Latent-space Bayesian optimization (LSBO) extends Bayesian optimization to structured domains, such as molecular design, by searching in the continuous latent space of a generative model. However, most LSBO methods assume a fixed objective, whereas real design campaigns often face temporal drift (e.g., evolving preferences or shifting targets). Bringing time-varying BO into LSBO is nontrivial: drift can affect not only the surrogate, but also the latent search space geometry induced by the representation. We propose Time-Aware Latent-space Bayesian Optimization (TALBO), which incorporates time in both the surrogate and the learned generative representation via a GP-prior variational autoencoder, yielding a latent space aligned as objectives evolve. To evaluate timevarying LSBO systematically, we adapt widely used molecular design tasks to drifting multi-property objectives and introduce metrics tailored to changing targets. Across these benchmarks, TALBO consistently outperforms strong LSBO baselines and remains robust across drift speeds and design choices, while remaining competitive under actually time-invariant objectives.
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for computational tractability. Inference is made tractable through a collapsed variational bound with similar computational complexity to that of the traditional Bayesian GP-LVM. Inference over partially-observed test cases is achieved by optimizing a "partially-collapsed" bound. Modeling high-dimensional time series systems is enabled through use of a dynamical GP …
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share covariance structure. Our hierarchical model is seen to subsume several previously proposed multitask learning models and performs well on three distinct real-world data sets.
EURECOM（欧洲通信研究院）；University of California, Irvine（加州大学欧文分校）
Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate …
University of Pennsylvania（宾夕法尼亚大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University College London（伦敦大学学院）；Massachusetts Institute of Technology（麻省理工学院）
Bayesian optimization over the latent spaces of deep autoencoder models (DAEs) has recently emerged as a promising new approach for optimizing challenging black-box functions over structured, discrete, hard-to-enumerate search spaces (e.g., molecules). Here the DAE dramatically simplifies the search space by mapping inputs into a continuous latent space where familiar Bayesian optimization tools can be more readily applied. Despite this simplification, the latent space typically remains high-dimensional. Thus, even with a well-suited latent space, these approaches do not necessarily provide a …
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a low-dimensional generative model of the sample-based stochastic prior as well as a surrogate for the forward evaluation. Its Bayesian formulation captures epistemic uncertainty introduced by the limited number of input and output examples, automatically selects an appropriate dimensionality for the learned latent representation of the data, and rigorously propagates…
Active Preference Learning over Latent Preference Archetypes for Many-Objective Bayesian Optimization
University of Manchester（曼彻斯特大学）；University of Edinburgh（爱丁堡大学）；Aalto University（阿尔托大学）；University of Amsterdam（阿姆斯特丹大学）；ELLIS Institute Finland（芬兰ELLIS研究所）
Institute for Computing and Information Sciences（计算与信息科学研究所）；Radboud University Nijmegen（拉德堡德大学奈梅亨分校）
We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is consistent under certain conditions and that is quite robust to the violations of these conditions. In simulations, BGCF substantially outperforms two state-of-the-art alternative approaches. An illustration on the `Holzinger & Swineford 1939' dataset indicates that BGCF is favorable over the so-called robust maximum likelihood (MLR) even if the data match the assumptions of MLR.
