177 research outputs found
Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks
Empirical evidence suggests that heavy-tailed degree distributions occurring
in many real networks are well-approximated by power laws with exponents
that may take values either less than and greater than two. Models based on
various forms of exchangeability are able to capture power laws with , and admit tractable inference algorithms; we draw on previous results to
show that cannot be generated by the forms of exchangeability used
in existing random graph models. Preferential attachment models generate power
law exponents greater than two, but have been of limited use as statistical
models due to the inherent difficulty of performing inference in
non-exchangeable models. Motivated by this gap, we design and implement
inference algorithms for a recently proposed class of models that generates
of all possible values. We show that although they are not exchangeable,
these models have probabilistic structure amenable to inference. Our methods
make a large class of previously intractable models useful for statistical
inference.Comment: Accepted for publication in the proceedings of Conference on
Uncertainty in Artificial Intelligence (UAI) 201
Aspects administratifs et institutionnels
Intervention aux premières Rencontres FORMIST (Formation à l\u27information scientifique et technique)
Disentangling Disentanglement in Variational Autoencoders
We develop a generalisation of disentanglement in variational autoencoders (VAEs)—decomposition of the latent representation—characterising it as the fulfilment of two factors: a) the latent encodings of the data having an appropriate level of overlap, and b) the aggregate encoding of the data conforming to a desired structure, represented through the prior. Decomposition permits disentanglement, i.e. explicit independence between latents, as a special case, but also allows for a much richer class of properties to be imposed on the learnt representation, such as sparsity, clustering, independent subspaces, or even intricate hierarchical dependency relationships. We show that the β-VAE varies from the standard VAE predominantly in its control of latent overlap and that for the standard choice of an isotropic Gaussian prior, its objective is invariant to rotations of the latent representation. Viewed from the decomposition perspective, breaking this invariance with simple manipulations of the prior can yield better disentanglement with little or no detriment to reconstructions. We further demonstrate how other choices of prior can assist in producing different decompositions and introduce an alternative training objective that allows the control of both decomposition factors in a principled manner
Diffusion Models for Constrained Domains
Denoising diffusion models are a recent class of generative models which
achieve state-of-the-art results in many domains such as unconditional image
generation and text-to-speech tasks. They consist of a noising process
destroying the data and a backward stage defined as the time-reversal of the
noising diffusion. Building on their success, diffusion models have recently
been extended to the Riemannian manifold setting. Yet, these Riemannian
diffusion models require geodesics to be defined for all times. While this
setting encompasses many important applications, it does not include manifolds
defined via a set of inequality constraints, which are ubiquitous in many
scientific domains such as robotics and protein design. In this work, we
introduce two methods to bridge this gap. First, we design a noising process
based on the logarithmic barrier metric induced by the inequality constraints.
Second, we introduce a noising process based on the reflected Brownian motion.
As existing diffusion model techniques cannot be applied in this setting, we
derive new tools to define such models in our framework. We empirically
demonstrate the applicability of our methods to a number of synthetic and
real-world tasks, including the constrained conformational modelling of protein
backbones and robotic arms
Continuous Hierarchical Representations with Poincar\'e Variational Auto-Encoders
The variational auto-encoder (VAE) is a popular method for learning a
generative model and embeddings of the data. Many real datasets are
hierarchically structured. However, traditional VAEs map data in a Euclidean
latent space which cannot efficiently embed tree-like structures. Hyperbolic
spaces with negative curvature can. We therefore endow VAEs with a Poincar\'e
ball model of hyperbolic geometry as a latent space and rigorously derive the
necessary methods to work with two main Gaussian generalisations on that space.
We empirically show better generalisation to unseen data than the Euclidean
counterpart, and can qualitatively and quantitatively better recover
hierarchical structures.Comment: Advances in Neural Information Processing System
Spectral Diffusion Processes
Score-based generative modelling (SGM) has proven to be a very effective
method for modelling densities on finite-dimensional spaces. In this work we
propose to extend this methodology to learn generative models over functional
spaces. To do so, we represent functional data in spectral space to dissociate
the stochastic part of the processes from their space-time part. Using
dimensionality reduction techniques we then sample from their stochastic
component using finite dimensional SGM. We demonstrate our method's
effectiveness for modelling various multimodal datasets.Comment: 17 pages, 11 figures, Score-based Method Workshop at 36th Conference
on Neural Information Processing Systems (NeurIPS 2022
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