Direct Optimization through $\arg \max$ for Discrete Variational Auto-Encoder

Lorberbom, Guy; Gane, Andreea; Jaakkola, Tommi S.; Hazan, Tamir

doi:10.48550/arxiv.1806.02867

Cited by 3 publications

(6 citation statements)

References 13 publications

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“…This derivative requires A function evaluations, similar to RAM. Lorberbom et al (2018) extend the single variable result to multivariate distributions similar to Eqs. ( 4) and ( 5).…”

Section: Argmaxmentioning

confidence: 87%

“…Each expectation can be computed by sampling thereby trading off computational effort for increased variance. Lorberbom et al (2018) show that…”

Section: Argmaxmentioning

confidence: 99%

“…SF suffers from high variance and many remedies have been proposed to reduce this variance (Mnih & Gregor (2014); Gregor et al (2013); Gu et al (2015); Mnih & Rezende (2016); Tucker et al (2017); Grathwohl et al (2017)). Unbiased estimators that require multiple function evaluations have also been proposed Tokui & Sato (2017), Titsias & Lázaro-Gredilla (2015), Lorberbom et al (2018), Yin & Zhou (2018). These estimators have lower variance but can be computationally demanding.…”

Section: Related Workmentioning

confidence: 99%

“…Recently, Lorberbom et al (2018) proposed another FD estimator that we refer to as ARGMAX. For a single variable, ARGMAX relies on an identity that approximates…”

Section: Argmaxmentioning

confidence: 99%

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Improved Gradient-Based Optimization Over Discrete Distributions

Andriyash,

Vahdat,

Macready

2018

Preprint

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In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirically that reduced bias leads to a better performance in variational inference and on binary optimization tasks.

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“…This derivative requires A function evaluations, similar to RAM. Lorberbom et al (2018) extend the single variable result to multivariate distributions similar to Eqs. ( 4) and ( 5).…”

Section: Argmaxmentioning

confidence: 87%

“…Each expectation can be computed by sampling thereby trading off computational effort for increased variance. Lorberbom et al (2018) show that…”

Section: Argmaxmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…Recently, Lorberbom et al (2018) proposed another FD estimator that we refer to as ARGMAX. For a single variable, ARGMAX relies on an identity that approximates…”

Section: Argmaxmentioning

confidence: 99%

See 2 more Smart Citations

Improved Gradient-Based Optimization Over Discrete Distributions

Andriyash,

Vahdat,

Macready

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Some works rely on explicit summation of the expectation, either for the marginal distribution (Titsias & Lázaro-Gredilla, 2015) or globally summing some categories while sampling from the remainder (Liang et al, 2018;Liu et al, 2019). Other approaches use a finite difference approximation to the gradient (Lorberbom et al, 2018;. Yin et al (2019) introduced ARSM, which uses multiple model evaluations where the number adapts automatically to the uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Estimating Gradients for Discrete Random Variables by Sampling without Replacement

Kool¹,

Hoof²,

Welling³

2020

Preprint

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We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the Rao-Blackwellization of three different estimators. Combining our estimator with RE-INFORCE, we obtain a policy gradient estimator and we reduce its variance using a built-in control variate which is obtained without additional model evaluations. The resulting estimator is closely related to other gradient estimators. Experiments with a toy problem, a categorical Variational Auto-Encoder and a structured prediction problem show that our estimator is the only estimator that is consistently among the best estimators in both high and low entropy settings.

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Fast Generating A Large Number of Gumbel-Max Variables

Wang

Zhang

et al. 2020

Proceedings of the Web Conference 2020

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The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a nonnegative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element i (or a Gumbel-Max variable i) in proportion to its positive weight v i , the Gumbel-Max Trick first computes a Gumbel random variable д i for each positive weight element i, and then samples the element i with the largest value of д i + ln v i . Recently, applications including similarity estimation and graph embedding require to generate k independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large k (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, FastGM, that reduces the time complexity from O(kn + ) to O(k ln k + n + ), where n + is the number of positive elements in the vector of interest. Instead of computing k independent Gumbel random variables directly, we find that there exists a technique to generate these variables in descending order. Using this technique, our method FastGM computes variables д i + ln v i for all positive elements i in descending order. As a result, FastGM significantly reduces the computation time because we can stop the procedure of Gumbel random variables computing for many elements especially for those with small weights. Experiments on a variety of real-world datasets show that FastGM is orders of magnitude faster than state-of-theart methods without sacrificing accuracy and incurring additional expenses.

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Direct Optimization through $\arg \max$ for Discrete Variational Auto-Encoder

Cited by 3 publications

References 13 publications

Improved Gradient-Based Optimization Over Discrete Distributions

Improved Gradient-Based Optimization Over Discrete Distributions

Estimating Gradients for Discrete Random Variables by Sampling without Replacement

Fast Generating A Large Number of Gumbel-Max Variables

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