Recent research tries to extend image restoration capabilities from human perception to machine perception, thereby enhancing the performance of high-level vision tasks in degraded environments. These methods, primarily based on supervised learning, typically involve the retraining of restoration networks or high-level vision networks. However, collecting paired data in real-world scenarios and retraining large-scale models are challenge. To this end, we propose an unsupervised learning method called \textbf{Va}riational \textbf{T}ranslator (VaT), which does not require retraining existing restoration and high-level vision networks. Instead, it establishes a lightweight network that serves as an intermediate bridge between them. By variational inference, VaT approximates the joint distribution of restoration output and high-level vision input, dividing the optimization objective into preserving content and maximizing marginal likelihood associated with high-level vision tasks. By cleverly leveraging self-training paradigms, VaT achieves the above optimization objective without requiring labels. As a result, the translated images maintain a close resemblance to their original content while also demonstrating exceptional performance on high-level vision tasks. Extensive experiments in dehazing and low-light enhancement for detection and classification show the superiority of our method over other state-of-the-art unsupervised counterparts, even significantly surpassing supervised methods in some complex real-world scenarios.Code is available at https://github.com/Fire-friend/VaT.
Weight space symmetries in neural network architectures, such as permutation symmetries in MLPs, give rise to Bayesian neural network (BNN) posteriors with many equivalent modes. This multimodality poses a challenge for variational inference (VI) techniques, which typically rely on approximating the posterior with a unimodal distribution. In this work, we investigate the impact of weight space permutation symmetries on VI. We demonstrate, both theoretically and empirically, that these symmetries lead to biases in the approximate posterior, which degrade predictive performance and posterior fit if not explicitly accounted for. To mitigate this behavior, we leverage the symmetric structure of the posterior and devise a symmetrization mechanism for constructing permutation invariant variational posteriors. We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective with a modified KL regularization term. We demonstrate experimentally that our approach mitigates the aforementioned biases and results in improved predictions and a higher ELBO.
Unexpected stimuli induce "error" or "surprise" signals in the brain. The theory of predictive coding promises to explain these observations in terms of Bayesian inference by suggesting that the cortex implements variational inference in a probabilistic graphical model. However, when applied to machine learning tasks, this family of algorithms has yet to perform on par with other variational approaches in high-dimensional, structured inference problems. To address this, we introduce a novel predictive coding algorithm for structured generative models, that we call divide-and-conquer predictive coding (DCPC). DCPC differs from other formulations of predictive coding, as it respects the correlation structure of the generative model and provably performs maximum-likelihood updates of model parameters, all without sacrificing biological plausibility. Empirically, DCPC achieves better numerical performance than competing algorithms and provides accurate inference in a number of problems not previously addressed with predictive coding. We provide an open implementation of DCPC in Pyro on Github.
The gamma belief network (GBN), often regarded as a deep topic model, has demonstrated its potential for uncovering multi-layer interpretable latent representations in text data. Its notable capability to acquire interpretable latent factors is partially attributed to sparse and non-negative gamma-distributed latent variables. However, the existing GBN and its variations are constrained by the linear generative model, thereby limiting their expressiveness and applicability. To address this limitation, we introduce the generalized gamma belief network (Generalized GBN) in this paper, which extends the original linear generative model to a more expressive non-linear generative model. Since the parameters of the Generalized GBN no longer possess an analytic conditional posterior, we further propose an upward-downward Weibull inference network to approximate the posterior distribution of the latent variables. The parameters of both the generative model and the inference network are jointly trained within the variational inference framework. Finally, we conduct comprehensive experiments on both expressivity and disentangled representation learning tasks to evaluate the performance of the Generalized GBN against state-of-the-art Gaussian variational autoencoders serving as baselines.
The spatial context of single-cell gene expression data is crucial for many downstream analyses, yet often remains inaccessible due to practical and technical limitations, restricting the utility of such datasets. In this paper, we propose a generic representation learning and transfer learning framework dp-VAE, capable of reconstructing the spatial coordinates associated with the provided gene expression data. Central to our approach is a distance-preserving regularizer integrated into the loss function during training, ensuring the model effectively captures and utilizes spatial context signals from reference datasets. During the inference stage, the produced latent representation of the model can be used to reconstruct or impute the spatial context of the provided gene expression by solving a constrained optimization problem. We also explore the theoretical connections between distance-preserving loss, distortion, and the bi-Lipschitz condition within generative models. Finally, we demonstrate the effectiveness of dp-VAE in different tasks involving training robustness, out-of-sample evaluation, and transfer learning inference applications by testing it over 27 publicly available datasets. This underscores its applicability to a wide range of genomics studies that were previously hindered by the absence of spatial data.
