Multi-modality image fusion aims to combine different modalities to produce fused images that retain the complementary features of each modality, such as functional highlights and texture details. To leverage strong generative priors and address challenges such as unstable training and lack of interpretability for GAN-based generative methods, we propose a novel fusion algorithm based on the denoising diffusion probabilistic model (DDPM). The fusion task is formulated as a conditional generation problem under the DDPM sampling framework, which is further divided into an unconditional generation subproblem and a maximum likelihood subproblem. The latter is modeled in a hierarchical Bayesian manner with latent variables and inferred by the expectation-maximization (EM) algorithm. By integrating the inference solution into the diffusion sampling iteration, our method can generate high-quality fused images with natural image generative priors and cross-modality information from source images. Note that all we required is an unconditional pre-trained generative model, and no fine-tuning is needed. Our extensive experiments indicate that our approach yields promising fusion results in infrared-visible image fusion and medical image fusion. The code is available at https://github.com/Zhaozixiang1228/MMIF-DDFM.
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Foundational image-language models have generated considerable interest due to their efficient adaptation to downstream tasks by prompt learning. Prompt learning treats part of the language model input as trainable while freezing the rest, and optimizes an Empirical Risk Minimization objective. However, Empirical Risk Minimization is known to suffer from distributional shifts which hurt generalizability to prompts unseen during training. By leveraging the regularization ability of Bayesian methods, we frame prompt learning from the Bayesian perspective and formulate it as a variational inference problem. Our approach regularizes the prompt space, reduces overfitting to the seen prompts and improves the prompt generalization on unseen prompts. Our framework is implemented by modeling the input prompt space in a probabilistic manner, as an a priori distribution which makes our proposal compatible with prompt learning approaches that are unconditional or conditional on the image. We demonstrate empirically on 15 benchmarks that Bayesian prompt learning provides an appropriate coverage of the prompt space, prevents learning spurious features, and exploits transferable invariant features. This results in better generalization of unseen prompts, even across different datasets and domains. Code available at: https://github.com/saic-fi/Bayesian Prompt-Learning
Score Priors Guided Deep Variational Inference for Unsupervised Real-World Single Image Denoising
PDF ↗Real-world single image denoising is crucial and practical in computer vision. Bayesian inversions combined with score priors now have proven effective for single image denoising but are limited to white Gaussian noise. Moreover, applying existing score-based methods for real-world denoising requires not only the explicit train of score priors on the target domain but also the careful design of sampling procedures for posterior inference, which is complicated and impractical. To address these limitations, we propose a score priors-guided deep variational inference, namely ScoreDVI, for practical real-world denoising. By considering the deep variational image posterior with a Gaussian form, score priors are extracted based on easily accessible minimum MSE Non-i.i.d Gaussian denoisers and variational samples, which in turn facilitate optimizing the variational image posterior. Such a procedure adaptively applies cheap score priors to denoising. Additionally, we exploit a Non-i.i.d Gaussian mixture model and variational noise posterior to model the real-world noise. This scheme also enables the pixel-wise fusion of multiple image priors and variational image posteriors. Besides, we develop a noise-aware prior assignment strategy that dynamically adjusts the weight of image priors in the optimization. Our method outperforms other single image-based real-world denoising methods and achieves comparable performance to dataset-based unsupervised methods.
Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical heuristics or simplifying assumptions. Utilizing insights from the development of scalable Bayesian posterior samplers, we present a complete recipe for formulating forward processes in SGMs, ensuring convergence to the desired target distribution. Our approach reveals that several existing SGMs can be seen as specific manifestations of our framework. Building upon this method, we introduce Phase Space Langevin Diffusion (PSLD), which relies on score-based modeling within an augmented space enriched by auxiliary variables akin to physical phase space. Empirical results exhibit the superior sample quality and improved speed-quality trade-off of PSLD compared to various competing approaches on established image synthesis benchmarks. Remarkably, PSLD achieves sample quality akin to state-of-the-art SGMs (FID: 2.10 for unconditional CIFAR-10 generation). Lastly, we demonstrate the applicability of PSLD in conditional synthesis using pre-trained score networks, offering an appealing alternative as an SGM backbone for future advancements. Code and model checkpoints can be accessed at https://github.com/mandt-lab/PSLD.
