Performance degradation owing to data heterogeneity and low output interpretability are the most significant challenges faced by federated learning in practical applications. Personalized federated learning diverges from traditional approaches, as it no longer seeks to train a single model, but instead tailors a unique personalized model for each client. However, previous work focused only on personalization from the perspective of neural network parameters and lack of robustness and interpretability. In this work, we establish a novel framework for personalized federated learning, incorporating Bayesian methodology which enhances the algorithm's ability to quantify uncertainty. Furthermore, we introduce normalizing flow to achieve personalization from the parameter posterior perspective and theoretically analyze the impact of normalizing flow on out-of-distribution (OOD) detection for Bayesian neural networks. Finally, we evaluated our approach on heterogeneous datasets, and the experimental results indicate that the new algorithm not only improves accuracy but also outperforms the baseline significantly in OOD detection due to the reliable output of the Bayesian approach.

With the rise of increasingly powerful and user-facing NLP systems, there is growing interest in assessing whether they have a good representation of uncertainty by evaluating the quality of their predictive distribution over outcomes. We identify two main perspectives that drive starkly different evaluation protocols. The first treats predictive probability as an indication of model confidence; the second as an indication of human label variation. We discuss their merits and limitations, and take the position that both are crucial for trustworthy and fair NLP systems, but that exploiting a single predictive distribution is limiting. We recommend tools and highlight exciting directions towards models with disentangled representations of uncertainty about predictions and uncertainty about human labels.

Statistical heterogeneity of clients' local data is an important characteristic in federated learning, motivating personalized algorithms tailored to the local data statistics. Though there has been a plethora of algorithms proposed for personalized supervised learning, discovering the structure of local data through personalized unsupervised learning is less explored. We initiate a systematic study of such personalized unsupervised learning by developing algorithms based on optimization criteria inspired by a hierarchical Bayesian statistical framework. We develop adaptive algorithms that discover the balance between using limited local data and collaborative information. We do this in the context of two unsupervised learning tasks: personalized dimensionality reduction and personalized diffusion models. We develop convergence analyses for our adaptive algorithms which illustrate the dependence on problem parameters (e.g., heterogeneity, local sample size). We also develop a theoretical framework for personalized diffusion models, which shows the benefits of collaboration even under heterogeneity. We finally evaluate our proposed algorithms using synthetic and real data, demonstrating the effective sample amplification for personalized tasks, induced through collaboration, despite data heterogeneity.

Matting with a static background, often referred to as ``Background Matting" (BGM), has garnered significant attention within the computer vision community due to its pivotal role in various practical applications like webcasting and photo editing. Nevertheless, achieving highly accurate background matting remains a formidable challenge, primarily owing to the limitations inherent in conventional RGB images. These limitations manifest in the form of susceptibility to varying lighting conditions and unforeseen shadows. In this paper, we leverage the rich depth information provided by the RGB-Depth (RGB-D) cameras to enhance background matting performance in real-time, dubbed DART. Firstly, we adapt the original RGB-based BGM algorithm to incorporate depth information. The resulting model's output undergoes refinement through Bayesian inference, incorporating a background depth prior. The posterior prediction is then translated into a "trimap," which is subsequently fed into a state-of-the-art matting algorithm to generate more precise alpha mattes. To ensure real-time matting capabilities, a critical requirement for many real-world applications, we distill the backbone of our model from a larger and more versatile BGM network. Our experiments demonstrate the superior performance of the proposed method. Moreover, thanks to the distillation operation, our method achieves a remarkable processing speed of 33 frames per second (fps) on a mid-range edge-computing device. This high efficiency underscores DART's immense potential for deployment in mobile applications}

Neural network sparsification is a promising avenue to save computational time and memory costs, especially in an age where many successful AI models are becoming too large to na\"ively deploy on consumer hardware. While much work has focused on different weight pruning criteria, the overall sparsifiability of the network, i.e., its capacity to be pruned without quality loss, has often been overlooked. We present Sparsifiability via the Marginal likelihood (SpaM), a pruning framework that highlights the effectiveness of using the Bayesian marginal likelihood in conjunction with sparsity-inducing priors for making neural networks more sparsifiable. Our approach implements an automatic Occam's razor that selects the most sparsifiable model that still explains the data well, both for structured and unstructured sparsification. In addition, we demonstrate that the pre-computed posterior Hessian approximation used in the Laplace approximation can be re-used to define a cheap pruning criterion, which outperforms many existing (more expensive) approaches. We demonstrate the effectiveness of our framework, especially at high sparsity levels, across a range of different neural network architectures and datasets.

