We aim for source-free domain adaptation, where the task is to deploy a model pre-trained on source domains to target domains. The challenges stem from the distribution shift from the source to the target domain, coupled with the unavailability of any source data and labeled target data for optimization. Rather than fine-tuning the model by updating the parameters, we propose to perturb the source model to achieve adaptation to target domains. We introduce perturbations into the model parameters by variational Bayesian inference in a probabilistic framework. By doing so, we can effectively adapt the model to the target domain while largely preserving the discriminative ability. Importantly, we demonstrate the theoretical connection to learning Bayesian neural networks, which proves the generalizability of the perturbed model to target domains. To enable more efficient optimization, we further employ a parameter sharing strategy, which substantially reduces the learnable parameters compared to a fully Bayesian neural network. Our model perturbation provides a new probabilistic way for domain adaptation which enables efficient adaptation to target domains while maximally preserving knowledge in source models. Experiments on several source-free benchmarks under three different evaluation settings verify the effectiveness of the proposed variational model perturbation for source-free domain adaptation.
Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically intractable trajectories which result in likelihoods and posterior distributions that are similarly intractable. Bayesian inference for ODE systems via simulation methods require numerical approximations to produce inference with high accuracy at a cost of heavy computational power and slow convergence. At the same time, Artificial Neural Networks (ANN) offer tractability that can be utilized to construct an approximate but tractable likelihood and posterior distribution. In this paper we propose a hybrid approach, where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories as a function of the unknown initial values and system parameters. Suitable choices of a collocation grid and customized loss functions are proposed to fine tune the ODE trajectories and Laplace approximation. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions, the Susceptible-Infectious-Removed (SIR) model for infectious diseases, based on simulated and real-life influenza datasets. The novelty and attractiveness of our proposed approach include (i) a new development of Bayesian inference using ANN architectures for ODE based dynamical systems, and (ii) a computationally fast posterior inference by avoiding convergence issues of benchmark Markov Chain Monte Carlo methods. These two features establish the developed approach as an accurate alternative to traditional Bayesian computational methods, with improved computational cost.
Markov Chain Monte Carlo (MCMC) algorithms do not scale well for large datasets leading to difficulties in Neural Network posterior sampling. In this paper, we propose Penalty Bayesian Neural Networks - PBNNs, as a new algorithm that allows the evaluation of the likelihood using subsampled batch data (mini-batches) in a Bayesian inference context towards addressing scalability. PBNN avoids the biases inherent in other naive subsampling techniques by incorporating a penalty term as part of a generalization of the Metropolis Hastings algorithm. We show that it is straightforward to integrate PBNN with existing MCMC frameworks, as the variance of the loss function merely reduces the acceptance probability. By comparing with alternative sampling strategies on both synthetic data and the MNIST dataset, we demonstrate that PBNN achieves good predictive performance even for small mini-batch sizes of data. We show that PBNN provides a novel approach for calibrating the predictive distribution by varying the mini-batch size, significantly reducing predictive overconfidence.
We consider Bayesian inference from multiple time series described by a common state-space model (SSM) structure, but where different subsets of parameters are shared between different submodels. An important example is disease-dynamics, where parameters can be either disease or location specific. Parameter inference in these models can be improved by systematically aggregating information from the different time series, most notably for short series. Particle Gibbs (PG) samplers are an efficient class of algorithms for inference in SSMs, in particular when conjugacy can be exploited to marginalize out model parameters from the state update. We present two different PG samplers that marginalize static model parameters on-the-fly: one that updates one model at a time conditioned on the datasets for the other models, and one that concurrently updates all models by stacking them into a high-dimensional SSM. The distinctive features of each sampler make them suitable for different modelling contexts. We provide insights on when each sampler should be used and show that they can be combined to form an efficient PG sampler for a model with strong dependencies between states and parameters. The performance is illustrated on two linear-Gaussian examples and on a real-world example on the spread of mosquito-borne diseases.