We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R\'enyi's $\alpha$-divergence to learn complex operators while quantifying uncertainty. By incorporating Bayesian neural networks as the building blocks for the branch and trunk networks, our framework endows DeepONet with uncertainty quantification. The use of R\'enyi's $\alpha$-divergence, instead of the Kullback-Leibler divergence (KLD), commonly used in standard variational inference, mitigates issues related to prior misspecification that are prevalent in Variational Bayesian DeepONets. This approach offers enhanced flexibility and robustness. We demonstrate that modifying the variational objective function yields superior results in terms of minimising the mean squared error and improving the negative log-likelihood on the test set. Our framework's efficacy is validated across various mechanical systems, where it outperforms both deterministic and standard KLD-based VI DeepONets in predictive accuracy and uncertainty quantification. The hyperparameter $\alpha$, which controls the degree of robustness, can be tuned to optimise performance for specific problems. We apply this approach to a range of mechanics problems, including gravity pendulum, advection-diffusion, and diffusion-reaction systems. Our findings underscore the potential of $\alpha$-VI DeepONet to advance the field of data-driven operator learning and its applications in engineering and scientific domains.
Graph Neural Networks (GNNs)-based recommendation algorithms typically assume that training and testing data are drawn from independent and identically distributed (IID) spaces. However, this assumption often fails in the presence of out-of-distribution (OOD) data, resulting in significant performance degradation. In this study, we construct a Structural Causal Model (SCM) to analyze interaction data, revealing that environmental confounders (e.g., the COVID-19 pandemic) lead to unstable correlations in GNN-based models, thus impairing their generalization to OOD data. To address this issue, we propose a novel approach, graph representation learning via causal diffusion (CausalDiffRec) for OOD recommendation. This method enhances the model's generalization on OOD data by eliminating environmental confounding factors and learning invariant graph representations. Specifically, we use backdoor adjustment and variational inference to infer the real environmental distribution, thereby eliminating the impact of environmental confounders. This inferred distribution is then used as prior knowledge to guide the representation learning in the reverse phase of the diffusion process to learn the invariant representation. In addition, we provide a theoretical derivation that proves optimizing the objective function of CausalDiffRec can encourage the model to learn environment-invariant graph representations, thereby achieving excellent generalization performance in recommendations under distribution shifts. Our extensive experiments validate the effectiveness of CausalDiffRec in improving the generalization of OOD data, and the average improvement is up to 10.69% on Food, 18.83% on KuaiRec, 22.41% on Yelp2018, and 11.65% on Douban datasets.
In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real measurements with virtual observations derived from the physical model. In particular, weighted residuals are employed as probes to the governing PDE in order to formulate and solve a Bayesian inverse problem without ever formulating nor solving a forward model. The formulation treats the state variables of the physical model as latent variables, inferred using Stochastic Variational Inference (SVI), along with the usual unknowns. The approximate posterior employed uses neural networks to approximate the inverse mapping from state variables to the unknowns. We illustrate the proposed method in a biomedical setting where we infer spatially varying material properties from noisy tissue deformation data. We demonstrate that WNVI is not only as accurate and more efficient than traditional methods that rely on repeatedly solving the (non)linear forward problem as a black-box, but it can also handle ill-posed forward problems (e.g., with insufficient boundary conditions).
A new gradient-based particle sampling method, MPM-ParVI, based on material point method (MPM), is proposed for variational inference. MPM-ParVI simulates the deformation of a deformable body (e.g. a solid or fluid) under external effects driven by the target density; transient or steady configuration of the deformable body approximates the target density. The continuum material is modelled as an interacting particle system (IPS) using MPM, each particle carries full physical properties, interacts and evolves following conservation dynamics. This easy-to-implement ParVI method offers deterministic sampling and inference for a class of probabilistic models such as those encountered in Bayesian inference (e.g. intractable densities) and generative modelling (e.g. score-based).
Random noise attenuation (NA) is a key step in seismic field data processing. With the rise of artificial intelligence, deep learning (DL) algorithms are gradually introduced into seismic random noise suppression. The most commonly used DL paradigm takes mean squared error (MSE) as loss function, the default assumption is that its error term obeys independently identically distribution (IID) Gaussian, and its noise level involved preset-hyperparameters in the local area of data cannot be adjusted adaptively in the training phase. This leads to the poor generalization of deep denoiser on Non-IID noises. In this study, we propose a DL framework based on Non-IID pixel-wise Gaussian noise modeling, which integrates NA and noise level estimation into a unique Bayesian framework. The framework can adaptively characterize the noise and data distribution in the local area of noisy data through the variational inference (VI) technique, which allows the network to see more noises of varying degrees and learn effective information from them. Thus, our proposed framework called VI-Non-IID inclines to have better noise characterization and generalization capabilities, which brings better performance on seismic field NA. Furthermore, we conduct a series of experiments on seismic synthetic and field data to test the performance of two implementations of VI-NonIID: VI-Non-IID (Unet) and VI-Non-IID denoising convolution network (DnCNN). A lot of results validate the superiority of our proposed VI-Non-IID framework. Specifically, VI-Non-IID can explicitly predict the denoised data and its corresponding noise level map simultaneously, and succeed in attenuating unknown field noises while preserving the useful seismic signals.
