Knowledge Vault 2/26 - ICLR 2014-2023
Lucas Theis, Aron van den Oord, Matthias Bethge ICLR 2016 - A note on the evaluation of generative models
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Concept Graph & Resume using Claude 3 Opus | Chat GPT4 | Gemini Adv | Llama 3:

graph LR classDef evaluation fill:#f9d4d4, font-weight:bold, font-size:14px; classDef applications fill:#d4f9d4, font-weight:bold, font-size:14px; classDef loglikelihood fill:#d4d4f9, font-weight:bold, font-size:14px; classDef objectives fill:#f9f9d4, font-weight:bold, font-size:14px; classDef samples fill:#f9d4f9, font-weight:bold, font-size:14px; classDef parzen fill:#d4f9f9, font-weight:bold, font-size:14px; classDef mixtures fill:#f9d4d4, font-weight:bold, font-size:14px; classDef recommendations fill:#d4f9d4, font-weight:bold, font-size:14px; A[Lucas Theis et al
ICLR 2016 ] --> B[Explores evaluation methods'
relations, suitability. 1] A --> C[Generative models: compression,
generation, learning. 2] A --> D[Log-likelihood hard to evaluate. 3] D --> E[Alternatives due to
learning, generation. 4] B --> F[Success in one application
doesn't translate. 5] A --> G[Training objectives impact
trade-offs, results. 6] G --> H[Objectives theoretically equal,
practically differ. 7] A --> I[Samples intuitive but insufficient. 8] I --> J[Generating nice samples is easy. 9] I --> K[Nearest neighbors detect overfitting. 10] K --> L[Euclidean distance misaligns
perceptual similarity. 11] K --> M[Tests mainly detect
lookup behavior. 12] A --> N[Parzen windows approximate
log-likelihood. 13] N --> O[Parzen poor approximation
even in simple settings. 14] N --> P[Parzen fails to rank
models meaningfully. 15] D --> Q[Evaluate log-likelihood directly
for density estimation. 16] Q --> R[Log-likelihoods can be
infinite on discretized data. 17] R --> S[Uniform noise bounds log-likelihood. 18] S --> T[Discrete log-likelihood relates
to compression. 19] A --> U[Sample quality and log-likelihood
capture different properties. 20] U --> V[Excellent model with 99%
noise reduces log-likelihood slightly. 21] U --> W[1% good model, 99% noise:
identical compression, different samples. 22] U --> X[99% good model, 1% noise:
identical samples, different compression. 23] U --> Y[Sample quality and classification
arbitrarily mixed. 24] B --> Z[Evaluate on intended application. 25] Z --> AA[Avoid Parzen window estimates. 26] Z --> AB[Don't solely rely on
nearest neighbor tests. 27] Z --> AC[Use samples as diagnostic
or when relevant. 28] Z --> AD[Evaluate representations on
downstream tasks. 29] B --> AE[Careful evaluation crucial as
performance doesn't correlate. 30] class A,B,F,Z,AA,AB,AC,AD,AE evaluation; class C applications; class D,E,Q,R,S,T loglikelihood; class G,H objectives; class I,J,K,L,M samples; class N,O,P parzen; class U,V,W,X,Y mixtures;

Resume:

1.-The paper explores how different evaluation methods for generative models relate to each other and their suitability for various applications.

2.-Generative models can be used for compression, content generation, texture synthesis, image reconstruction, and unsupervised representation learning.

3.-Log-likelihood is often hard to evaluate, leading to alternative evaluation methods and approximations.

4.-Dissatisfaction with progress in generative modeling for unsupervised representation learning and content generation also led to alternative evaluation methods.

5.-The paper argues that success in one application doesn't necessarily translate to others, so evaluation should consider the intended application.

6.-The choice of training objective (e.g. maximum likelihood, MMD, JS divergence, adversarial networks) impacts the trade-offs and results.

7.-While theoretically equivalent given the right model and infinite data, in practice the objectives lead to different generative model behaviors.

8.-Evaluating generative models by drawing samples and examining them is an intuitive diagnostic tool but insufficient to assess density estimation or representations.

9.-Simply generating nice samples is easy (e.g. storing and retrieving training images) but doesn't reflect learning or density estimation capabilities.

10.-Looking at nearest neighbors to samples is used to detect overfitting, but small image changes can yield very different neighbors.

11.-Euclidean distance used for nearest neighbors doesn't align well with perceptual image similarity.

12.-Nearest neighbor tests mainly just detect lookup table behavior rather than meaningful generalization in generative models.

13.-Parzen window estimates, building a tractable model from model samples, are used as a log-likelihood approximation.

14.-Parzen window estimates are a very poor approximation of log-likelihood even in simple low-dimensional settings with many samples.

15.-Parzen window estimates also fail to provide meaningful rankings of models compared to log-likelihood.

16.-Log-likelihood should be directly evaluated or properly approximated to assess density estimation performance.

17.-Log-likelihoods can be infinite when fitting densities to discretized data if the model detects the discretization.

18.-Adding uniform noise to discretized data bounds the continuous log-likelihood based on the discrete model's log-likelihood.

19.-The discrete model's log-likelihood relates to its compression performance on the discrete data.

20.-Sample quality and log-likelihood capture quite different properties of a generative model.

21.-Mixing an excellent model with 99% noise only reduces log-likelihood slightly (<4.61 nats) while drastically changing samples.

22.-Mixture models with 1% good model and 99% noise have nearly identical compression but very different samples.

23.-Mixture models with 99% good model and 1% noise can have nearly identical samples but very different compression.

24.-A similar argument shows that sample quality and classification performance using the model representations can be mixed arbitrarily.

25.-Generative models should be evaluated on the intended application (e.g. log-likelihood for compression, samples for content generation, psychophysics for perception).

26.-Avoid Parzen window estimates.

27.-Don't rely solely on nearest neighbor tests to assess overfitting.

28.-Use samples as a diagnostic tool or when directly relevant to the application, not as a general proxy.

29.-For unsupervised representation learning, evaluate the learned representations on downstream tasks.

30.-Careful generative model evaluation is crucial since performance on different applications does not necessarily correlate.

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