Despite the tremendous progress in the estimation of generative models, the development of tools for diagnosing their failures and assessing their performance has advanced at a much slower pace. Recent developments have investigated metrics that quantify which parts of the true distribution are modeled well, and, on the contrary, what the model fails to capture, akin to precision and recall in information retrieval. In this paper, we present a general evaluation framework for generative models that measures the trade-off between precision and recall using R\'enyi divergences. Our framework provides a novel perspective on existing techniques and extends them to more general domains. As a key advantage, it allows for efficient algorithms that are directly applicable to continuous distributions directly without discretization. We further showcase the proposed techniques on a set of image synthesis models.
Learning disentangled representations is considered a cornerstone problem in representation learning. Recently, Locatello et al. (2019) demonstrated that unsupervised disentanglement learning without inductive biases is theoretically impossible and that existing inductive biases and unsupervised methods do not allow to consistently learn disentangled representations. However, in many practical settings, one might have access to a very limited amount of supervision, for example through manual labeling of training examples. In this paper, we investigate the impact of such supervision on state-of-the-art disentanglement methods and perform a large scale study, training over 29000 models under well-defined and reproducible experimental conditions. We first observe that a very limited number of labeled examples (0.01--0.5% of the data set) is sufficient to perform model selection on state-of-the-art unsupervised models. Yet, if one has access to labels for supervised model selection, this raises the natural question of whether they should also be incorporated into the training process. As a case-study, we test the benefit of introducing (very limited) supervision into existing state-of-the-art unsupervised disentanglement methods exploiting both the values of the labels and the ordinal information that can be deduced from them. Overall, we empirically validate that with very little and potentially imprecise supervision it is possible to reliably learn disentangled representations.
Deep generative models are becoming a cornerstone of modern machine learning. Recent work on conditional generative adversarial networks has shown that learning complex, high-dimensional distributions over natural images is within reach. While the latest models are able to generate high-fidelity, diverse natural images at high resolution, they rely on a vast quantity of labeled data. In this work we demonstrate how one can benefit from recent work on self- and semi-supervised learning to outperform state-of-the-art (SOTA) on both unsupervised ImageNet synthesis, as well as in the conditional setting. In particular, the proposed approach is able to match the sample quality (as measured by FID) of the current state-of-the art conditional model BigGAN on ImageNet using only 10% of the labels and outperform it using 20% of the labels.
Learning useful representations with little or no supervision is a key challenge in artificial intelligence. We provide an in-depth review of recent advances in representation learning with a focus on autoencoder-based models. To organize these results we make use of meta-priors believed useful for downstream tasks, such as disentanglement and hierarchical organization of features. In particular, we uncover three main mechanisms to enforce such properties, namely (i) regularizing the (approximate or aggregate) posterior distribution, (ii) factorizing the encoding and decoding distribution, or (iii) introducing a structured prior distribution. While there are some promising results, implicit or explicit supervision remains a key enabler and all current methods use strong inductive biases and modeling assumptions. Finally, we provide an analysis of autoencoder-based representation learning through the lens of rate-distortion theory and identify a clear tradeoff between the amount of prior knowledge available about the downstream tasks, and how useful the representation is for this task.
In recent years, the interest in unsupervised learning of disentangled representations has significantly increased. The key assumption is that real-world data is generated by a few explanatory factors of variation and that these factors can be recovered by unsupervised learning algorithms. A large number of unsupervised learning approaches based on auto-encoding and quantitative evaluation metrics of disentanglement have been proposed; yet, the efficacy of the proposed approaches and utility of proposed notions of disentanglement has not been challenged in prior work. In this paper, we provide a sober look on recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than 12000 models covering the six most prominent methods, and evaluate them across six disentanglement metrics in a reproducible large-scale experimental study on seven different data sets. On the positive side, we observe that different methods successfully enforce properties "encouraged" by the corresponding losses. On the negative side, we observe in our study that well-disentangled models seemingly cannot be identified without access to ground-truth labels even if we are allowed to transfer hyperparameters across data sets. Furthermore, increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. These results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.
Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods, such as the Frechet Inception Distance (FID), correlate well with the perceived quality of samples and are sensitive to mode dropping. However, these metrics are unable to distinguish between different failure cases since they only yield one-dimensional scores. We propose a novel definition of precision and recall for distributions which disentangles the divergence into two separate dimensions. The proposed notion is intuitive, retains desirable properties, and naturally leads to an efficient algorithm that can be used to evaluate generative models. We relate this notion to total variation as well as to recent evaluation metrics such as Inception Score and FID. To demonstrate the practical utility of the proposed approach we perform an empirical study on several variants of Generative Adversarial Networks and Variational Autoencoders. In an extensive set of experiments we show that the proposed metric is able to disentangle the quality of generated samples from the coverage of the target distribution.
Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative approximation errors, we propose a novel notion of lightweight coresets that allows for both multiplicative and additive errors. We provide a single algorithm to construct lightweight coresets for k-means clustering as well as soft and hard Bregman clustering. The algorithm is substantially faster than existing constructions, embarrassingly parallel, and the resulting coresets are smaller. We further show that the proposed approach naturally generalizes to statistical k-means clustering and that, compared to existing results, it can be used to compute smaller summaries for empirical risk minimization. In extensive experiments, we demonstrate that the proposed algorithm outperforms existing data summarization strategies in practice.
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably good and small summaries, they are inherently problem dependent - the practitioner has to commit to a fixed clustering objective before even exploring the data. However, can one construct small data summaries for a wide range of clustering problems simultaneously? In this work, we affirmatively answer this question by proposing an efficient algorithm that constructs such one-shot summaries for k-clustering problems while retaining strong theoretical guarantees.
We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset construction for machine learning. In Section 2, we present both the intuition behind and a theoretically sound framework to construct coresets for general problems and apply it to $k$-means clustering. In Section 3 we summarize existing coreset construction algorithms for a variety of machine learning problems such as maximum likelihood estimation of mixture models, Bayesian non-parametric models, principal component analysis, regression and general empirical risk minimization.
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss functions which are *unbounded*. In our main application, this allows us to obtain bounds for $k$-Means clustering under weak assumptions on the underlying distribution. If the fourth moment is bounded, we prove a rate of $\mathcal{O}\left(m^{-\frac12}\right)$ compared to the previously known $\mathcal{O}\left(m^{-\frac14}\right)$ rate. Furthermore, we show that the rate also depends on the kurtosis - the normalized fourth moment which measures the "tailedness" of a distribution. We further provide improved rates under progressively stronger assumptions, namely, bounded higher moments, subgaussianity and bounded support.