Feature grid Scene Representation Networks (SRNs) have been applied to scientific data as compact functional surrogates for analysis and visualization. As SRNs are black-box lossy data representations, assessing the prediction quality is critical for scientific visualization applications to ensure that scientists can trust the information being visualized. Currently, existing architectures do not support inference time reconstruction quality assessment, as coordinate-level errors cannot be evaluated in the absence of ground truth data. We propose a parameter-efficient multi-decoder SRN (MDSRN) ensemble architecture consisting of a shared feature grid with multiple lightweight multi-layer perceptron decoders. MDSRN can generate a set of plausible predictions for a given input coordinate to compute the mean as the prediction of the multi-decoder ensemble and the variance as a confidence score. The coordinate-level variance can be rendered along with the data to inform the reconstruction quality, or be integrated into uncertainty-aware volume visualization algorithms. To prevent the misalignment between the quantified variance and the prediction quality, we propose a novel variance regularization loss for ensemble learning that promotes the Regularized multi-decoder SRN (RMDSRN) to obtain a more reliable variance that correlates closely to the true model error. We comprehensively evaluate the quality of variance quantification and data reconstruction of Monte Carlo Dropout, Mean Field Variational Inference, Deep Ensemble, and Predicting Variance compared to the proposed MDSRN and RMDSRN across diverse scalar field datasets. We demonstrate that RMDSRN attains the most accurate data reconstruction and competitive variance-error correlation among uncertain SRNs under the same neural network parameter budgets.
We propose a variational inference approach to sample from the posterior distribution for solving inverse problems. From a pre-trained diffusion model, our approach trains a conditional flow model to minimize the divergence between the proposal variational distribution and the posterior distribution implicitly defined through the diffusion model. Once trained, the flow model is capable of sampling from the posterior distribution with a single NFE, amortized with respect to the measurement. The proposed method paves a new path for distilling a diffusion prior for efficient posterior sampling. We show that our method is applicable to standard signals in Euclidean space, as well as signals on manifold.
This paper explores a federated learning approach that automatically selects the number of latent processes in multi-output Gaussian processes (MGPs). The MGP has seen great success as a transfer learning tool when data is generated from multiple sources/units/entities. A common approach in MGPs to transfer knowledge across units involves gathering all data from each unit to a central server and extracting common independent latent processes to express each unit as a linear combination of the shared latent patterns. However, this approach poses key challenges in (i) determining the adequate number of latent processes and (ii) relying on centralized learning which leads to potential privacy risks and significant computational burdens on the central server. To address these issues, we propose a hierarchical model that places spike-and-slab priors on the coefficients of each latent process. These priors help automatically select only needed latent processes by shrinking the coefficients of unnecessary ones to zero. To estimate the model while avoiding the drawbacks of centralized learning, we propose a variational inference-based approach, that formulates model inference as an optimization problem compatible with federated settings. We then design a federated learning algorithm that allows units to jointly select and infer the common latent processes without sharing their data. We also discuss an efficient learning approach for a new unit within our proposed federated framework. Simulation and case studies on Li-ion battery degradation and air temperature data demonstrate the advantageous features of our proposed approach.
Humans and many animals show remarkably adaptive behavior and can respond differently to the same input depending on their internal goals. The brain not only represents the intermediate abstractions needed to perform a computation but also actively maintains a representation of the computation itself (task abstraction). Such separation of the computation and its abstraction is associated with faster learning, flexible decision-making, and broad generalization capacity. We investigate if such benefits might extend to neural networks trained with task abstractions. For such benefits to emerge, one needs a task inference mechanism that possesses two crucial abilities: First, the ability to infer abstract task representations when no longer explicitly provided (task inference), and second, manipulate task representations to adapt to novel problems (task recomposition). To tackle this, we cast task inference as an optimization problem from a variational inference perspective and ground our approach in an expectation-maximization framework. We show that gradients backpropagated through a neural network to a task representation layer are an efficient heuristic to infer current task demands, a process we refer to as gradient-based inference (GBI). Further iterative optimization of the task representation layer allows for recomposing abstractions to adapt to novel situations. Using a toy example, a novel image classifier, and a language model, we demonstrate that GBI provides higher learning efficiency and generalization to novel tasks and limits forgetting. Moreover, we show that GBI has unique advantages such as preserving information for uncertainty estimation and detecting out-of-distribution samples.
Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to reduce computational complexity and improve model efficiency. However, inferring the posterior distribution of inducing points is not straightforward. Traditional variational inference approaches to posterior approximation often lead to significant bias. To address this issue, we propose an alternative method called Denoising Diffusion Variational Inference (DDVI) that uses a denoising diffusion stochastic differential equation (SDE) to generate posterior samples of inducing variables. We rely on score matching methods for denoising diffusion model to approximate score functions with a neural network. Furthermore, by combining classical mathematical theory of SDEs with the minimization of KL divergence between the approximate and true processes, we propose a novel explicit variational lower bound for the marginal likelihood function of DGP. Through experiments on various datasets and comparisons with baseline methods, we empirically demonstrate the effectiveness of DDVI for posterior inference of inducing points for DGP models.
We introduce neural information field filter, a Bayesian state and parameter estimation method for high-dimensional nonlinear dynamical systems given large measurement datasets. Solving such a problem using traditional methods, such as Kalman and particle filters, is computationally expensive. Information field theory is a Bayesian approach that can efficiently reconstruct dynamical model state paths and calibrate model parameters from noisy measurement data. To apply the method, we parameterize the time evolution state path using the span of a finite linear basis. The existing method has to reparameterize the state path by initial states to satisfy the initial condition. Designing an expressive yet simple linear basis before knowing the true state path is crucial for inference accuracy but challenging. Moreover, reparameterizing the state path using the initial state is easy to perform for a linear basis, but is nontrivial for more complex and expressive function parameterizations, such as neural networks. The objective of this paper is to simplify and enrich the class of state path parameterizations using neural networks for the information field theory approach. To this end, we propose a generalized physics-informed conditional prior using an auxiliary initial state. We show the existing reparameterization is a special case. We parameterize the state path using a residual neural network that consists of a linear basis function and a Fourier encoding fully connected neural network residual function. The residual function aims to correct the error of the linear basis function. To sample from the intractable posterior distribution, we develop an optimization algorithm, nested stochastic variational inference, and a sampling algorithm, nested preconditioned stochastic gradient Langevin dynamics. A series of numerical and experimental examples verify and validate the proposed method.
Are score function estimators an underestimated approach to learning with $k$-subset sampling? Sampling $k$-subsets is a fundamental operation in many machine learning tasks that is not amenable to differentiable parametrization, impeding gradient-based optimization. Prior work has focused on relaxed sampling or pathwise gradient estimators. Inspired by the success of score function estimators in variational inference and reinforcement learning, we revisit them within the context of $k$-subset sampling. Specifically, we demonstrate how to efficiently compute the $k$-subset distribution's score function using a discrete Fourier transform, and reduce the estimator's variance with control variates. The resulting estimator provides both exact samples and unbiased gradient estimates while also applying to non-differentiable downstream models, unlike existing methods. Experiments in feature selection show results competitive with current methods, despite weaker assumptions.
Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4$\times$ super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.
Estimating a distribution given access to its unnormalized density is pivotal in Bayesian inference, where the posterior is generally known only up to an unknown normalizing constant. Variational inference and Markov chain Monte Carlo methods are the predominant tools for this task; however, both are often challenging to apply reliably, particularly when the posterior has complex geometry. Here, we introduce Soft Contrastive Variational Inference (SoftCVI), which allows a family of variational objectives to be derived through a contrastive estimation framework. The approach parameterizes a classifier in terms of a variational distribution, reframing the inference task as a contrastive estimation problem aiming to identify a single true posterior sample among a set of samples. Despite this framing, we do not require positive or negative samples, but rather learn by sampling the variational distribution and computing ground truth soft classification labels from the unnormalized posterior itself. The objectives have zero variance gradient when the variational approximation is exact, without the need for specialized gradient estimators. We empirically investigate the performance on a variety of Bayesian inference tasks, using both simple (e.g. normal) and expressive (normalizing flow) variational distributions. We find that SoftCVI can be used to form objectives which are stable to train and mass-covering, frequently outperforming inference with other variational approaches.
This work proposes a variational inference (VI) framework for hyperspectral unmixing in the presence of endmember variability (HU-EV). An EV-accounted noisy linear mixture model (LMM) is considered, and the presence of outliers is also incorporated into the model. Following the marginalized maximum likelihood (MML) principle, a VI algorithmic structure is designed for probabilistic inference for HU-EV. Specifically, a patch-wise static endmember assumption is employed to exploit spatial smoothness and to try to overcome the ill-posed nature of the HU-EV problem. The design facilitates lightweight, continuous optimization-based updates under a variety of endmember priors. Some of the priors, such as the Beta prior, were previously used under computationally heavy, sampling-based probabilistic HU-EV methods. The effectiveness of the proposed framework is demonstrated through synthetic, semi-real, and real-data experiments.