Pith. sign in

REVIEW 3 major objections 5 minor 29 references

Revisiting Unbiased Implicit Variational Inference

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Unbiased implicit variational inference can drop its MCMC loop: a learned conditional normalizing flow proposal yields debiased score gradients, and the resulting AISIVI algorithm matches state-of-the-art SIVI methods.

desk verdict A genuinely useful SIVI training recipe that replaces UIVI's MCMC with a learned IS proposal; the 'without bias' claim is overstated and the empirical section needs more care, but the core idea is sound and worth refereeing. read the letter →

arxiv 2506.03839 v1 pith:2YTSK2E4 submitted 2025-06-04 cs.LG stat.ML

Tobias Pielok , Bernd Bischl , David Rügamer This is my paper
classification cs.LGstat.ML
keywords semi-implicitvariationalinferenceimportancesamplingconditionalnormalizingflowsunbiasedgradientestimationreverseKLdivergenceimplicitpathestimatorMonteCarlo
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that unbiased implicit variational inference (UIVI), long dismissed for its expensive inner MCMC loop, can be rebuilt around importance sampling. The central claim is that the score gradient of a semi-implicit distribution can be estimated without bias by an importance-weighted estimator whose proposal is the reverse conditional $q_{\epsilon|z}$, and that this optimal proposal can be learned stably by minimizing an expected forward Kullback-Leibler divergence using only samples from the joint $q_{z,\epsilon}$. The resulting algorithm, AISIVI, alternates a conditional normalizing flow update with reverse-KL training of the SIVI model, and reports state-of-the-art or on-par performance on benchmark problems including a 100-dimensional conditioned diffusion model. If the claim holds, semi-implicit variational models can be trained on the classic reverse-KL objective with simple, parallelizable, memory-constant gradient estimates and no MCMC.

What carries the argument

The load-bearing object is the importance-sampling score estimator $s_{IS,k}$, defined as the $z$-gradient of a log average of weighted conditional densities $p_\epsilon(\epsilon_i) q_{z|\epsilon}(z|\epsilon_i)/\tau_{\epsilon|z}(\epsilon_i|z)$, with the proposal $\tau_{\epsilon|z}$ modeled by a conditional normalizing flow built from affine coupling layers. The design works because, at the exact match $\tau_{\epsilon|z} = q_{\epsilon|z}$, each weight simplifies to $q_z(z)$ via the Bayes identity $q_{\epsilon|z}(\epsilon|z) = p_\epsilon(\epsilon) q_{z|\epsilon}(z|\epsilon)/q_z(z)$, so the estimator reduces exactly to the desired score $\nabla_z \log q_z(z)$. The flow is trained by the expected forward KL objective, whose gradient is just the negative expectation of $\nabla_\theta \log \tau_{\epsilon|z}(\epsilon|z)$ under joint samples; no evaluation of $q_{\epsilon|z}$ is needed. The second piece of machinery is the logaddexp-based aggregation rule that combines score estimates from disjoint $\epsilon$-batches into a single estimate of the combined batch, which keeps memory constant in $k$ and makes the inner sweep over latent samples fully parallelizable.

What would settle it

On a low-dimensional target such as the banana density, train AISIVI with a deliberately weak proposal, e.g., a single-layer flow or a Gaussian condition, and compare $s_{IS,k}$ against a nearly exact $\nabla_z \log q_z$ obtained by dense quadrature. If the estimator's bias does not shrink as $k$ grows or as the proposal is trained, the claim that forward-KL training keeps the proposal close enough to $q_{\epsilon|z}$ is refuted; a complementary diagnostic is to track the effective sample size of the importance weights, because persistent weight collapse would show that the support condition is not being maintained.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the MCMC step of UIVI is unnecessary. Proposition 3.1 shows that when the importance proposal $\tau_{\epsilon|z}$ is the reverse conditional $q_{\epsilon|z}$, the estimator $s_{IS,k}(z) = \nabla_z \log\left(\frac{1}{k}\sum_i \frac{p_\epsilon(\epsilon_i) q_{z|\epsilon}(z|\epsilon_i)}{\tau_{\epsilon|z}(\epsilon_i|z)}\right)$ is debiased; in fact, at this exact match each per-sample weight equals $q_z(z)$, so the estimator coincides with $\nabla_z \log q_z(z)$ for any $k$. Proposition 3.2 provides the training objective for $\tau_{\epsilon|z}$: minimizing $E_{z\sim q_z}[D_{\mathrm{KL}}(q_{\epsilon|z} \| \tau_{\epsilon|z})]$ is equivalent to minimizing $D_{\mathrm{KL}}(q_{z,\epsilon} \| \tau_{\epsilon|z} q_z)$, and the gradient of this objective is $-E_{z,\epsilon\sim q_{z,\epsilon}} \nabla_\theta \log \tau_{\epsilon|z}(\epsilon|z)$, which requires only joint samples, not the intractable conditional. The paper also contributes a log-space batch-aggregation rule that keeps memory constant in the inner batch size and makes the estimator fully parallelizable. Empirically, AISIVI approaches KSIVI on the 100-dimensional diffusion benchmark, outperforms UIVI, PVI, IWHVI, and the paper's own BSIVI baseline, and stays competitive on Bayesian logistic regression and toy densities.