We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. By minimizing a hinge-loss using the linear expectation operator, we can perform posterior inference efficiently without dealing with a highly nonlinear link likelihood function; by using a fully-Bayesian formulation, we can avoid tuning regularization constants. Experimental results on real datasets appear to demonstrate the benefits inher…
School of Engineering, University of Warwick, UK（华威大学工程学院，英国）；Warwick Center for Predictive Modelling, University of Warwick, UK（华威大学预测建模中心，英国）；Department of Statistics, University of Warwick, UK（华威大学统计系，英国）；Division of Translational Medicine, Warwick Medical School, UK（华威医学院转化医学部，英国）；Dept of Clinical Biochemistry, Division of Pathology, University Hospital Coventry and Warwickshire, Coventry, UK（考文垂和华威郡大学医院病理学部临床生物化学系，考文垂，英国）
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo estimate for the marginal likelihood that approximately integrates over the latent variables. This is used to construct a Markov Chain to explore the posterior of the hyperparameters. We demonstrate the procedure on simulated and real examples, showing its ability to capture uncertainty and multimodality of the hyperparameters and improved uncertainty quanti…
Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated from a latent position model. Furthermore, the presence of communities within the network might generate community-specific submanifold structures in the embedding, but this is not explicitly accounted for in most statistical models for networks. In this article, a class of models called latent structure block models (LSBM) is proposed to address such scenarios…
Real engineering and scientific applications often involve one or more qualitative inputs. Standard Gaussian processes (GPs), however, cannot directly accommodate qualitative inputs. The recently introduced latent variable Gaussian process (LVGP) overcomes this issue by first mapping each qualitative factor to underlying latent variables (LVs), and then uses any standard GP covariance function over these LVs. The LVs are estimated similarly to the other GP hyperparameters through maximum likelihood estimation, and then plugged into the prediction expressions. However, this plug-in approach wil…
Technion - Israel Institute of Technology（以色列理工学院）
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian network models, namely networks that include hidden variables, where asymptotic approximation deviates from the standard BIC score. Our algorithms solve two central difficulties in asymptotic evaluation of marginal likelihood integrals, namely, evaluation of regular dimensionality drop for latent Bayesian network models and computation of non-standard approxim…
To address three important issues involved in latent variable models (LVMs), including capturing infrequent patterns, achieving small-sized but expressive models and alleviating overfitting, several studies have been devoted to "diversifying" LVMs, which aim at encouraging the components in LVMs to be diverse. Most existing studies fall into a frequentist-style regularization framework, where the components are learned via point estimation. In this paper, we investigate how to "diversify" LVMs in the paradigm of Bayesian learning. We propose two approaches that have complementary advantages. O…
John A. Paulson School of Engineering and Applied Sciences（约翰·A·保尔森工程与应用科学学院）；Harvard University（哈佛大学）
Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased …
University of California, Irvine（加州大学欧文分校）；Microsoft Research New England（微软新英格兰研究院）；Stanford University（斯坦福大学）
Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including probabilistic topic models and latent linear Bayesian networks, using only second-order observed moments. The sufficient conditions for identifiability of these models are primarily based on weak expansion constraints on the topic-word matrix, for topic models, and on the directed acyclic graph, for Bayesian networks. Because no assumptions are made on the d…
We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques.…
Volkswagen Group of America Innovation Center California（大众汽车美国创新中心加州）；BayzAI
The lossless data compression algorithm based on Bayesian Attention Networks is derived from first principles. Bayesian Attention Networks are defined by introducing an attention factor per a training sample loss as a function of two sample inputs, from training sample and prediction sample. By using a sharpened Jensen's inequality we show that the attention factor is completely defined by a correlation function of the two samples w.r.t. the model weights. Due to the attention factor the solution for a prediction sample is mostly defined by a few training samples that are correlated with the p…
Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spaces
School of Mathematical Sciences, Lancaster University, UK（数学科学学院，兰卡斯特大学）；Department of Applied Maths and Theoretical Physics, University of Cambridge, UK（应用数学与理论物理系，剑桥大学）
Mila - Québec AI Institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）；ÉTS Montréal（蒙特利尔高等技术学院）
Learning predictors that do not rely on spurious correlations involves building causal representations. However, learning such a representation is very challenging. We, therefore, formulate the problem of learning a causal representation from high dimensional data and study causal recovery with synthetic data. This work introduces a latent variable decoder model, Decoder BCD, for Bayesian causal discovery and performs experiments in mildly supervised and unsupervised settings. We present a series of synthetic experiments to characterize important factors for causal discovery and show that usin…
In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accuracy for observable variables, the theoretical analysis of estimating latent variables has not been thoroughly investigated. In a previous study, we determined the accuracy of a Bayes estimation for the jo…
Università degli Studi della Campania “Luigi Vanvitelli”（坎帕尼亚大学“路易吉·万维泰利”）
