We propose a novel framework for real-time communication-aware coverage control in networked robot swarms. Our framework unifies the robot dynamics with network-level message-routing to reach consensus on swarm formations in the presence of communication uncertainties by leveraging local information. Specifically, we formulate the communication-aware coverage as a cooperative graphical game, and use variational inference to reach mixed strategy Nash equilibria of the stage games. We experimentally validate the proposed approach in a mobile ad-hoc wireless network scenario using teams of aerial vehicles and terrestrial user equipment (UE) operating over a large geographic region of interest. We show that our approach can provide wireless coverage to stationary and mobile UEs under realistic network conditions.
It is difficult to use subsampling with variational inference in hierarchical models since the number of local latent variables scales with the dataset. Thus, inference in hierarchical models remains a challenge at large scale. It is helpful to use a variational family with structure matching the posterior, but optimization is still slow due to the huge number of local distributions. Instead, this paper suggests an amortized approach where shared parameters simultaneously represent all local distributions. This approach is similarly accurate as using a given joint distribution (e.g., a full-rank Gaussian) but is feasible on datasets that are several orders of magnitude larger. It is also dramatically faster than using a structured variational distribution.
The recent introduction of thermodynamic integration techniques has provided a new framework for understanding and improving variational inference (VI). In this work, we present a careful analysis of the thermodynamic variational objective (TVO), bridging the gap between existing variational objectives and shedding new insights to advance the field. In particular, we elucidate how the TVO naturally connects the three key variational schemes, namely the importance-weighted VI, Renyi-VI, and MCMC-VI, which subsumes most VI objectives employed in practice. To explain the performance gap between theory and practice, we reveal how the pathological geometry of thermodynamic curves negatively affects TVO. By generalizing the integration path from the geometric mean to the weighted Holder mean, we extend the theory of TVO and identify new opportunities for improving VI. This motivates our new VI objectives, named the Holder bounds, which flatten the thermodynamic curves and promise to achieve a one-step approximation of the exact marginal log-likelihood. A comprehensive discussion on the choices of numerical estimators is provided. We present strong empirical evidence on both synthetic and real-world datasets to support our claims.
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning methods to reconstruct this latent DS in a data-driven, unsupervised way. In many areas of science it is common to sample time series observations from many data modalities simultaneously, e.g. electrophysiological and behavioral time series in a typical neuroscience experiment. However, current machine learning tools for reconstructing DSs usually focus on just one data modality. Here we propose a general framework for multi-modal data integration for the purpose of nonlinear DS reconstruction and the analysis of cross-modal relations. This framework is based on dynamically interpretable recurrent neural networks as general approximators of nonlinear DSs, coupled to sets of modality-specific decoder models from the class of generalized linear models. Both an expectation-maximization and a variational inference algorithm for model training are advanced and compared. We show on nonlinear DS benchmarks that our algorithms can efficiently compensate for too noisy or missing information in one data channel by exploiting other channels, and demonstrate on experimental neuroscience data how the algorithm learns to link different data domains to the underlying dynamics.
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint explicitly casts inference algorithms under the framework of numerical optimisation. We show that common approximations to Newton's method from the optimisation literature, namely Gauss-Newton and quasi-Newton methods (e.g., the BFGS algorithm), are still valid under this 'Bayes-Newton' framework. This leads to a suite of novel algorithms which are guaranteed to result in positive semi-definite (PSD) covariance matrices, unlike standard VI and EP. Our unifying viewpoint provides new insights into the connections between various inference schemes. All the presented methods apply to any model with a Gaussian prior and non-conjugate likelihood, which we demonstrate with (sparse) Gaussian processes and state space models.
Causal structures for observational survival data provide crucial information regarding the relationships between covariates and time-to-event. We derive motivation from the information theoretic source coding argument, and show that incorporating the knowledge of the directed acyclic graph (DAG) can be beneficial if suitable source encoders are employed. As a possible source encoder in this context, we derive a variational inference based conditional variational autoencoder for causal structured survival prediction, which we refer to as DAGSurv. We illustrate the performance of DAGSurv on low and high-dimensional synthetic datasets, and real-world datasets such as METABRIC and GBSG. We demonstrate that the proposed method outperforms other survival analysis baselines such as Cox Proportional Hazards, DeepSurv and Deephit, which are oblivious to the underlying causal relationship between data entities.
Latent Dirichlet Allocation (LDA) is a probabilistic model used to uncover latent topics in a corpus of documents. Inference is often performed using variational Bayes (VB) algorithms, which calculate a lower bound to the posterior distribution over the parameters. Deriving the variational update equations for new models requires considerable manual effort; variational message passing (VMP) has emerged as a "black-box" tool to expedite the process of variational inference. But applying VMP in practice still presents subtle challenges, and the existing literature does not contain the steps that are necessary to implement VMP for the standard smoothed LDA model, nor are available black-box probabilistic graphical modelling software able to do the word-topic updates necessary to implement LDA. In this paper, we therefore present a detailed derivation of the VMP update equations for LDA. We see this as a first step to enabling other researchers to calculate the VMP updates for similar graphical models.
