phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | approximate posterior inference with continuous latent variables— “How can we perform efficient approximate inference and learning with directed probabilistic models whose continuous latent variables and/or parameters have intractable posterior distributions?” | |
| claim-type | method— “We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case.” | |
| method — evidence | — “We trained generative models of images from the MNIST and Frey Face datasets3 and compared learning algorithms in terms of the variational lower bound, and the estimated marginal likelihood.” | |
| transfer | from statistics / variational Bayesian inference: variational Bayes / approximate posterior inference combined with neural networks (a recognition/encoder model) to learn deep generative models— “fitting an approximate inference model” | transfers[0] |
| mechanism | the reparameterization trick: rewrite latent-variable sampling as a deterministic function of noise so the variational lower bound (ELBO) becomes differentiable and trainable by stochastic gradient descent— “a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods” | mechanisms[0] |
| extends | variational inference (variational Bayes)— “a stochastic variational inference and learning algorithm that scales to large datasets” | claim_relations[0] |
| builds-on | predictive sparse decomposition (PSD) [KRL08]— “Related are also encoder-decoder architectures such as the predictive sparse decomposition (PSD) [KRL08], from which we drew some inspiration.” | claim_relations[1] |
| extends | the wake-sleep algorithm [HDFN95]— “The wake-sleep algorithm [HDFN95] is, to the best of our knowledge, the only other on-line learning method in the literature that is applicable to the same general class of continuous latent variable models.” | claim_relations[2] |
| sense | the algorithm's name - AEVB IN THE PAPER, VAE IN THE FIELD: the authors name their algorithm Auto-Encoding VB and use that name throughout; the term the field kept appears once, as what you arrive at when the recognition model happens to be a neural network— “we propose the Auto- Encoding VB (AEVB) algorithm” | senses[0] |
| sense | the variational auto-encoder - AS A SPECIAL CASE, NOT THE SUBJECT: it is what AEVB becomes when a neural network is used for the recognition model, stated in a single consequence clause— “When a neural network is used for the recognition model, we arrive at the variational auto-encoder” | senses[1] |
| sense | the recognition model - TWO NAMES IN ONE PARENTHESIS: an approximate inference model, also called a recognition model, fitted to a posterior that cannot be computed— “posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator” | senses[2] |
| control | comparison against the wake-sleep algorithm using the same encoder and the same parameters — held— “We compared performance of AEVB to the wake-sleep algorithm [HDFN95].” — rules out that AEVB's advantage over wake-sleep comes from the network architecture or parameter count rather than from the learning method— “We employed the same encoder (also called recognition model) for the wake-sleep algorithm and the variational autoencoder.” | controls[0] |
| edge | approximate inference model —same-as→ recognition model— “by fitting an approximate inference model (also called a recognition model)” | concept_edges[0] |
| relation | reparameterization —causes→ lower bound estimator — the reparameterisation YIELDS an estimator that ordinary SGD can optimise— “we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods”— “yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods” | concept_edges[1] |
| outcome | control — held— “We employed the same encoder (also called recognition model) for the wake-sleep algorithm and the variational autoencoder.”— “We compared performance of AEVB to the wake-sleep algorithm [HDFN95].” | controls[0] |
| for which use | limitation — the derivation as presented: OUR METHOD CAN BE APPLIED TO ONLINE, NON-STATIONARY SETTINGS ... BUT HERE WE ASSUME A FIXED DATASET FOR SIMPLICITY— “Note that our method can be applied to online, non-stationary settings, e.g. streaming data, but here we assume a fixed dataset for simplicity.” | limitations[0] |
| for which use | limitation — the marginal-likelihood numbers reported: they use 3 LATENT VARIABLES, because FOR HIGHER DIMENSIONAL LATENT SPACE THE ESTIMATES BECAME UNRELIABLE | limitations[1] |
| for which use | limitation — results obtained with this method: the approximate posterior is assumed to take an approximately Gaussian form with approximately diagonal covariance, which the authors call a simplifying choice and not a limitation of the method | limitations[2] |
| for which use | limitation — an auto-encoding objective read as a representation-learning objective: the paper states it is well known that the | limitations[3] |
| for which use | limitation — the claim that the estimator works in the intractable case: it holds under mild differentiability conditions, with the prior and likelihood assumed to have PDFs differentiable almost everywhere Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| replication | untested | |
| limitation | The derivation assumes a fixed dataset for simplicity rather than the online or non-stationary case. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| limitation | The marginal-likelihood evaluation only works for very low-dimensional latent spaces; estimates degrade beyond three latent variables. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| limitation | The approximate posterior is assumed Gaussian with diagonal covariance, and the paper argues in advance that this is a choice rather than a limitation. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| limitation | The reconstruction criterion that gives the method its auto-encoding name is stated to be insufficient on its own for learning useful representations. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| limitation | The guarantee is conditional on differentiability, which is assumed to hold almost everywhere rather than shown. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | A reparameterization of the variational lower bound yields an estimator that can be optimized with standard stochastic gradient methods. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[0] |
| evidence status note | finding — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.findings[0] |
| finding | Posterior inference is made efficient by fitting an approximate inference (recognition) model to the intractable posterior using the proposed lower-bound estimator. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[1] |
| evidence status note | finding — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.findings[1] |
| variable | continuous latent variables (independent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[0] |
| variable | variational lower bound (dependent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[1] |
| definition | SGVB (Stochastic Gradient Variational Bayes) estimator Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[0] |
| evidence status note | definition — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.definitions[0] |
| definition | recognition model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[1] |
| evidence status note | definition — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.definitions[1] |
| key-terms | variational, latent, posterior, inference, estimator, reparameterization, gradient, likelihood |
| concept | AEVB Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[4] |
| concept | recognition model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[5] |
| concept | approximate inference model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[6] |
| concept | reparameterization Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[7] |
| concept | lower bound estimator Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[8] |
| Bayesian | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[0] |
| chi-square χ² | as written: Chi-Squared Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
| variance σ² | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[3] |
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