Load-bearing premise

The method's guarantees depend on the conditional normalizing flow $\tau_{\epsilon|z}$ matching the true reverse conditional $q_{\epsilon|z}$ closely, with full support, at every stage of training; Proposition 3.1 proves unbiasedness only at the exact match, and the paper provides no bound on the bias introduced when the flow is imperfect.

Editorial extensions

If this is right

  • The inner MCMC loop of UIVI becomes unnecessary; SIVI models can be trained on the reverse KL objective using only samples from the model and a learned proposal.
  • Because the estimator is consistent for any proposal whose support covers $q_{\epsilon|z}$, bias and variance can be pushed down by increasing the inner batch size $k$, which the memory-constant aggregation makes cheap.
  • The conditional normalizing flow's training is a standard maximum-likelihood-type update on joint samples, so the method inherits the stability of normalizing flow training rather than the brittleness of adversarial or density-ratio estimation.
  • The empirical parity with KSIVI on a 100-dimensional conditioned diffusion problem suggests that the classic ELBO objective has not been superseded for semi-implicit models; the perceived failure of UIVI was a computational artifact of MCMC, not a defect of the divergence.
  • On the reported benchmarks, AISIVI reaches a log-marginal-likelihood close to KSIVI in 10K iterations where KSIVI needed 100K, suggesting a substantial compute advantage in the reported setup.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable consequence the paper does not pursue: the same recipe of learning the reverse conditional by an expected forward KL applies to any reparametrizable implicit distribution, not only SIVI, so hierarchical variational models with intractable conditionals could amortize their latent proposals the same way.
  • The deterministic reduction at $\tau_{\epsilon|z} = q_{\epsilon|z}$ suggests a practical diagnostic: track the effective sample size of the importance weights during training; when it collapses, the flow has drifted out of support and the score estimate has become unreliable, which could trigger a flow reset or an increase in flow capacity.
  • Because the forward KL is mass covering, one might expect $\tau_{\epsilon|z}$ to be broader than $q_{\epsilon|z}$; a natural extension would be to anneal the forward KL during training to trade off mass covering against sharpness of the learned conditional.
  • The paper's comparison with IWHVI uses a conditional Gaussian proposal trained jointly; a missing ablation is a flow-based proposal trained with IWHVI's joint objective, which would isolate whether AISIVI's gains come from the sequential forward-KL training or from the expressiveness of the flow architecture.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper revisits unbiased implicit variational inference (UIVI) and proposes replacing its inner MCMC loop with importance sampling using a learned conditional normalizing flow proposal. The authors introduce two algorithms: BSIVI, which uses a plain Monte Carlo score estimator, and AISIVI, which uses an importance-sampling estimator with a proposal τ(ε|z) trained by minimizing an expected forward KL divergence. They prove that the importance-sampling score estimator is unbiased when τ matches the reverse conditional q_{ε|z} (Proposition 3.1), that minimizing the expected forward KL is equivalent to minimizing a joint KL and hence recovers q_{ε|z} at the optimum (Proposition 3.2), and that the score estimates can be aggregated with constant memory using logaddexp. Experiments on toy densities, Bayesian logistic regression, and a 100-dimensional conditioned diffusion process compare AISIVI with KSIVI, PVI, UIVI, and IWHVI, reporting that AISIVI approaches KSIVI in the diffusion benchmark while outperforming the other SIVI variants.

