly Detection via Robust Probabilistic Latent Variable Models (NeurIPS 2016 · 30 citations)
- 2017 · Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions (AAAI 2017 · 28 citations)
- 2018 · Learning Latent Permutations with Gumbel-Sinkhorn Networks (ICLR 2018 · 148 citations)
- 2019 · Latent Space Autoregression for Novelty Detection (CVPR 2019 · 500 citations)
- 2020 · Sparse and Continuous Attention Mechanisms (NeurIPS 2020 · 16 citations)
- 2021 · Group Fairness by Probabilistic Modeling with Latent Fair Decisions (AAAI 2021 · 14 citations)
- 2022 · Function Classes for Identifiable Nonlinear Independent Component Analysis (NeurIPS 2022 · 3 citations)
- 2023 · Learning Joint Latent Space EBM Prior Model for Multi-Layer Generator (CVPR 2023 · 7 citations)
- 2024 · Total Variation Floodgate for Variable Importance Inference in Classification (ICML 2024 · 0 citations)
- 2025 · Gaussian Graphical Modelling Without Independence Assumptions for Uncentered Data (AAAI 2025 · 1 citation)
- 2026 · Beyond Softmax: A Natural Parameterization for Categorical Random Variables (ICML 2026 · 0 citations)
Earliest papers here
- Multi-view Anomaly Detection via Robust Probabilistic Latent Variable Models (NeurIPS 2016 · 30 citations)
- Completely random measures for modelling block-structured sparse networks (NeurIPS 2016 · 28 citations)
- Progressive EM for Latent Tree Models and Hierarchical Topic Detection (AAAI 2016 · 27 citations)
What has been tried
82 papers here report 699 measured changes (a component added, removed or swapped, compared with a baseline): helped 69%, no clear effect 9%, hurt 16%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase the threshold τ | Gaussian distribution · false positive rate | Helped | Learning Local Neighborhoods of Non-Gaussian Graphical Models (AAAI 2025 · 0 citations) | |
| Vary latent dimension D and sample number N | Adult · AUC | 0.7822–0.7857 | Mixed | Learning Monotonic Probabilities with a Generative Cost Model (ICML 2025 · 0 citations) |
| Add C-sharing across integral-unit groups | QT-CP, K=128 · optimization-step time (ms) | OOM -> 25 | Helped | Scaling Continuous Latent Variable Models as Probabilistic Integral Circuits (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 7 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 2 of 7 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 24 papers; from OpenAlex and the papers' affiliations).
- Massachusetts Institute of Technology · 2 papers
- Meta · 2 papers
- Harvard University · 2 papers
Use it
Download BibTeX of 36 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Likelihood-free and graphical model estimation (161 papers)
- Tractable probabilistic models (90 papers)
- Exact inference for probabilistic programs (103 papers)
- Gradient estimation for discrete variables (74 papers)
- Mutual information estimation (27 papers)
Elsewhere in the topic
- Flow matching and flow sampling (144 papers)
- Posterior sampling with diffusion guidance (137 papers)
- Score-based generative modeling analysis (128 papers)
- Structured latent VAEs (125 papers)
- Disentangled and discrete latent models (92 papers)
- Variational inference theory and gradients (89 papers)
- Hamiltonian Monte Carlo (89 papers)
- Regularizing VAE latent information (89 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).