Planning for sequential robotics tasks often requires integrated symbolic and geometric reasoning. TAMP algorithms typically solve these problems by performing a tree search over high-level task sequences while checking for kinematic and dynamic feasibility. This can be inefficient because, typically, candidate task plans resulting from the tree search ignore geometric information. This often leads to motion planning failures that require expensive backtracking steps to find alternative task plans. We propose a novel approach to TAMP called Stein Task and Motion Planning (STAMP) that relaxes the hybrid optimization problem into a continuous domain. This allows us to leverage gradients from differentiable physics simulation to fully optimize discrete and continuous plan parameters for TAMP. In particular, we solve the optimization problem using a gradient-based variational inference algorithm called Stein Variational Gradient Descent. This allows us to find a distribution of solutions within a single optimization run. Furthermore, we use an off-the-shelf differentiable physics simulator that is parallelized on the GPU to run parallelized inference over diverse plan parameters. We demonstrate our method on a variety of problems and show that it can find multiple diverse plans in a single optimization run while also being significantly faster than existing approaches.
We present VBPI-Mixtures, an algorithm designed to enhance the accuracy of phylogenetic posterior distributions, particularly for tree-topology and branch-length approximations. Despite the Variational Bayesian Phylogenetic Inference (VBPI), a leading-edge black-box variational inference (BBVI) framework, achieving remarkable approximations of these distributions, the multimodality of the tree-topology posterior presents a formidable challenge to sampling-based learning techniques such as BBVI. Advanced deep learning methodologies such as normalizing flows and graph neural networks have been explored to refine the branch-length posterior approximation, yet efforts to ameliorate the posterior approximation over tree topologies have been lacking. Our novel VBPI-Mixtures algorithm bridges this gap by harnessing the latest breakthroughs in mixture learning within the BBVI domain. As a result, VBPI-Mixtures is capable of capturing distributions over tree-topologies that VBPI fails to model. We deliver state-of-the-art performance on difficult density estimation tasks across numerous real phylogenetic datasets.
Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, whose layers perform mean-field variational inference over an MLN. It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations effectively mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over graphs, images, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.
Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method--Reparameterized Variational Rejection Sampling (RVRS)--offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well-suited for black-box inference, especially for models with local latent variables.
What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural criteria. First, when the original diffusion is reversible with invariant measure $\rho_*$, the independent projection serves as the Wasserstein gradient flow for the relative entropy $H(\cdot\,|\,\rho_*)$ constrained to the space of product measures. This is related to recent Langevin-based sampling schemes proposed in the statistical literature on mean field variational inference. In addition, we provide both qualitative and quantitative results on the long-time convergence of the independent projection, with quantitative results in the log-concave case derived via a new variant of the logarithmic Sobolev inequality. Second, among all processes with independent coordinates, the independent projection is shown to exhibit the slowest growth rate of path-space entropy relative to the original diffusion. This sheds new light on the classical McKean-Vlasov equation and recent variants proposed for non-exchangeable systems, which can be viewed as special cases of the independent projection.
We tackle the task of scalable unsupervised object-centric representation learning on 3D scenes. Existing approaches to object-centric representation learning show limitations in generalizing to larger scenes as their learning processes rely on a fixed global coordinate system. In contrast, we propose to learn view-invariant 3D object representations in localized object coordinate systems. To this end, we estimate the object pose and appearance representation separately and explicitly map object representations across views while maintaining object identities. We adopt an amortized variational inference pipeline that can process sequential input and scalably update object latent distributions online. To handle large-scale scenes with a varying number of objects, we further introduce a Cognitive Map that allows the registration and query of objects on a per-scene global map to achieve scalable representation learning. We explore the object-centric neural radiance field (NeRF) as our 3D scene representation, which is jointly modeled within our unsupervised object-centric learning framework. Experimental results on synthetic and real datasets show that our proposed method can infer and maintain object-centric representations of 3D scenes and outperforms previous models.
We release a new Bayesian neural network library for PyTorch for large-scale deep networks. Our library implements mainstream approximate Bayesian inference algorithms: variational inference, MC-dropout, stochastic-gradient MCMC, and Laplace approximation. The main differences from other existing Bayesian neural network libraries are as follows: 1) Our library can deal with very large-scale deep networks including Vision Transformers (ViTs). 2) We need virtually zero code modifications for users (e.g., the backbone network definition codes do not neet to be modified at all). 3) Our library also allows the pre-trained model weights to serve as a prior mean, which is very useful for performing Bayesian inference with the large-scale foundation models like ViTs that are hard to optimise from scratch with the downstream data alone. Our code is publicly available at: \url{https://github.com/SamsungLabs/BayesDLL}\footnote{A mirror repository is also available at: \url{https://github.com/minyoungkim21/BayesDLL}.}.
Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques. We demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to tens of thousands demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming SOTA Gaussian process methods. Furthermore, our method guarantees theoretically controlled prediction error for DGP models and demonstrates remarkable performance on various datasets. We are optimistic that NOVI has the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical applications
Deep learning methods for communications over unknown nonlinear channels have attracted considerable interest recently. In this paper, we consider semi-supervised learning methods, which are based on variational inference, for decoding unknown nonlinear channels. These methods, which include Monte Carlo expectation maximization and a variational autoencoder, make efficient use of few pilot symbols and the payload data. The best semi-supervised learning results are achieved with a variational autoencoder. For sufficiently many payload symbols, the variational autoencoder also has lower error rate compared to meta learning that uses the pilot data of the present as well as previous transmission blocks.
Deep learning's immense capabilities are often constrained by the complexity of its models, leading to an increasing demand for effective sparsification techniques. Bayesian sparsification for deep learning emerges as a crucial approach, facilitating the design of models that are both computationally efficient and competitive in terms of performance across various deep learning applications. The state-of-the-art -- in Bayesian sparsification of deep neural networks -- combines structural shrinkage priors on model weights with an approximate inference scheme based on stochastic variational inference. However, model inversion of the full generative model is exceptionally computationally demanding, especially when compared to standard deep learning of point estimates. In this context, we advocate for the use of Bayesian model reduction (BMR) as a more efficient alternative for pruning of model weights. As a generalization of the Savage-Dickey ratio, BMR allows a post-hoc elimination of redundant model weights based on the posterior estimates under a straightforward (non-hierarchical) generative model. Our comparative study highlights the advantages of the BMR method relative to established approaches based on hierarchical horseshoe priors over model weights. We illustrate the potential of BMR across various deep learning architectures, from classical networks like LeNet to modern frameworks such as Vision Transformers and MLP-Mixers.
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of dimensionality for intrinsically high-dimensional data. This limitation is pronounced in graphical models such as Markov random fields, common for image distributions, where the approximation efficiency of score functions remains unestablished. To address this, we observe score functions can often be well-approximated in graphical models through variational inference denoising algorithms. Furthermore, these algorithms are amenable to efficient neural network representation. We demonstrate this in examples of graphical models, including Ising models, conditional Ising models, restricted Boltzmann machines, and sparse encoding models. Combined with off-the-shelf discretization error bounds for diffusion-based sampling, we provide an efficient sample complexity bound for diffusion-based generative modeling when the score function is learned by deep neural networks.
In this paper, we address the unsupervised speech enhancement problem based on recurrent variational autoencoder (RVAE). This approach offers promising generalization performance over the supervised counterpart. Nevertheless, the involved iterative variational expectation-maximization (VEM) process at test time, which relies on a variational inference method, results in high computational complexity. To tackle this issue, we present efficient sampling techniques based on Langevin dynamics and Metropolis-Hasting algorithms, adapted to the EM-based speech enhancement with RVAE. By directly sampling from the intractable posterior distribution within the EM process, we circumvent the intricacies of variational inference. We conduct a series of experiments, comparing the proposed methods with VEM and a state-of-the-art supervised speech enhancement approach based on diffusion models. The results reveal that our sampling-based algorithms significantly outperform VEM, not only in terms of computational efficiency but also in overall performance. Furthermore, when compared to the supervised baseline, our methods showcase robust generalization performance in mismatched test conditions.
The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the similarities and differences remain mysterious. This paper clarifies their relationship in several ways: via separate descriptions of the two update mechanisms in terms of probabilistic programs and sampling semantics, and via different notions of likelihood (for Pearl and for Jeffrey). Moreover, it is shown that Jeffrey's update rule arises via variational inference. In terms of categorical probability theory, this amounts to an analysis of the situation in terms of the behaviour of the multiset functor, extended to the Kleisli category of the distribution monad.
Topic models have a rich history with various applications and have recently been reinvigorated by neural topic modeling. However, these numerous topic models adopt totally distinct datasets, implementations, and evaluations. This impedes quick utilization and fair comparisons, and thereby hinders their research progress and applications. To tackle this challenge, we in this paper propose a Topic Modeling System Toolkit (TopMost). Compared to existing toolkits, TopMost stands out by supporting more extensive features. It covers a broader spectrum of topic modeling scenarios with their complete lifecycles, including datasets, preprocessing, models, training, and evaluations. Thanks to its highly cohesive and decoupled modular design, TopMost enables rapid utilization, fair comparisons, and flexible extensions of diverse cutting-edge topic models. Our code, tutorials, and documentation are available at https://github.com/bobxwu/topmost.
Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference algorithm that applies to continuous variables, intractable posteriors and large-scale real-time data in sensor networks. In a centralized setting, variational inference is a fundamental technique for performing approximate Bayesian estimation, in which an intractable posterior density is approximated with a parametric density. Our key contribution lies in the derivation of a separable lower bound on the centralized estimation objective, which enables distributed variational inference with one-hop communication in a sensor network. Our distributed evidence lower bound (DELBO) consists of a weighted sum of observation likelihood and divergence to prior densities, and its gap to the measurement evidence is due to consensus and modeling errors. To solve binary classification and regression problems while handling streaming data, we design an online distributed algorithm that maximizes DELBO, and specialize it to Gaussian variational densities with non-linear likelihoods. The resulting distributed Gaussian variational inference (DGVI) efficiently inverts a $1$-rank correction to the covariance matrix. Finally, we derive a diagonalized version for online distributed inference in high-dimensional models, and apply it to multi-robot probabilistic mapping using indoor LiDAR data.
Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors, most methods in Gaussian process (GP) dynamics model learning are trained on one-step ahead predictions. This can become problematic in several scenarios, e.g. if measurements are provided at irregularly-sampled time steps or physical system properties have to be conserved. Thus, we aim for a GP model of the true continuous-time dynamics. Higher-order numerical integrators provide the necessary tools to address this problem by discretizing the dynamics function with arbitrary accuracy. Many higher-order integrators require dynamics evaluations at intermediate time steps making exact GP inference intractable. In previous work, this problem is often tackled by approximating the GP posterior with variational inference. However, exact GP inference is preferable in many scenarios, e.g. due to its mathematical guarantees. In order to make direct inference tractable, we propose to leverage multistep and Taylor integrators. We demonstrate how to derive flexible inference schemes for these types of integrators. Further, we derive tailored sampling schemes that allow to draw consistent dynamics functions from the learned posterior. This is crucial to sample consistent predictions from the dynamics model. We demonstrate empirically and theoretically that our approach yields an accurate representation of the continuous-time system.
Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational complexity due to the high dimensionality of the parameter space. In this work, we propose a novel scheme that addresses this limitation by constructing a low-dimensional subspace of the neural network parameters-referred to as an active subspace-by identifying the parameter directions that have the most significant influence on the output of the neural network. We demonstrate that the significantly reduced active subspace enables effective and scalable Bayesian inference via either Monte Carlo (MC) sampling methods, otherwise computationally intractable, or variational inference. Empirically, our approach provides reliable predictions with robust uncertainty estimates for various regression tasks.
Meta-learning is a framework in which machine learning models train over a set of datasets in order to produce predictions on new datasets at test time. Probabilistic meta-learning has received an abundance of attention from the research community in recent years, but a problem shared by many existing probabilistic meta-models is that they require a very large number of datasets in order to produce high-quality predictions with well-calibrated uncertainty estimates. In many applications, however, such quantities of data are simply not available. In this dissertation we present a significantly more data-efficient approach to probabilistic meta-learning through per-datapoint amortisation of inference in Bayesian neural networks, introducing the Amortised Pseudo-Observation Variational Inference Bayesian Neural Network (APOVI-BNN). First, we show that the approximate posteriors obtained under our amortised scheme are of similar or better quality to those obtained through traditional variational inference, despite the fact that the amortised inference is performed in a single forward pass. We then discuss how the APOVI-BNN may be viewed as a new member of the neural process family, motivating the use of neural process training objectives for potentially better predictive performance on complex problems as a result. Finally, we assess the predictive performance of the APOVI-BNN against other probabilistic meta-models in both a one-dimensional regression problem and in a significantly more complex image completion setting. In both cases, when the amount of training data is limited, our model is the best in its class.
Asynchronous time series, also known as temporal event sequences, are the basis of many applications throughout different industries. Temporal point processes(TPPs) are the standard method for modeling such data. Existing TPP models have focused on parameterizing the conditional distribution of future events instead of explicitly modeling event interactions, imposing challenges for event predictions. In this paper, we propose a novel approach that leverages Neural Relational Inference (NRI) to learn a relation graph that infers interactions while simultaneously learning the dynamics patterns from observational data. Our approach, the Contrastive Relational Inference-based Hawkes Process (CRIHP), reasons about event interactions under a variational inference framework. It utilizes intensity-based learning to search for prototype paths to contrast relationship constraints. Extensive experiments on three real-world datasets demonstrate the effectiveness of our model in capturing event interactions for event sequence modeling tasks. Code will be integrated into the EasyTPP framework.
The Knowledge Tracing (KT) task plays a crucial role in personalized learning, and its purpose is to predict student responses based on their historical practice behavior sequence. However, the KT task suffers from data sparsity, which makes it challenging to learn robust representations for students with few practice records and increases the risk of model overfitting. Therefore, in this paper, we propose a Cognition-Mode Aware Variational Representation Learning Framework (CMVF) that can be directly applied to existing KT methods. Our framework uses a probabilistic model to generate a distribution for each student, accounting for uncertainty in those with limited practice records, and estimate the student's distribution via variational inference (VI). In addition, we also introduce a cognition-mode aware multinomial distribution as prior knowledge that constrains the posterior student distributions learning, so as to ensure that students with similar cognition modes have similar distributions, avoiding overwhelming personalization for students with few practice records. At last, extensive experimental results confirm that CMVF can effectively aid existing KT methods in learning more robust student representations. Our code is available at https://github.com/zmy-9/CMVF.