Significance. If the central claims hold, AISIVI provides a scalable, memory-constant, fully parallelizable way to train semi-implicit variational models on the standard reverse-KL objective without MCMC, while retaining the expressivity of implicit distributions. The paper has real strengths: Proposition 3.1's proof is a clean pointwise cancellation using the identity p_ε(ε)/q_{ε|z}(ε|z) · q_{z|ε}(z|ε) = q_z(z); Proposition 3.2 is a correct change-of-measure argument; the consistency arguments in Appendices A.1 and A.2 are standard and correct; and the logaddexp aggregation in Appendix A.3 is a useful and correct technical contribution. The empirical comparison includes several strong baselines and a high-dimensional benchmark. However, the headline 'without bias' claim is only rigorously established at the exact fixed point τ = q_{ε|z}, and the practical regime relies on an imperfect learned proposal, for which no finite-k bias bound or diagnostic is provided. The implementation also leaves an ambiguity about gradient flow through reparameterized proposal samples that is load-bearing for whether the implemented estimator is the analyzed one.

major comments (3)
  1. [Section 3.3.2, Eq. (15), Proposition 3.1] The 'without bias' claim is proven only at the exact fixed point τ_{ε|z} = q_{ε|z}; for a learned imperfect proposal, s_IS,k is consistent but has finite-k bias, and the paper provides no bound on that bias. The mass-covering argument in Section 3.3.2 addresses support, not importance-weight variance, and support is already automatic for the Gaussian-base affine CNFs used in the experiments. In the diffusion experiment (Section 5.3, k=256, d=100) no effective-sample-size or bias diagnostics are reported, so the abstract's 'without bias' claim is not supported in the tested regime. Please either provide a finite-k bias bound, weaken the claims to 'asymptotically unbiased' or 'reduced-bias' and clearly state the exact-τ idealization, and/or report empirical diagnostics such as effective sample size and a comparison against a large-k reference estimator.
  2. [Algorithm 2, Eq. (15)] Algorithm 2 stops the gradient only on log w_{i,j}; it does not state whether ε_{i,j} is detached from z_i when forming log q_{z|ε}(z_i|ε_{i,j}). If ε_{i,j} is generated by a reparameterized conditional flow, backpropagation through log q_{z|ε} introduces terms ∂ε_{i,j}/∂z_i, and the implemented estimator is not the one analyzed in Eq. (15), where samples and the proposal density are held fixed. Please specify the exact detach operations on the sampled ε and on log τ, and verify with released code that the gradient matches Eq. (15).
  3. [Section 5.3, Table 2] The UIVI baseline is reported with an inner batch size of 2 'due to computational constraints', but UIVI's accuracy depends on MCMC mixing, not on the number of inner samples at a fixed wall-clock budget. This comparison may understate UIVI and should be clarified or supplemented with a UIVI configuration given a reasonable MCMC budget; otherwise the claim that AISIVI 'successfully adapts UIVI's core ideas' is not cleanly supported by the table.
minor comments (5)
  1. [Section 5.2, Table 2] The units '0.6K' and '1.4K' in Table 2 should be written explicitly as seconds (e.g., 600 s and 1400 s) to avoid confusion with iteration counts.
  2. [Section 5.3] The text uses 'IWHI' in the diffusion experiment but 'IWHVI' elsewhere; please use the acronym consistently.
  3. [Figure 3 caption] There is a typo: 'Comparision' should be 'Comparison'.
  4. [Appendix A.1, Eq. (13)] The bias approximation for s_MC,k is a heuristic delta-method expansion, not a bound; this should be stated explicitly in the main text where Eq. (13) is introduced.
  5. [Algorithm 1 and Algorithm 2] Algorithm 1 states k > m, but Algorithm 2 does not specify whether the same assumption is needed; please clarify the relationship between k and m for AISIVI.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the score identity and forward-KL proposal training are externally anchored and not equivalent to the fitted quantities by construction.

