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Register a new userSetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data
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Jinwoo Kim
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Generative modeling of set-structured data, such as point clouds, requires reasoning over local and global structures at various scales. However, adopting multi-scale frameworks for ordinary sequential data to a set-structured data is nontrivial as it should be invariant to the permutation of its elements. In this paper, we propose SetVAE, a hierarchical variational autoencoder for sets. Motivated by recent progress in set encoding, we build SetVAE upon attentive modules that first partition the set and project the partition back to the original cardinality. Exploiting this module, our hierarchical VAE learns latent variables at multiple scales, capturing coarse-to-fine dependency of the set elements while achieving permutation invariance. We evaluate our model on point cloud generation task and achieve competitive performance to the prior arts with substantially smaller model capacity. We qualitatively demonstrate that our model generalizes to unseen set sizes and learns interesting subset relations without supervision. Our implementation is available at https://github.com/jw9730/setvae.
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Compositional structures between parts and objects are inherent in natural scenes. Modeling such compositional hierarchies via unsupervised learning can bring various benefits such as interpretability and transferability, which are important in many downstream tasks. In this paper, we propose the first deep latent variable model, called RICH, for learning Representation of Interpretable Compositional Hierarchies. At the core of RICH is a latent scene graph representation that organizes the entities of a scene into a tree structure according to their compositional relationships. During inference, taking top-down approach, RICH is able to use higher-level representation to guide lower-level decomposition. This avoids the difficult problem of routing between parts and objects that is faced by bottom-up approaches. In experiments on images containing multiple objects with different part compositions, we demonstrate that RICH is able to learn the latent compositional hierarchy and generate imaginary scenes.
Generative adversarial training (GAT) is a recently introduced adversarial defense method. Previous works have focused on empirical evaluations of its application to training robust predictive models. In this paper we focus on theoretical understanding of the GAT method and extending its application to generative modeling and out-of-distribution detection. We analyze the optimal solutions of the maximin formulation employed by the GAT objective, and make a comparative analysis of the minimax formulation employed by GANs. We use theoretical analysis and 2D simulations to understand the convergence property of the training algorithm. Based on these results, we develop an incremental generative training algorithm, and conduct comprehensive evaluations of the algorithms application to image generation and adversarial out-of-distribution detection. Our results suggest that generative adversarial training is a promising new direction for the above applications.
Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called textit{graphon autoencoder} to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.
Constraint-based learning reduces the burden of collecting labels by having users specify general properties of structured outputs, such as constraints imposed by physical laws. We propose a novel framework for simultaneously learning these constraints and using them for supervision, bypassing the difficulty of using domain expertise to manually specify constraints. Learning requires a black-box simulator of structured outputs, which generates valid labels, but need not model their corresponding inputs or the input-label relationship. At training time, we constrain the model to produce outputs that cannot be distinguished from simulated labels by adversarial training. Providing our framework with a small number of labeled inputs gives rise to a new semi-supervised structured prediction model; we evaluate this model on multiple tasks --- tracking, pose estimation and time series prediction --- and find that it achieves high accuracy with only a small number of labeled inputs. In some cases, no labels are required at all.
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph structure or adding hard constraints to feature-space algorithms. Following a different path, we define a metric regression scheme where we train metric-constrained linear combinations of dissimilarity matrices. The idea is that the input matrices can be pre-computed dissimilarity measures obtained from any kind of available data (e.g. node attributes or edge structure). As the model inputs are distance measures, we do not need to assume the existence of any underlying feature space. Main challenge is that metric constraints (especially positive-definiteness and sub-additivity), are not automatically respected if, for example, the coefficients of the linear combination are allowed to be negative. Both positive and sub-additive constraints are linear inequalities, but the computational complexity of imposing them scales as O(D3), where D is the size of the input matrices (i.e. the size of the data set). This becomes quickly prohibitive, even when D is relatively small. We propose a new graph-based technique for optimizing under such constraints and show that, in some cases, our approach may reduce the original computational complexity of the optimization process by one order of magnitude. Contrarily to existing methods, our scheme applies to any (possibly non-convex) metric-constrained objective function.
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