Prompt tuning, in which prompts are optimized to adapt large-scale pre-trained language models to downstream tasks instead of fine-tuning the full model parameters, has been shown to be particularly effective when the prompts are trained in the multi-task transfer learning setting. These methods generally involve individually training prompts for each source task and then aggregating them to provide the initialization of the prompt for the target task. However, this approach critically ignores the fact that some of the source tasks could be negatively or positively interfering with each other. We argue that when we extract knowledge from source tasks via training source prompts, we need to consider this correlation among source tasks for better transfer to target tasks. To this end, we propose a Bayesian approach where we work with the posterior distribution of prompts across source tasks. We obtain representative source prompts corresponding to the samples from the posterior utilizing Stein Variational Gradient Descent, which are then aggregated to constitute the initial target prompt. We show extensive experimental results on the standard benchmark NLP tasks, where our Bayesian multi-task transfer learning approach outperforms the state-of-the-art methods in many settings. Furthermore, our approach requires no auxiliary models other than the prompt itself, achieving high degree of parameter-efficiency.
The Interpreter Understands Your Meaning: End-to-end Spoken Language Understanding Aided by Speech Translation
PDF ↗End-to-end spoken language understanding (SLU) remains elusive even with current large pretrained language models on text and speech, especially in multilingual cases. Machine translation has been established as a powerful pretraining objective on text as it enables the model to capture high-level semantics of the input utterance and associations between different languages, which is desired for speech models that work on lower-level acoustic frames. Motivated particularly by the task of cross-lingual SLU, we demonstrate that the task of speech translation (ST) is a good means of pretraining speech models for end-to-end SLU on both intra- and cross-lingual scenarios. By introducing ST, our models reach higher performance over baselines on monolingual and multilingual intent classification as well as spoken question answering using SLURP, MINDS-14, and NMSQA benchmarks. To verify the effectiveness of our methods, we also create new benchmark datasets from both synthetic and real sources, for speech summarization and low-resource/zero-shot transfer from English to French or Spanish. We further show the value of preserving knowledge for the ST pretraining task for better downstream performance, possibly using Bayesian transfer regularizers.
Hallucination Detection for Generative Large Language Models by Bayesian Sequential Estimation
PDF ↗Large Language Models (LLMs) have made remarkable advancements in the field of natural language generation. However, the propensity of LLMs to generate inaccurate or non-factual content, termed “hallucinations”, remains a significant challenge. Current hallucination detection methods often necessitate the retrieval of great numbers of relevant evidence, thereby increasing response times. We introduce a unique framework that leverages statistical decision theory and Bayesian sequential analysis to optimize the trade-off between costs and benefits during the hallucination detection process. This approach does not require a predetermined number of observations. Instead, the analysis proceeds in a sequential manner, enabling an expeditious decision towards “belief” or “disbelief” through a stop-or-continue strategy. Extensive experiments reveal that this novel framework surpasses existing methods in both efficiency and precision of hallucination detection. Furthermore, it requires fewer retrieval steps on average, thus decreasing response times.
Deep Learning/Other Representation Learning
Recent research indicates that the performance of machine learning models can be improved by aligning the geometry of the latent space with the underlying data structure. Rather than relying solely on Euclidean space, researchers have proposed using hyperbolic and spherical spaces with constant curvature, or combinations thereof, to better model the latent space and enhance model performance. However, little attention has been given to the problem of automatically identifying the optimal latent geometry for the downstream task. We mathematically define this novel formulation and coin it as neural latent geometry search (NLGS). More specifically, we introduce an initial attempt to search for a latent geometry composed of a product of constant curvature model spaces with a small number of query evaluations, under some simplifying assumptions. To accomplish this, we propose a novel notion of distance between candidate latent geometries based on the Gromov-Hausdorff distance from metric geometry. In order to compute the Gromov-Hausdorff distance, we introduce a mapping function that enables the comparison of different manifolds by embedding them in a common high-dimensional ambient space. We then design a graph search space based on the notion of smoothness between latent geometries and employ the calculated distances as an additional inductive bias. Finally, we use Bayesian optimization to search for the optimal latent geometry in a query-efficient manner. This is a general method which can be applied to search for the optimal latent geometry for a variety of models and downstream tasks. We perform experiments on synthetic and real-world datasets to identify the optimal latent geometry for multiple machine learning problems.
