A key challenge in crowdsourcing is inferring the ground truth from noisy and unreliable data. To do so, existing approaches rely on collecting redundant information from the crowd, and aggregating it with some probabilistic method. However, oftentimes such methods are computationally inefficient, are restricted to some specific settings, or lack theoretical guarantees. In this paper, we revisit the problem of binary classification from crowdsourced data. Specifically we propose Streaming Bayesian Inference for Crowdsourcing (SBIC), a new algorithm that does not suffer from any of these limitations. First, SBIC has low complexity and can be used in a real-time online setting. Second, SBIC has the same accuracy as the best state-of-the-art algorithms in all settings. Third, SBIC has provable asymptotic guarantees both in the online and offline settings.

Sum-product networks (SPNs) are flexible density estimators and have received significant attention due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be desired: Even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc and based on intuition rather than a clear learning principle. In this paper, we introduce a well-principled Bayesian framework for SPN structure learning.

Bayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in particular, the search space of the next query may depend on previous ones. Example challenges arise in the physical sciences in the form of local movement constraints, required monotonicity in certain variables, and transitions influencing the accuracy of measurements.

Modern applications of machine learning (ML) deal with increasingly heterogeneous datasets comprised of data collected from overlapping latent subpopulations. As a result, traditional models trained over large datasets may fail to recognize highly predictive localized effects in favour of weakly predictive global patterns. This is a problem because localized effects are critical to developing individualized policies and treatment plans in applications ranging from precision medicine to advertising. To address this challenge, we propose to estimate sample-specific models that tailor inference and prediction at the individual level. In contrast to classical ML models that estimate a single, complex model (or only a few complex models), our approach produces a model personalized to each sample. These sample-specific models can be studied to understand subgroup dynamics that go beyond coarse-grained class labels. Crucially, our approach does not assume that relationships between samples (e.g. a similarity network) are known a priori. Instead, we use unmodeled covariates to learn a latent distance metric over the samples. We apply this approach to financial, biomedical, and electoral data as well as simulated data and show that sample-specific models provide fine-grained interpretations of complicated phenomena without sacrificing predictive accuracy compared to state-of-the-art models such as deep neural networks.

Recently, 3D Gaussian Splatting (3DGS) has become popular in reconstructing dense 3D representations of appearance and geometry. However, the learning pipeline in 3DGS inherently lacks the ability to quantify uncertainty, which is an important factor in applications like robotics mapping and navigation. In this paper, we propose an uncertainty estimation method built upon the Bayesian inference framework. Specifically, we propose a method to build variational multi-scale 3D Gaussians, where we leverage explicit scale information in 3DGS parameters to construct diversified parameter space samples. We develop an offset table technique to draw local multi-scale samples efficiently by offsetting selected attributes and sharing other base attributes. Then, the offset table is learned by variational inference with multi-scale prior. The learned offset posterior can quantify the uncertainty of each individual Gaussian component, and be used in the forward pass to infer the predictive uncertainty. Extensive experimental results on various benchmark datasets show that the proposed method provides well-aligned calibration performance on estimated uncertainty and better rendering quality compared with the previous methods that enable uncertainty quantification with view synthesis. Besides, by leveraging the model parameter uncertainty estimated by our method, we can remove noisy Gaussians automatically, thereby obtaining a high-fidelity part of the reconstructed scene, which is of great help in improving the visual quality.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models.

Recent methods are proposed to improve performance of domain adaptation by inferring domain index under an adversarial variational bayesian framework, where domain index is unavailable. However, existing methods typically assume that the global domain indices are sampled from a vanilla gaussian prior, overlooking the inherent structures among different domains. To address this challenge, we propose a Bayesian Domain Adaptation with Gaussian Mixture Domain-Indexing(GMDI) algorithm. GMDI employs a Gaussian Mixture Model for domain indices, with the number of component distributions in the "domain-themes" space adaptively determined by a Chinese Restaurant Process. By dynamically adjusting the mixtures at the domain indices level, GMDI significantly improves domain adaptation performance. Our theoretical analysis demonstrates that GMDI achieves a more stringent evidence lower bound, closer to the log-likelihood. For classification, GMDI outperforms all approaches, and surpasses the state-of-the-art method, VDI, by up to 3.4%, reaching 99.3%. For regression, GMDI reduces MSE by up to 21% (from 3.160 to 2.493), achieving the lowest errors among all methods. Source code is publicly available from https://github.com/lingyf3/GMDI.

Modern CNN-based object detectors assign anchors for ground-truth objects under the restriction of object-anchor Intersection-over-Unit (IoU). In this study, we propose a learning-to-match approach to break IoU restriction, allowing objects to match anchors in a flexible manner. Our approach, referred to as FreeAnchor, updates hand-crafted anchor assignment to "free" anchor matching by formulating detector training as a maximum likelihood estimation (MLE) procedure. FreeAnchor targets at learning features which best explain a class of objects in terms of both classification and localization. FreeAnchor is implemented by optimizing detection customized likelihood and can be fused with CNN-based detectors in a plug-and-play manner.

While Bayesian neural networks (BNNs) hold the promise of being flexible, wellcalibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational methods in approximating the Bayesian predictive distribution. For single-hidden layer ReLU BNNs, we prove a fundamental limitation in function-space of two of the most commonly used distributions defined in weight-space: mean-field Gaussian and Monte Carlo dropout. We find there are simple cases where neither method can have substantially increased uncertainty in between well-separated regions of low uncertainty. We provide strong empirical evidence that exact inference does not have this pathology, hence it is due to the approximation and not the model. In contrast, for deep networks, we prove a universality result showing that there exist approximate posteriors in the above classes which provide flexible uncertainty estimates. However, we find empirically that pathologies of a similar form as in the single-hidden layer case can persist when performing variational inference in deeper networks. Our results motivate careful consideration of the implications of approximate inference methods in BNNs.

Neural networks are most often trained under the assumption that data come from a stationary distribution.