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with respect to time. Our natural gradient approach enables application of parallel filtering and smoothing, further reducing the temporal span complexity to be logarithmic in the number of time steps. We derive a sparse approximation that constructs a state-space model over a reduced set of spatial inducing points, and show that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties. To further improve the spatial scaling we propose a mean-field assumption of independence between spatial locations which, when coupled with sparsity and parallelisation, leads to an efficient and accurate method for large spatio-temporal problems.
Crowdsourcing systems enable us to collect large-scale dataset, but inherently suffer from noisy labels of low-paid workers. We address the inference and learning problems using such a crowdsourced dataset with noise. Due to the nature of sparsity in crowdsourcing, it is critical to exploit both probabilistic model to capture worker prior and neural network to extract task feature despite risks from wrong prior and overfitted feature in practice. We hence establish a neural-powered Bayesian framework, from which we devise deepMF and deepBP with different choice of variational approximation methods, mean field (MF) and belief propagation (BP), respectively. This provides a unified view of existing methods, which are special cases of deepMF with different priors. In addition, our empirical study suggests that deepBP is a new approach, which is more robust against wrong prior, feature overfitting and extreme workers thanks to the more sophisticated BP than MF.
The predominant approach for language modeling is to process sequences from left to right, but this eliminates a source of information: the order by which the sequence was generated. One strategy to recover this information is to decode both the content and ordering of tokens. Existing approaches supervise content and ordering by designing problem-specific loss functions and pre-training with an ordering pre-selected. Other recent works use iterative search to discover problem-specific orderings for training, but suffer from high time complexity and cannot be efficiently parallelized. We address these limitations with an unsupervised parallelizable learner that discovers high-quality generation orders purely from training data -- no domain knowledge required. The learner contains an encoder network and decoder language model that perform variational inference with autoregressive orders (represented as permutation matrices) as latent variables. The corresponding ELBO is not differentiable, so we develop a practical algorithm for end-to-end optimization using policy gradients. We implement the encoder as a Transformer with non-causal attention that outputs permutations in one forward pass. Permutations then serve as target generation orders for training an insertion-based Transformer language model. Empirical results in language modeling tasks demonstrate that our method is context-aware and discovers orderings that are competitive with or even better than fixed orders.
Recent years have witnessed an increasing use of coordinated accounts on social media, operated by misinformation campaigns to influence public opinion and manipulate social outcomes. Consequently, there is an urgent need to develop an effective methodology for coordinated group detection to combat the misinformation on social media. However, existing works suffer from various drawbacks, such as, either limited performance due to extreme reliance on predefined signatures of coordination, or instead an inability to address the natural sparsity of account activities on social media with useful prior domain knowledge. Therefore, in this paper, we propose a coordination detection framework incorporating neural temporal point process with prior knowledge such as temporal logic or pre-defined filtering functions. Specifically, when modeling the observed data from social media with neural temporal point process, we jointly learn a Gibbs-like distribution of group assignment based on how consistent an assignment is to (1) the account embedding space and (2) the prior knowledge. To address the challenge that the distribution is hard to be efficiently computed and sampled from, we design a theoretically guaranteed variational inference approach to learn a mean-field approximation for it. Experimental results on a real-world dataset show the effectiveness of our proposed method compared to the SOTA model in both unsupervised and semi-supervised settings. We further apply our model on a COVID-19 Vaccine Tweets dataset. The detection result suggests the presence of suspicious coordinated efforts on spreading misinformation about COVID-19 vaccines.
Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian processes in novel areas of science, a rapidly-growing line of research has focused on constructively extending these models to handle non-Euclidean domains, including Riemannian manifolds, such as spheres and tori. We propose techniques that generalize this class to model vector fields on Riemannian manifolds, which are important in a number of application areas in the physical sciences. To do so, we present a general recipe for constructing gauge independent kernels, which induce Gaussian vector fields, i.e. vector-valued Gaussian processes coherent with geometry, from scalar-valued Riemannian kernels. We extend standard Gaussian process training methods, such as variational inference, to this setting. This enables vector-valued Gaussian processes on Riemannian manifolds to be trained using standard methods and makes them accessible to machine learning practitioners.
Existing deep hierarchical topic models are able to extract semantically meaningful topics from a text corpus in an unsupervised manner and automatically organize them into a topic hierarchy. However, it is unclear how to incorporate prior beliefs such as knowledge graph to guide the learning of the topic hierarchy. To address this issue, we introduce TopicNet as a deep hierarchical topic model that can inject prior structural knowledge as an inductive bias to influence learning. TopicNet represents each topic as a Gaussian-distributed embedding vector, projects the topics of all layers into a shared embedding space, and explores both the symmetric and asymmetric similarities between Gaussian embedding vectors to incorporate prior semantic hierarchies. With an auto-encoding variational inference network, the model parameters are optimized by minimizing the evidence lower bound and a regularization term via stochastic gradient descent. Experiments on widely used benchmarks show that TopicNet outperforms related deep topic models on discovering deeper interpretable topics and mining better document~representations.
