Arbitrary conditioning is an important problem in unsupervised learning, where we seek to model the conditional densities $p(\mathbf{x}_u \mid \mathbf{x}_o)$ that underly some data, for all possible non-intersecting subsets $o, u \subset \{1, \dots , d\}$. However, the vast majority of density estimation only focuses on modeling the joint distribution $p(\mathbf{x})$, in which important conditional dependencies between features are opaque. We propose a simple and general framework, coined Posterior Matching, that enables Variational Autoencoders (VAEs) to perform arbitrary conditioning, without modification to the VAE itself. Posterior Matching applies to the numerous existing VAE-based approaches to joint density estimation, thereby circumventing the specialized models required by previous approaches to arbitrary conditioning. We find that Posterior Matching is comparable or superior to current state-of-the-art methods for a variety of tasks with an assortment of VAEs (e.g.~discrete, hierarchical, VaDE).
With a principled representation of uncertainty and closed form posterior updates, Gaussian processes (GPs) are a natural choice for online decision making. However, Gaussian processes typically require at least $\mathcal{O}(n^2)$ computations for $n$ training points, limiting their general applicability. Stochastic variational Gaussian processes (SVGPs) can provide scalable inference for a dataset of fixed size, but are difficult to efficiently condition on new data. We propose online variational conditioning (OVC), a procedure for efficiently conditioning SVGPs in an online setting that does…
The literature about history matching is vast and despite the impressive number of methods proposed and the significant progresses reported in the last decade, conditioning reservoir models to dynamic data is still a challenging task. Ensemble-based methods are among the most successful and efficient techniques currently available for history matching. These methods are usually able to achieve reasonable data matches, especially if an iterative formulation is employed. However, they sometimes fail to preserve the geological realism of the model, which is particularly evident in reservoir with …
Self-Conditioning Enables Deep Sequential Reasoning in Flow Matching
Shanghai Qi Zhi Institute（上海人工智能实验室）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Georgia Institute of Technology（佐治亚理工学院）；Xiongan AI Institute（雄安人工智能研究院）
Imperial College London（帝国理工学院）；St. Petersburg State University（圣彼得堡国立大学）；St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所圣彼得堡分所）；University College London（伦敦大学学院）
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable estimates via sampling. Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations. This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector. These methods are prohibitively ex…
D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching
Sibley School of Mechanical and Aerospace Engineering, Cornell University（科尼尔大学机械与航空航天工程学院）；Department of Aerospace and Mechanical Engineering, University of Notre Dame（诺丁汉大学航空航天与机械工程系）
Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true post…
Amortised inference enables scalable learning of sequential latent-variable models (LVMs) with the evidence lower bound (ELBO). In this setting, variational posteriors are often only partially conditioned. While the true posteriors depend, e.g., on the entire sequence of observations, approximate posteriors are only informed by past observations. This mimics the Bayesian filter -- a mixture of smoothing posteriors. Yet, we show that the ELBO objective forces partially-conditioned amortised posteriors to approximate products of smoothing posteriors instead. Consequently, the learned generative …
Maximum likelihood learning with exponential families leads to moment-matching of the sufficient statistics, a classic result. This can be generalized to conditional exponential families and/or when there are hidden data. This document gives a first-principles explanation of these generalized moment-matching conditions, along with a self-contained derivation.
ETH Zurich（苏黎世联邦理工学院）；EPFL（洛桑联邦理工学院）；Prescient Design, Genentech（基因泰克Prescient Design部门）；Swiss Data Science Center（瑞士数据科学中心）
We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct modeling of the global and local graph structure and helps to overcome the expressivity and mode collapse issues of one-shot graph generators. Our novel GAN, called SPECTRE, enables the one-shot generation of much larger graphs than previously possible with one-shot models. SPECTRE outperforms state-of-the-art deep autoregressive generators in ter…
PhylaFlow: Hybrid Flow Matching in Billera-Holmes-Vogtmann Tree Space for Phylogenetic Inference
Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard（埃里克和wendy Schmidt中心，MIT和哈佛大学Broad研究所）；Department of Biomedical Informatics, Harvard Medical School（哈佛医学院生物医学信息学系）；Centennial High School（Centennial高中）；Infectious Disease and Microbiome Program, Broad Institute of MIT and Harvard（传染病与微生物组计划，MIT和哈佛大学Broad研究所）
Deep learning techniques are increasingly being considered for geological applications where -- much like in computer vision -- the challenges are characterized by high-dimensional spatial data dominated by multipoint statistics. In particular, a novel technique called generative adversarial networks has been recently studied for geological parametrization and synthesis, obtaining very impressive results that are at least qualitatively competitive with previous methods. The method obtains a neural network parametrization of the geology -- so-called a generator -- that is capable of reproducing…
XS-VLA: Teaching Tiny Vision-Language-Action Models with Spatial Supervision and Demonstration Conditioning
Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；National College for Excellent Engineers, Beihang University（北京航空航天大学卓越工程师学院）；Wuxi Dexteroushands Robotic Technology Co.（无锡灵犀机器人技术有限公司）
Shortest-Path Flow Matching with Mixture-Conditioned Bases for OOD Generalization to Unseen Conditions
Wellcome Sanger Institute（Wellcome桑格研究所）；Institute for Molecular Medicine Finland (FIMM)（芬兰分子医学研究所）；University of Helsinki（赫尔辛基大学）；School of Computing and Information Systems（计算与信息系统学院）；University of Cambridge（剑桥大学）；Cambridge Centre for AI in Medicine（剑桥人工智能医学中心）；MediaTek Research（MediaTek研究）；Cambridge Stem Cell Institute（剑桥干细胞研究所）