full rationale

The derivation chain is self-contained. The key identity Eq. 9 is taken from Titsias & Ruiz (2019), an external result, and Proposition 3.1 reduces the IS score estimator to this identity via Bayes' rule (Eq. 25), not by assuming the conclusion. The 'optimal proposal' tau* = q_{epsilon|z} is derived from minimizing the expected forward KL (Eqs. 17-24); that objective's gradient (Eq. 19) requires only samples from q_{z,epsilon}, not from q_{epsilon|z}, so the training procedure does not presuppose access to the quantity it is learning. BSIVI's s_MC,k estimator is a standard Monte Carlo estimator whose bias approximation is derived independently in Appendix A.1. No prediction is a renamed fit: tau is an auxiliary proposal, and the reported benchmarks compare against external KSIVI and PVI baselines. The only self-citations (e.g., Pielok et al. 2023 in related work) are non-load-bearing. The finite-k bias for imperfect tau is an unquantified correctness risk (the support assumption in Section 3.3.2 and the diffusion experiment with k=256), but that is not a circularity because the paper explicitly proves unbiasedness only at the exact fixed point tau = q_{epsilon|z}.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central derivation rests on standard exchange-of-limits regularity, the reparametrization assumption (Section 2.1), and two unproven practical premises: the support condition supp(q_{ϵ|z}) ⊆ supp(τ_{ϵ|z}) held to follow from mass-covering forward KL, and the CNF being flexible enough to reach the reverse conditional at its optimum (Eq. 24). No new physical or mathematical entities are introduced; the conditional normalizing flow is an existing tool.

free parameters (3)
  • inner batch size k (number of epsilon samples) = 256 to 91,820 across experiments
    Adjusted per experiment to match wall-clock budget (e.g., 9182 for AISIVI and 91,820 for BSIVI on the logistic task; 256 and 40,960 on the diffusion task). Since estimator bias decreases with k, cross-method comparisons depend on this hand-set quantity.
  • number of conditional affine coupling layers = 6 (toy), 16 (logistic), 32 (diffusion)
    Chosen per benchmark; no sensitivity analysis is provided, so performance may depend on this choice differently across methods.
  • learning rate and optimizer
    Not specified in the paper; required for an independent re-implementation, so treated here as an undocumented free choice.
assumptions (4)
  • standard math Regularity: order of integration, summation, and differentiation can be interchanged (Appendix A, first line).
    Needed for all proofs; standard but unstated assumptions on densities.
  • domain assumption Reparametrization trick applies to the conditional q_{z|y} (Section 2.1).
    Assumed so that h_φ is differentiable and Eq. 5 holds.
  • domain assumption Support condition supp(q_{ϵ|z}) ⊆ supp(τ_{ϵ|z}) holds for the learned flow (Section 3.3.2).
    Needed for consistency of s_IS,k (Appendix A.2); asserted via expected mass-covering property, not verified.
  • domain assumption The CNF family is flexible enough that the forward KL optimum reaches τ* = q_{ϵ|z} (Eq. 24).
    Needed to justify 'optimal proposal'; real NFs with finite layers may not attain it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Revisiting Unbiased Implicit Variational Inference." pith.science (2026). https://pith.science/paper/2YTSK2E4

@misc{pith2026250603839,
  author       = {Pith},
  title        = {Pith review of: Revisiting Unbiased Implicit Variational Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2YTSK2E4}},
  note         = {Machine review of arXiv:2506.03839}
}
read the original abstract

Recent years have witnessed growing interest in semi-implicit variational inference (SIVI) methods due to their ability to rapidly generate samples from complex distributions. However, since the likelihood of these samples is non-trivial to estimate in high dimensions, current research focuses on finding effective SIVI training routines. Although unbiased implicit variational inference (UIVI) has largely been dismissed as imprecise and computationally prohibitive because of its inner MCMC loop, we revisit this method and show that UIVI's MCMC loop can be effectively replaced via importance sampling and the optimal proposal distribution can be learned stably by minimizing an expected forward Kullback-Leibler divergence without bias. Our refined approach demonstrates superior performance or parity with state-of-the-art methods on established SIVI benchmarks.

Figures

Figures reproduced from arXiv: 2506.03839 by the authors.