In drug discovery, aqueous solubility is an important pharmacokinetic property which affects absorption and assay availability of drug. Thus, in silico prediction of solubility has been studied for its utility in virtual screening and lead optimization. Recently, machine learning (ML) methods using experimental data has been popular because physics-based methods like quantum mechanics and molecular dynamics are not suitable for high-throughput tasks due to its computational costs. However, ML method can exhibit over-fitting problem in a data-deficient condition, and this is the case for most chemical property datasets. In addition, ML methods are regarded as a black box function in that it is difficult to interpret contribution of hidden features to outputs, hindering analysis and modification of structure-activity relationship. To deal with mentioned issues, we developed Bayesian graph neural networks (GNNs) with the self-attention readout layer. Unlike most GNNs using self-attention in node updates, self-attention applied at readout layer enabled a model to improve prediction performance as well as to identify atom-wise importance, which can help lead optimization as exemplified for three FDA-approved drugs. Also, Bayesian inference enables us to separate more or less accurate results according to uncertainty in solubility prediction task We expect that our accurate, reliable and interpretable model can be used for more careful decision-making and various applications in the development of drugs.
A Bayesian pseudocoreset is a small synthetic dataset for which the posterior over parameters approximates that of the original dataset. While promising, the scalability of Bayesian pseudocoresets is not yet validated in realistic problems such as image classification with deep neural networks. On the other hand, dataset distillation methods similarly construct a small dataset such that the optimization using the synthetic dataset converges to a solution with performance competitive with optimization using full data. Although dataset distillation has been empirically verified in large-scale settings, the framework is restricted to point estimates, and their adaptation to Bayesian inference has not been explored. This paper casts two representative dataset distillation algorithms as approximations to methods for constructing pseudocoresets by minimizing specific divergence measures: reverse KL divergence and Wasserstein distance. Furthermore, we provide a unifying view of such divergence measures in Bayesian pseudocoreset construction. Finally, we propose a novel Bayesian pseudocoreset algorithm based on minimizing forward KL divergence. Our empirical results demonstrate that the pseudocoresets constructed from these methods reflect the true posterior even in high-dimensional Bayesian inference problems.
Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 outputs x 50k datapoints), with ResNet-50 on Imagenet (50M parameters, 1000 outputs x 1.2M datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output~dimensions).
In this paper, we investigate signal detection in multiple-input-multiple-output (MIMO) communication systems with hardware impairments, such as power amplifier nonlinearity and in-phase/quadrature imbalance. To deal with the complex combined effects of hardware imperfections, neural network (NN) techniques, in particular deep neural networks (DNNs), have been studied to directly compensate for the impact of hardware impairments. However, it is difficult to train a DNN with limited pilot signals, hindering its practical applications. In this work, we investigate how to achieve efficient Bayesian signal detection in MIMO systems with hardware imperfections. Characterizing combined hardware imperfections often leads to complicated signal models, making Bayesian signal detection challenging. To address this issue, we first train an NN to "model" the MIMO system with hardware imperfections and then perform Bayesian inference based on the trained NN. Modelling the MIMO system with NN enables the design of NN architectures based on the signal flow of the MIMO system, minimizing the number of NN layers and parameters, which is crucial to achieving efficient training with limited pilot signals. We then represent the trained NN with a factor graph, and design an efficient message passing based Bayesian signal detector, leveraging the unitary approximate message passing (UAMP) algorithm. The implementation of a turbo receiver with the proposed Bayesian detector is also investigated. Extensive simulation results demonstrate that the proposed technique delivers remarkably better performance than state-of-the-art methods.
We introduce Sequential Neural Posterior Score Estimation (SNPSE), a score-based method for Bayesian inference in simulator-based models. Our method, inspired by the remarkable success of score-based methods in generative modelling, leverages conditional score-based diffusion models to generate samples from the posterior distribution of interest. The model is trained using an objective function which directly estimates the score of the posterior. We embed the model into a sequential training procedure, which guides simulations using the current approximation of the posterior at the observation of interest, thereby reducing the simulation cost. We also introduce several alternative sequential approaches, and discuss their relative merits. We then validate our method, as well as its amortised, non-sequential, variant on several numerical examples, demonstrating comparable or superior performance to existing state-of-the-art methods such as Sequential Neural Posterior Estimation (SNPE).