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backpropagation and the variational inference by backpropagation frameworks, in order to efficiently draw samples from the posterior distribution of transformation parameters. To address the modelling issues, we formulate a Bayesian model for image registration that overcomes the existing barriers when using a dense, high-dimensional, and diffeomorphic transformation parametrisation. This results in improved calibration of uncertainty estimates. We compare the model in terms of both image registration accuracy and uncertainty quantification to VoxelMorph, a state-of-the-art image registration model based on deep learning.
Variational Inference (VI) offers a method for approximating intractable likelihoods. In neural VI, inference of approximate posteriors is commonly done using an encoder. Alternatively, encoderless VI offers a framework for learning generative models from data without encountering suboptimalities caused by amortization via an encoder (e.g. in presence of missing or uncertain data). However, in absence of an encoder, such methods often suffer in convergence due to the slow nature of gradient steps required to learn the approximate posterior parameters. In this paper, we introduce Relay VI (RVI), a framework that dramatically improves both the convergence and performance of encoderless VI. In our experiments over multiple datasets, we study the effectiveness of RVI in terms of convergence speed, loss, representation power and missing data imputation. We find RVI to be a unique tool, often superior in both performance and convergence speed to previously proposed encoderless as well as amortized VI models (e.g. VAE).
As one of the most popular generative models, Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. However, when the decoder network is sufficiently expressive, VAE may lead to posterior collapse; that is, uninformative latent representations may be learned. To this end, in this paper, we propose an alternative model, DU-VAE, for learning a more Diverse and less Uncertain latent space, and thus the representation can be learned in a meaningful and compact manner. Specifically, we first theoretically demonstrate that it will result in better latent space with high diversity and low uncertainty awareness by controlling the distribution of posterior's parameters across the whole data accordingly. Then, without the introduction of new loss terms or modifying training strategies, we propose to exploit Dropout on the variances and Batch-Normalization on the means simultaneously to regularize their distributions implicitly. Furthermore, to evaluate the generalization effect, we also exploit DU-VAE for inverse autoregressive flow based-VAE (VAE-IAF) empirically. Finally, extensive experiments on three benchmark datasets clearly show that our approach can outperform state-of-the-art baselines on both likelihood estimation and underlying classification tasks.
Sampling and Variational Inference (VI) are two large families of methods for approximate inference that have complementary strengths. Sampling methods excel at approximating arbitrary probability distributions, but can be inefficient. VI methods are efficient, but may misrepresent the true distribution. Here, we develop a general framework where approximations are stochastic mixtures of simple component distributions. Both sampling and VI can be seen as special cases: in sampling, each mixture component is a delta-function and is chosen stochastically, while in standard VI a single component is chosen to minimize divergence. We derive a practical method that interpolates between sampling and VI by solving an optimization problem over a mixing distribution. Intermediate inference methods then arise by varying a single parameter. Our method provably improves on sampling (reducing variance) and on VI (reducing bias+variance despite increasing variance). We demonstrate our method's bias/variance trade-off in practice on reference problems, and we compare outcomes to commonly used sampling and VI methods. This work takes a step towards a highly flexible yet simple family of inference methods that combines the complementary strengths of sampling and VI.
Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they are emerging as a promising choice for capturing the patterns in asynchronous sequences, in the context of temporal point process. In this paper, we first review recent research emphasis and difficulties in modeling asynchronous event sequences with deep temporal point process, which can be concluded into four fields: encoding of history sequence, formulation of conditional intensity function, relational discovery of events and learning approaches for optimization. We introduce most of recently proposed models by dismantling them into the four parts, and conduct experiments by remodularizing the first three parts with the same learning strategy for a fair empirical evaluation. Besides, we extend the history encoders and conditional intensity function family, and propose a Granger causality discovery framework for exploiting the relations among multi-types of events. Because the Granger causality can be represented by the Granger causality graph, discrete graph structure learning in the framework of Variational Inference is employed to reveal latent structures of the graph. Further experiments show that the proposed framework with latent graph discovery can both capture the relations and achieve an improved fitting and predicting performance.
In this paper, we propose VISinger, a complete end-to-end high-quality singing voice synthesis (SVS) system that directly generates audio waveform from lyrics and musical score. Our approach is inspired by VITS, which adopts VAE-based posterior encoder augmented with normalizing flow-based prior encoder and adversarial decoder to realize complete end-to-end speech generation. VISinger follows the main architecture of VITS, but makes substantial improvements to the prior encoder based on the characteristics of singing. First, instead of using phoneme-level mean and variance of acoustic features, we introduce a length regulator and a frame prior network to get the frame-level mean and variance on acoustic features, modeling the rich acoustic variation in singing. Second, we further introduce an F0 predictor to guide the frame prior network, leading to stabler singing performance. Finally, to improve the singing rhythm, we modify the duration predictor to specifically predict the phoneme to note duration ratio, helped with singing note normalization. Experiments on a professional Mandarin singing corpus show that VISinger significantly outperforms FastSpeech+Neural-Vocoder two-stage approach and the oracle VITS; ablation study demonstrates the effectiveness of different contributions.
In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.