Figure 1
Figure 1. We sample from a semi-implicit distribution q(z) by sampling from the latent distribution p(ϵ) and subsequently from the conditional distribution q(z|ϵ). The simple distributions p(ϵ) and q(z|ϵ) can induce a complicated distribution q(z) and conse￾quently a potentially even more complicated reverse conditional distribution q(ϵ|z). AISIVI learns a mass-covering representation τ (ϵ|z) of q(ϵ|z) to estimate ∇z log q(z)… view at source ↗
Figure 2
Figure 2. Histograms based on 100000 samples produced by the true distribution, AISIVI, and BSIVI function space (Sun et al., 2019; Ma et al., 2019; Pielok et al., 2023). These approaches frequently incorporate implicit inference mechanisms within their frameworks. Several approaches have improved variational inference by incorporating importance sampling. IWAE (Burda et al., 2016) introduces a tighter bound through multiple … view at source ↗
Figure 3
Figure 3. Comparision of marginal and pairwise density estimates of β(1), β(2), β(3) where the SGLD estimates are marked in black [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Scatter plot of every pairwise correlation coefficient ρi,j between the estimates and SGLD. which gives rise to the prior distribution pprior(x). The observations are perturbed at 20 time points, given by y = (y5∆t, y10∆t, . . . , y100∆t), where y5k∆t ∼ N (x5k∆t, σ2 ),…
Figure 5
Figure 5. Figure 5: Approximations of KSIVI, PVI, IWHVI, UIVI, AISIVI, and BSIVI for the discretized conditioned diffusion process are shown. The red dots represent the observations, the magenta line the ground truth estimated via parallel SGLD, and the blue line the estimated posterior m…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

29 extracted references · 22 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    Stabilizing training of affine coupling layers for high-dimensional variational inference

    Andrade, D. Stabilizing training of affine coupling layers for high-dimensional variational inference. Machine Learning: Science and Technology, 5, 12 2024. doi:10.1088/2632-2153/ad9a39

    work page doi:10.1088/2632-2153/ad9a39 2024

  3. [3]

    B., and Salakhutdinov, R

    Burda, Y., Grosse, R. B., and Salakhutdinov, R. Importance weighted autoencoders. In Bengio, Y. and LeCun, Y. (eds.), 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings , 2016. URL http://arxiv.org/abs/1509.00519

    arXiv 2016

  4. [4]

    Kernel semi-implicit variational inference

    Cheng, Z., Yu, L., Xie, T., Zhang, S., and Zhang, C. Kernel semi-implicit variational inference. In Forty-first International Conference on Machine Learning, 2024. URL https://openreview.net/forum?id=w5oUo0LhO1

    work page 2024

  5. [5]

    A stein variational newton method

    Detommaso, G., Cui, T., Spantini, A., Marzouk, Y., and Scheichl, R. A stein variational newton method. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS'18, pp.\ 9187–9197, Red Hook, NY, USA, 2018. Curran Associates Inc

    work page 2018

  6. [6]

    Density estimation using real NVP

    Dinh, L., Sohl-Dickstein, J., and Bengio, S. Density estimation using real NVP . In International Conference on Learning Representations, 2017. URL https://openreview.net/forum?id=HkpbnH9lx

    2017

  7. [7]

    Learning to draw samples with amortized stein variational gradient descent

    Feng, Y., Wang, D., and Liu, Q. Learning to draw samples with amortized stein variational gradient descent. In Elidan, G., Kersting, K., and Ihler, A. (eds.), Proceedings of the Thirty-Third Conference on Uncertainty in Artificial Intelligence, UAI 2017, Sydney, Australia, August 11-15, 2017 . AUAI Press, 2017. URL http://auai.org/uai2017/proceedings/pape...

    work page 2017

  8. [8]

    Implicit reparameterization gradients

    Figurnov, M., Mohamed, S., and Mnih, A. Implicit reparameterization gradients. In Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., and Garnett, R. (eds.), Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018. URL https://proceedings.neurips.cc/paper_files/paper/2018/file/92c8c96e4c37100777c7190...

    work page 2018

Show all 29 references
  1. [9]

    Kingma, D. P. and Welling, M. Auto-encoding variational bayes. In Bengio, Y. and LeCun, Y. (eds.), 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings , 2014. URL http://arxiv.org/abs/1312.6114

    2014 arXiv

  2. [10]

    Lim, J. N. and Johansen, A. M. Particle semi-implicit variational inference. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/forum?id=p3gMGkHMkM

    2024

  3. [11]

    and Huang, B

    Lu, Y. and Huang, B. Structured output learning with conditional generative flows. In The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium o...

    2020 doi

  4. [12]

    Ma, C., Li, Y., and Hernandez-Lobato, J. M. Variational implicit processes. In Chaudhuri, K. and Salakhutdinov, R. (eds.), Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp.\ 4222--4233. PMLR, 09--15...