Robust machine learning models with accurately calibrated uncertainties are crucial for safety-critical applications. Probabilistic machine learning and especially the Bayesian formalism provide a systematic framework to incorporate robustness through the distributional estimates and reason about uncertainty. Recent works have shown that approximate inference approaches that take the weight space uncertainty of neural networks to generate ensemble prediction are the state-of-the-art. However, architecture choices have mostly been ad hoc, which essentially ignores the epistemic uncertainty from the architecture space. To this end, we propose a Unified probabilistic architecture and weight ensembling Neural Architecture Search (UraeNAS) that leverages advances in probabilistic neural architecture search and approximate Bayesian inference to generate ensembles form the joint distribution of neural network architectures and weights. The proposed approach showed a significant improvement both with in-distribution (0.86% in accuracy, 42% in ECE) CIFAR-10 and out-of-distribution (2.43% in accuracy, 30% in ECE) CIFAR-10-C compared to the baseline deterministic approach.
The accuracy of moving horizon estimation (MHE) suffers significantly in the presence of measurement outliers. Existing methods address this issue by treating measurements leading to large MHE cost function values as outliers, which are subsequently discarded. This strategy, achieved through solving combinatorial optimization problems, is confined to linear systems to guarantee computational tractability and stability. Contrasting these heuristic solutions, our work reexamines MHE from a Bayesian perspective, unveils the fundamental issue of its lack of robustness: MHE's sensitivity to outliers results from its reliance on the Kullback-Leibler (KL) divergence, where both outliers and inliers are equally considered. To tackle this problem, we propose a robust Bayesian inference framework for MHE, integrating a robust divergence measure to reduce the impact of outliers. In particular, the proposed approach prioritizes the fitting of uncontaminated data and lowers the weight of contaminated ones, instead of directly discarding all potentially contaminated measurements, which may lead to undesirable removal of uncontaminated data. A tuning parameter is incorporated into the framework to adjust the robustness degree to outliers. Notably, the classical MHE can be interpreted as a special case of the proposed approach as the parameter converges to zero. In addition, our method involves only minor modification to the classical MHE stage cost, thus avoiding the high computational complexity associated with previous outlier-robust methods and inherently suitable for nonlinear systems. Most importantly, our method provides robustness and stability guarantees, which are often missing in other outlier-robust Bayes filters. The effectiveness of the proposed method is demonstrated on simulations subject to outliers following different distributions, as well as on physical experiment data.
Meta-learning or learning to learn is a popular approach for learning new tasks with limited data (i.e., few-shot learning) by leveraging the commonalities among different tasks. However, meta-learned models can perform poorly when context data is limited, or when data is drawn from an out-of-distribution (OoD) task. Especially in safety-critical settings, this necessitates an uncertainty-aware approach to meta-learning. In addition, the often multimodal nature of task distributions can pose unique challenges to meta-learning methods. In this work, we present UnLiMiTD (uncertainty-aware meta-learning for multimodal task distributions), a novel method for meta-learning that (1) makes probabilistic predictions on in-distribution tasks efficiently, (2) is capable of detecting OoD context data at test time, and (3) performs on heterogeneous, multimodal task distributions. To achieve this goal, we take a probabilistic perspective and train a parametric, tuneable distribution over tasks on the meta-dataset. We construct this distribution by performing Bayesian inference on a linearized neural network, leveraging Gaussian process theory. We demonstrate that UnLiMiTD's predictions compare favorably to, and outperform in most cases, the standard baselines, especially in the low-data regime. Furthermore, we show that UnLiMiTD is effective in detecting data from OoD tasks. Finally, we confirm that both of these findings continue to hold in the multimodal task-distribution setting.
Bayesian interpretations of neural processing require that biological mechanisms represent and operate upon probability distributions in accordance with Bayes' theorem. Many have speculated that synaptic failure constitutes a mechanism of variational, i.e., approximate, Bayesian inference in the brain. Whereas models have previously used synaptic failure to sample over uncertainty in model parameters, we demonstrate that by adapting transmission probabilities to learned network weights, synaptic failure can sample not only over model uncertainty, but complete posterior predictive distributions as well. Our results potentially explain the brain's ability to perform probabilistic searches and to approximate complex integrals. These operations are involved in numerous calculations, including likelihood evaluation and state value estimation for complex planning.
Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a modern imaging technique used in material research to study nanoscale materials. Reconstruction of the parameters of an imaged object imposes an ill-posed inverse problem that is further complicated when only an in-plane GISAXS signal is available. Traditionally used inference algorithms such as Approximate Bayesian Computation (ABC) rely on computationally expensive scattering simulation software, rendering analysis highly time-consuming. We propose a simulation-based framework that combines variational auto-encoders and normalizing flows to estimate the posterior distribution of object parameters given its GISAXS data. We apply the inference pipeline to experimental data and demonstrate that our method reduces the inference cost by orders of magnitude while producing consistent results with ABC.
We derive an upper bound for the expected gain of informed traders in the Glosten-Milgrom model with finite horizon, fully analogous to a generalized second law of thermodynamics. This result extends that obtained by Touzo et al. a couple of years ago. The proof relies on Bayesian inference (exploiting the invariance of the problem under consecutive game sequences) and an interesting entropic inequality. We also provide numerical results both supporting the existence of a characteristic timescale in the model and illustrating the magnitude of gain fluctuations. Other possible extensions are discussed.
We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential $V$ in an ensemble $\{x^i\}_i$ contains implicit information about first or higher order derivatives, which can be made explicit with little computational effort (ensemble-based gradient inference -- EGI). We suggest to use this information for the improvement of established ensemble-based numerical methods for optimization and sampling such as Consensus-based optimization and Langevin-based samplers. Numerical studies indicate that the augmented algorithms are often superior to their gradient-free variants, in particular the augmented methods help the ensembles to escape their initial domain, to explore multimodal, non-Gaussian settings and to speed up the collapse at the end of optimization dynamics.} The code for the numerical examples in this manuscript can be found in the paper's Github repository (https://github.com/MercuryBench/ensemble-based-gradient.git).
In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of features that are representative of the entire set of features, and the selected features also have higher priority than others. This approach is commonly used for low-rank approximation, feature selection, and extracting hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Gibbs sampling for Bayesian inference is applied to carry out the optimization. We evaluate the proposed models on real-world datasets, including ten Chinese A-share stocks, and demonstrate that the proposed Bayesian ID algorithm with intervention (IID) produces comparable reconstructive errors to existing Bayesian ID algorithms while selecting features with higher scores or priority.
Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of this proposal is key for achieving a high performance. In adaptive IS (AIS) methods, a set of proposals is iteratively improved. AIS is a relevant and timely methodology although many limitations remain yet to be overcome, e.g., the curse of dimensionality in high-dimensional and multi-modal problems. Moreover, the Hamiltonian Monte Carlo (HMC) algorithm has become increasingly popular in machine learning and statistics. HMC has several appealing features such as its exploratory behavior, especially in high-dimensional targets, when other methods suffer. In this paper, we introduce the novel Hamiltonian adaptive importance sampling (HAIS) method. HAIS implements a two-step adaptive process with parallel HMC chains that cooperate at each iteration. The proposed HAIS efficiently adapts a population of proposals, extracting the advantages of HMC. HAIS can be understood as a particular instance of the generic layered AIS family with an additional resampling step. HAIS achieves a significant performance improvement in high-dimensional problems w.r.t. state-of-the-art algorithms. We discuss the statistical properties of HAIS and show its high performance in two challenging examples.
Robotic perception is currently at a cross-roads between modern methods, which operate in an efficient latent space, and classical methods, which are mathematically founded and provide interpretable, trustworthy results. In this paper, we introduce a Convolutional Bayesian Kernel Inference (ConvBKI) layer which learns to perform explicit Bayesian inference within a depthwise separable convolution layer to maximize efficency while maintaining reliability simultaneously. We apply our layer to the task of real-time 3D semantic mapping, where we learn semantic-geometric probability distributions for LiDAR sensor information and incorporate semantic predictions into a global map. We evaluate our network against state-of-the-art semantic mapping algorithms on the KITTI data set, demonstrating improved latency with comparable semantic label inference results.
Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.