Bayesian networks in their Factor Graph Reduced Normal Form (FGrn) are a powerful paradigm for implementing inference graphs. Unfortunately, the computational and memory costs of these networks may be considerable, even for relatively small networks, and this is one of the main reasons why these structures have often been underused in practice. In this work, through a detailed algorithmic and structural analysis, various solutions for cost reduction are proposed. An online version of the classic batch learning algorithm is also analyzed, showing very similar results (in an unsupervised context…
Corrected Integrated Laplace Approximation for Bayesian Inference in Latent Gaussian Models
Manning College of Information and Computer Sciences University of Massachusetts Amherst（信息与计算机科学学院 马萨诸塞大学阿姆赫斯特分校）；Department of Statistics University of British Columbia（统计学系 不列颠哥伦比亚大学）
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data and their hidden generation process, respectively. It has been pointed out that conventional statistical analysis is not applicable to these models, because redundancy of the latent variable produces singularities in the parameter space. In recent years, a method based on algebraic geometry has allowed us to analyze the accuracy of predicting observable variab…
Non-negative tensor factorization models enable predictive analysis on count data. Among them, Bayesian Poisson-Gamma models can derive full posterior distributions of latent factors and are less sensitive to sparse count data. However, current inference methods for these Bayesian models adopt restricted update rules for the posterior parameters. They also fail to share the update information to better cope with the data sparsity. Moreover, these models are not endowed with a component that handles the imbalance in count data values. In this paper, we propose a novel variational auto-encoder f…
Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into its epistemic and aleatoric components. First, we show how such a decomposition arises naturally in a Bayesian active learning scenario by following an information theoretic approach. Second, we use a similar decomposition to develop a novel risk sensitive objective for safe reinforcement learning (RL). This objective minimizes the effect of model bias in envi…
ShanghaiTech University（上海科技大学）；Changsha Institute for Computing and Digital Economy, Peking University（北京大学长沙计算与数字经济研究院）；Louisiana State University（路易斯安那州立大学）
We present a dimension-reduced KRnet map approach (DR-KRnet) for high-dimensional Bayesian inverse problems, which is based on an explicit construction of a map that pushes forward the prior measure to the posterior measure in the latent space. Our approach consists of two main components: data-driven VAE prior and density approximation of the posterior of the latent variable. In reality, it may not be trivial to initialize a prior distribution that is consistent with available prior data; in other words, the complex prior information is often beyond simple hand-crafted priors. We employ varia…
A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inference. The latent likelihood of the data and its gradients are computable in closed form via Tutte's directed matrix tree theorem using determinants and inverses of the out-Laplacian. This novel likelihood subsumes iid likelihood, is exchangeable and yields efficient unsupervised an…
UT-Battelle, LLC（UT-巴特尔有限责任公司）；U.S. Department of Energy（美国能源部）
Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g., balancing the Kullback Leibler (KL) and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolut…
We present the Infinite Latent Events Model, a nonparametric hierarchical Bayesian distribution over infinite dimensional Dynamic Bayesian Networks with binary state representations and noisy-OR-like transitions. The distribution can be used to learn structure in discrete timeseries data by simultaneously inferring a set of latent events, which events fired at each timestep, and how those events are causally linked. We illustrate the model on a sound factorization task, a network topology identification task, and a video game task.
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the non-Gaussianity of external influences has been proposed to estimate the data-generating processes of variables. However, the results of the estimation can be biased if there are latent classes. In this paper, we first review LiNGAM, its extended model, as well as the estimation procedure for LiNGAM in a Bayesian framework. We then propose a new Bayesian estimation p…
Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in some cases more natural and general. In this paper, we present regularized Bayesian inference (RegBayes), a novel computational framework that performs posterior inference with a regularization term on the desired post-data posterior distribution under an information theoretical f…
School of Electrical Information and Communication Engineering, Huazhong University of Science & Technology（华中科技大学电子信息与通信学院）；Microsoft AI & Research（微软人工智能与研究）；Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）
Recent techniques built on Generative Adversarial Networks (GANs), such as Cycle-Consistent GANs, are able to learn mappings among different domains built from unpaired datasets, through min-max optimization games between generators and discriminators. However, it remains challenging to stabilize the training process and thus cyclic models fall into mode collapse accompanied by the success of discriminator. To address this problem, we propose an novel Bayesian cyclic model and an integrated cyclic framework for inter-domain mappings. The proposed method motivated by Bayesian GAN explores the f…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust the variational parameters to improve the quality of the approximation. We demonstrate experimentally that this approximation is faster and potentially more accurate than sampling. We also introduce a simple new technique for handling evidence, which allows us to handle arbitrary distributions on o…
Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure of the network, with strong consistency results in the stochastic blockmodel framework. One of the main practical limitations of standard algorithms for community detection from spectral embeddings is that the number of communities and the latent dimension of the embedding must be specified in advance. In this article, a novel Bayesian mo…
We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of nonlinear relationship and no latent confounders. However, the estimation results could be distorted if either assumption is actually violated. In this paper, we first propose a new linear non-Gaussian acyclic structural equation model with individual-specific effects that allows latent confounders to be considered. We then propose an empirical Bayesian app…
We propose a Bayesian nonparametric method for low-pass filtering that can naturally handle unevenly-sampled and noise-corrupted observations. The proposed model is constructed as a latent-factor model for time series, where the latent factors are Gaussian processes with non-overlapping spectra. With this construction, the low-pass version of the time series can be identified as the low-frequency latent component, and therefore it can be found by means of Bayesian inference. We show that the model admits exact training and can be implemented with minimal numerical approximations. Finally, the …
NTT DATA Mathematical Systems Inc.（NTT数据数学系统公司）；Tokyo Institute of Technology（东京工业大学）
Latent Dirichlet allocation (LDA) obtains essential information from data by using Bayesian inference. It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been yet clarified since it is a singular statistical model where there is no one-to-one mapping from parameters to probability distributions. In this paper, we give the exact asymptotic form of its generalization error and marginal likelihood, by theoretical analysis of its learning coefficient using algebraic geometry. The theoretical result shows that the Bay…
Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the…
Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attempts to unite the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction. It inherits the advances of nonparametric Bayesian methods to infer the unknown latent social dimension, while for discriminative link predicti…
The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent's current un…
The rank-based association between two variables can be modeled by introducing a latent normal level to ordinal data. We demonstrate how this approach yields Bayesian inference for Kendall's rank correlation coefficient, improving on a recent Bayesian solution from asymptotic properties of the test statistic.
The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for function evaluations. We introduce a cost-aware multi-objective Bayesian optimisation with non-uniform evaluation cost over objective functions by defining cost-aware constraints over the search space. The cost-aware constraints are a sorted tuple of indexes that demonstrate the …
University of South Carolina（南卡罗来纳大学）；University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only requires a small number of simulations and can be applied to high-dimensional systems in the presence of intractable likelihood functions. The proposed approach uses linear latent projections to estimate the joint probability distribution between states, parameters, and observables using a mixture of Gaussian components generated by the reconstruction error …
Samsung AI Center（三星人工智能中心）；Rutgers University（罗格斯大学）
We propose a family of novel hierarchical Bayesian deep auto-encoder models capable of identifying disentangled factors of variability in data. While many recent attempts at factor disentanglement have focused on sophisticated learning objectives within the VAE framework, their choice of a standard normal as the latent factor prior is both suboptimal and detrimental to performance. Our key observation is that the disentangled latent variables responsible for major sources of variability, the relevant factors, can be more appropriately modeled using long-tail distributions. The typical Gaussian…
Institut Polytechnique de Paris（巴黎综合理工学院）；Université Paris-Saclay（巴黎萨克雷大学）；Aix Marseille University（艾克斯-马赛大学）
Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior distribution of the network parameters, most BNN approaches are either limited to small networks or rely on constraining assumptions such as parameter independence. These drawbacks have enabled prominence of simple, but computationally heavy approaches such as Deep Ensembles, whose training and testing costs increase linearly with the number of networks. In this wor…
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally line…
Analyzing the underlying structure of multiple time-sequences provides insights into the understanding of social networks and human activities. In this work, we present the \emph{Bayesian nonparametric Poisson process allocation} (BaNPPA), a latent-function model for time-sequences, which automatically infers the number of latent functions. We model the intensity of each sequence as an infinite mixture of latent functions, each of which is obtained using a function drawn from a Gaussian process. We show that a technical challenge for the inference of such mixture models is the unidentifiabilit…
University of Texas (UT) at Austin（德克萨斯大学奥斯汀分校）；University of Sao Paulo (USP)（圣保罗大学）
This paper introduces a privacy-aware Bayesian approach that combines ensembles of classifiers and clusterers to perform semi-supervised and transductive learning. We consider scenarios where instances and their classification/clustering results are distributed across different data sites and have sharing restrictions. As a special case, the privacy aware computation of the model when instances of the target data are distributed across different data sites, is also discussed. Experimental results show that the proposed approach can provide good classification accuracies while adhering to the d…