    2019

  5. [13]

    Adversarial variational bayes: unifying variational autoencoders and generative adversarial networks

    Mescheder, L., Nowozin, S., and Geiger, A. Adversarial variational bayes: unifying variational autoencoders and generative adversarial networks. In Proceedings of the 34th International Conference on Machine Learning - Volume 70, ICML'17, pp.\ 2391–2400. JMLR.org, 2017

    2017

  6. [14]

    Doubly semi-implicit variational inference

    Molchanov, D., Kharitonov, V., Sobolev, A., and Vetrov, D. Doubly semi-implicit variational inference. In Chaudhuri, K. and Sugiyama, M. (eds.), Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, volume 89 of Proceedings of Mac...

    2019

  7. [15]

    Owen, A. B. Monte Carlo theory, methods and examples. https://artowen.su.domains/mc/, 2013

    2013

  8. [16]

    J., Mohamed, S., and Lakshminarayanan, B

    Papamakarios, G., Nalisnick, E., Rezende, D. J., Mohamed, S., and Lakshminarayanan, B. Normalizing flows for probabilistic modeling and inference. J. Mach. Learn. Res., 22 0 (1), January 2021. ISSN 1532-4435

    2021

  9. [17]

    Pytorch: An imperative style, high-performance deep learning library

    Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S. Pytorch: An impera...

    2019

  10. [18]

    Approximate bayesian inference with stein functional variational gradient descent

    Pielok, T., Bischl, B., and R \"u gamer, D. Approximate bayesian inference with stein functional variational gradient descent. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=a2-aoqmeYM4

    2023

  11. [19]

    and Mohamed, S

    Rezende, D. and Mohamed, S. Variational inference with normalizing flows. In Bach, F. and Blei, D. (eds.), Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning Research, pp.\ 1530--1538, Lille, France, 07--09 Jul 20...

    2015

  12. [20]

    Roeder, G., Wu, Y., and Duvenaud, D. K. Sticking the landing: Simple, lower-variance gradient estimators for variational inference. In Guyon, I., Luxburg, U. V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R. (eds.), Advances in Neural Information Proce...

    2017

  13. [21]

    Kernel implicit variational inference

    Shi, J., Sun, S., and Zhu, J. Kernel implicit variational inference. In International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id=r1l4eQW0Z

    2018

  14. [22]

    and Vetrov, D

    Sobolev, A. and Vetrov, D. P. Importance weighted hierarchical variational inference. In Wallach, H., Larochelle, H., Beygelzimer, A., d Alch\' e -Buc, F., Fox, E., and Garnett, R. (eds.), Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2...

    2019

  15. [23]

    FUNCTIONAL VARIATIONAL BAYESIAN NEURAL NETWORKS

    Sun, S., Zhang, G., Shi, J., and Grosse, R. FUNCTIONAL VARIATIONAL BAYESIAN NEURAL NETWORKS . In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id=rkxacs0qY7

    2019

  16. [24]

    Titsias, M. K. and Ruiz, F. Unbiased implicit variational inference. In Chaudhuri, K. and Sugiyama, M. (eds.), Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, volume 89 of Proceedings of Machine Learning Research, pp.\ 167--...

    2019

  17. [25]

    and Teh, Y

    Welling, M. and Teh, Y. W. Bayesian learning via stochastic gradient langevin dynamics. In International Conference on Machine Learning, 2011. URL https://api.semanticscholar.org/CorpusID:2178983

    2011

  18. [26]

    and Zhou, M

    Yin, M. and Zhou, M. Semi-implicit variational inference. In Dy, J. and Krause, A. (eds.), Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pp.\ 5660--5669. PMLR, 10--15 Jul 2018. URL https://proceedin...

    2018

  19. [27]

    and Zhang, C

    Yu, L. and Zhang, C. Semi-implicit variational inference via score matching. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=sd90a2ytrt

    2023

  20. [28]

    Hierarchical semi-implicit variational inference with application to diffusion model acceleration

    Yu, L., Xie, T., Zhu, Y., Yang, T., Zhang, X., and Zhang, C. Hierarchical semi-implicit variational inference with application to diffusion model acceleration. In Proceedings of the 37th International Conference on Neural Information Processing Systems, NIPS '23, Red Hook, NY,...

    2023

  21. [29]

    Nested variational inference

    Zimmermann, H., Wu, H., Esmaeili, B., and van de Meent, J. Nested variational inference. In Ranzato, M., Beygelzimer, A., Dauphin, Y. N., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Process...

    2021

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.