Deep Learning/Algorithms
Weight-sharing quantization has emerged as a technique to reduce energy expenditure during inference in large neural networks by constraining their weights to a limited set of values. However, existing methods often assume weights are treated solely based on value, neglecting the unique role of weight position. This paper proposes a probabilistic framework based on Bayesian neural networks (BNNs) and a variational relaxation to identify which weights can be moved to which cluster center and to what degree based on their individual position-specific learned uncertainty distributions. We introduce a new initialization setting and a regularization term, enabling the training of BNNs with complex dataset-model combinations. Leveraging the flexibility of weight values from probability distributions, we enhance noise resilience and compressibility. Our iterative clustering procedure demonstrates superior compressibility and higher accuracy compared to state-of-the-art methods on both ResNet models and the more complex transformer-based architectures. In particular, our method outperforms the state-of-the-art quantization method top-1 accuracy by 1.6\% on ImageNet using DeiT-Tiny, with its 5 million+ weights now represented by only 296 unique values. Code available at https://github.com/subiawaud/PWFN.
Probabilistic Methods/Bayesian Models and Methods
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research has focused on problems where the observations are independent and identically distributed (i.i.d.), and there has been little work on the problems where the observations are dependent, such as time series data and sequential data in natural language processing. This paper aims to address this gap by studying the theory for sparse deep learning with dependent data. We show that sparse recurrent neural networks (RNNs) can be consistently estimated, and their predictions are asymptotically normally distributed under appropriate assumptions, enabling the prediction uncertainty to be correctly quantified. Our numerical results show that sparse deep learning outperforms state-of-the-art methods, such as conformal predictions, in prediction uncertainty quantification for time series data. Furthermore, our results indicate that the proposed method can consistently identify the autoregressive order for time series data and outperform existing methods in large-scale model compression. Our proposed method has important practical implications in fields such as finance, healthcare, and energy, where both accurate point estimates and prediction uncertainty quantification are of concern.
Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network
Probabilistic Methods/Structure Learning
Generative Flow Networks (GFlowNets), a class of generative models over discrete and structured sample spaces, have been previously applied to the problem of inferring the marginal posterior distribution over the directed acyclic graph (DAG) of a Bayesian Network, given a dataset of observations. Based on recent advances extending this framework to non-discrete sample spaces, we propose in this paper to approximate the joint posterior over not only the structure of a Bayesian Network, but also the parameters of its conditional probability distributions. We use a single GFlowNet whose sampling policy follows a two-phase process: the DAG is first generated sequentially one edge at a time, and then the corresponding parameters are picked once the full structure is known. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models of the Bayesian Network, making our approach applicable even to non-linear models parametrized by neural networks. We show that our method, called JSP-GFN, offers an accurate approximation of the joint posterior, while comparing favorably against existing methods on both simulated and real data.
Probabilistic Methods/Gaussian Processes
This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional data (e.g.‘point cloud data’) centered around some lower dimensional unknown manifolds. The geometry of manifold is in general different from the usual Euclidean geometry. Naively applying traditional smoothing methods such as Euclidean Gaussian Processes (GPs) to manifold-valued data and so ignoring the geometry of the space can potentially lead to highly misleading predictions and inferences. A manifold embedded in a high dimensional Euclidean space can be well described by a probabilistic mapping function and the corresponding latent space. We investigate the geometrical structure of the unknown manifolds using the Bayesian Gaussian Processes latent variable models(B-GPLVM) and Riemannian geometry. The distribution of the metric tensor is learned using B-GPLVM. The boundary of the resulting manifold is defined based on the uncertainty quantification of the mapping. We use the probabilistic metric tensor to simulate Brownian Motion paths on the unknown manifold. The heat kernel is estimated as the transition density of Brownian Motion and used as the covariance functions of GPUM. The applications of GPUM are illustrated in the simulation studies on the Swiss roll, high dimensional real datasets of WiFi signals and image data examples. Its performance is compared with the Graph Laplacian GP, Graph Mat\'{e}rn GP and Euclidean GP.
Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning
The success of meta-learning on out-of-distribution (OOD) tasks in the wild has proved to be hit-and-miss.To safeguard the generalization capability of the meta-learned prior knowledge to OOD tasks, in particularly safety-critical applications, necessitates detection of an OOD task followed by adaptation of the task towards the prior. Nonetheless, the reliability of estimated uncertainty on OOD tasks by existing Bayesian meta-learning methods is restricted by incomplete coverage of the feature distribution shift and insufficient expressiveness of the meta-learned prior. Besides, they struggle to adapt an OOD task, running parallel to the line of cross-domain task adaptation solutions which are vulnerable to overfitting.To this end, we build a single coherent framework that supports both detection and adaptation of OOD tasks, while remaining compatible with off-the-shelf meta-learning backbones. The proposed Energy-Based Meta-Learning (EBML) framework learns to characterize any arbitrary meta-training task distribution with the composition of two expressive neural-network-based energy functions. We deploy the sum of the two energy functions, being proportional to the joint distribution of a task, as a reliable score for detecting OOD tasks; during meta-testing, we adapt the OOD task to in-distribution tasks by energy minimization.Experiments on four regression and classification datasets demonstrate the effectiveness of our proposal.
Probabilistic Methods/Graphical Models
Credal networks extend Bayesian networks to allow for imprecision in probability values. Marginal MAP is a widely applicable mixed inference task that identifies the most likely assignment for a subset of variables (called MAP variables). However, the task is extremely difficult to solve in credal networks particularly because the evaluation of each complete MAP assignment involves exact likelihood computations (combinatorial sums) over the vertices of a complex joint credal set representing the space of all possible marginal distributions of the MAP variables. In this paper, we explore Credal Marginal MAP inference and develop new exact methods based on variable elimination and depth-first search as well as several approximation schemes based on the mini-bucket partitioning and stochastic local search. An extensive empirical evaluation demonstrates the effectiveness of our new methods on random as well as real-world benchmark problems.
Probabilistic Methods
Masked pre-training removes random input dimensions and learns a model that can predict the missing values. Empirical results indicate that this intuitive form of self-supervised learning yields models that generalize very well to new domains. A theoretical understanding is, however, lacking. This paper shows that masked pre-training with a suitable cumulative scoring function corresponds to maximizing the model's marginal likelihood, which is de facto the Bayesian model selection measure of generalization. Beyond shedding light on the success of masked pre-training, this insight also suggests that Bayesian models can be trained with appropriately designed self-supervision. Empirically, we confirm the developed theory and explore the main learning principles of masked pre-training in large language models.
Probabilistic Methods/Variational Inference
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.
Optimization/Optimization and Learning under Uncertainty
Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability. This uncertainty deviates the input from the intended value before evaluation, resulting in significant performance fluctuations in the final result. In this paper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO, which can effectively identify a robust optimum that performs consistently well under arbitrary input uncertainty. Our method directly models the uncertain inputs of arbitrary distributions by empowering the Gaussian Process with the Maximum Mean Discrepancy (MMD) and further accelerates the posterior inference via Nystrom approximation. Rigorous theoretical regret bound is established under MMD estimation error and extensive experiments on synthetic functions and real problems demonstrate that our approach can handle various input uncertainties and achieve a state-of-the-art performance.
Probabilistic Methods/Bayesian Models and Methods
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors.To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events.Our key tool is *probability generating functions*:they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments.Our inference method is provably correct and fully automated in a tool called *Genfer*, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra.Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy.On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors.To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events.Our key tool is *probability generating functions*:they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments.Our inference method is provably correct and fully automated in a tool called *Genfer*, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra.Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy.On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.
Miscellaneous Aspects of Machine Learning/Causality
Bayesian causal discovery aims to infer the posterior distribution over causal models from observed data, quantifying epistemic uncertainty and benefiting downstream tasks. However, computational challenges arise due to joint inference over combinatorial space of Directed Acyclic Graphs (DAGs) and nonlinear functions. Despite recent progress towards efficient posterior inference over DAGs, existing methods are either limited to variational inference on node permutation matrices for linear causal models, leading to compromised inference accuracy, or continuous relaxation of adjacency matrices constrained by a DAG regularizer, which cannot ensure resulting graphs are DAGs. In this work, we introduce a scalable Bayesian causal discovery framework based on a combination of stochastic gradient Markov Chain Monte Carlo (SG-MCMC) and Variational Inference (VI) that overcomes these limitations. Our approach directly samples DAGs from the posterior without requiring any DAG regularization, simultaneously draws function parameter samples and is applicable to both linear and nonlinear causal models. To enable our approach, we derive a novel equivalence to the permutation-based DAG learning, which opens up possibilities of using any relaxed gradient estimator defined over permutations. To our knowledge, this is the first framework applying gradient-based MCMC sampling for causal discovery. Empirical evaluation on synthetic and real-world datasets demonstrate our approach's effectiveness compared to state-of-the-art baselines.