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are connected to Frequentist and Bayesian statistics, respectively. Later, a more general type of game is introduced, termed Statistical game, in which a further parameter, the players' relative risk aversion, can be set. In this work, we show that Fisher and Bayesian games can be viewed as limiting cases of Statistical games. Therefore, Statistical games can be viewed as a unified framework, incorporating both Frequentist and Bayesian statistics. Furthermore, a philosophical framework is (re-)presented -- often referred to as minimax regret criterion -- as a general approach to decision making. The main motivation for this work was to embed Bayesian statistics into a broader decision-making framework, where, based on collected data, actions with consequences have to be made, which can be translated to utilities (or rewards/losses) of the decision-maker. The work starts with the simplest possible toy model, related to hypothesis testing and statistical inference. This choice has two main benefits: i.) it allows us to determine (conjecture) the behaviour of the equilibrium strategies in various limiting cases ii.) this way, we can introduce Statistical games without requiring additional stochastic parameters. The work contains game theoretical methods related to two-player, non-cooperative games to determine and prove equilibrium strategies of Fisher, Bayesian and Statistical games. It also relies on analytical tools for derivations concerning various limiting cases.

Image denoising is probably the oldest and still one of the most active research topic in image processing. Many methodological concepts have been introduced in the past decades and have improved performances significantly in recent years, especially with the emergence of convolutional neural networks and supervised deep learning. In this paper, we propose a survey of guided tour of supervised and unsupervised learning methods for image denoising, classifying the main principles elaborated during this evolution, with a particular concern given to recent developments in supervised learning. It is conceived as a tutorial organizing in a comprehensive framework current approaches. We give insights on the rationales and limitations of the most performant methods in the literature, and we highlight the common features between many of them. Finally, we focus on on the normalization equivariance properties that is surprisingly not guaranteed with most of supervised methods. It is of paramount importance that intensity shifting or scaling applied to the input image results in a corresponding change in the denoiser output.

Epicardial adipose tissue (EAT) is a type of visceral fat that can secrete large amounts of adipokines to affect the myocardium and coronary arteries. EAT volume and density can be used as independent risk markers measurement of volume by noninvasive magnetic resonance images is the best method of assessing EAT. However, segmenting EAT is challenging due to the low contrast between EAT and pericardial effusion and the presence of motion artifacts. we propose a novel feature latent space multilevel supervision network (SPDNet) with uncertainty-driven and adversarial calibration learning to enhance segmentation for more accurate EAT volume estimation. The network first addresses the blurring of EAT edges due to the medical images in the open medical environments with low quality or out-of-distribution by modeling the uncertainty as a Gaussian distribution in the feature latent space, which using its Bayesian estimation as a regularization constraint to optimize SwinUNETR. Second, an adversarial training strategy is introduced to calibrate the segmentation feature map and consider the multi-scale feature differences between the uncertainty-guided predictive segmentation and the ground truth segmentation, synthesizing the multi-scale adversarial loss directly improves the ability to discriminate the similarity between organizations. Experiments on both the cardiac public MRI dataset (ACDC) and the real-world clinical cohort EAT dataset show that the proposed network outperforms mainstream models, validating that uncertainty-driven and adversarial calibration learning can be used to provide additional information for modeling multi-scale ambiguities.

We present the Streaming Gaussian Dirichlet Random Field (S-GDRF) model, a novel approach for modeling a stream of spatiotemporally distributed, sparse, high-dimensional categorical observations. The proposed approach efficiently learns global and local patterns in spatiotemporal data, allowing for fast inference and querying with a bounded time complexity. Using a high-resolution data series of plankton images classified with a neural network, we demonstrate the ability of the approach to make more accurate predictions compared to a Variational Gaussian Process (VGP), and to learn a predictive distribution of observations from streaming categorical data. S-GDRFs open the door to enabling efficient informative path planning over high-dimensional categorical observations, which until now has not been feasible.

In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional forecasting methods concentrate on the short-term dynamics of time series data, GPs offer the potential to forecast not just the average prediction but the entire probability distribution over a future trajectory. This is particularly beneficial in financial contexts, where accurate predictions alone may not suffice if incorrect volatility assessments lead to capital losses. Moreover, in trade selection, GPs allow for the forecasting of multiple Sharpe ratios adjusted for transaction costs, aiding in decision-making. The functional data representation utilized in this study enables longer-term predictions by leveraging information from previous years, even as the forecast moves away from the current year's training data. Additionally, the augmented representation enriches the training set by incorporating multiple targets for future points in time, facilitating long-term predictions. Our implementation closely aligns with the methodology outlined in [1], which assessed effectiveness on commodity futures. However, our testing methodology differs. Instead of real data, we employ simulated data with similar characteristics. We construct a testing environment to evaluate both data representations and models under conditions of increasing noise, fat tails, and inappropriate kernels--conditions commonly encountered in practice. By simulating data, we can compare our forecast distribution over time against a full simulation of the actual distribution of our test set, thereby reducing the inherent uncertainty in testing time series models on real data. We enable feature prediction through augmentation and employ sub-sampling to ensure the feasibility of GPs. The experiments demonstrate the effectiveness of the functional and augmented data representations, quantify the impact of noise and fat tails on these models, and identify scenarios where simpler models suffice. We explore the consequences of choosing an incorrect initial kernel and illustrate how functional augmentation can mitigate this issue under certain circumstances. Furthermore, we showcase how augmentation enhances predictive capability in scenarios with limited training data and present innovative applications of augmented GP in trading exchange-traded futures.