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.

Federated learning encounters substantial challenges with heterogeneous data, leading to performance degradation and convergence issues. While considerable progress has been achieved in mitigating such an impact, the reliability aspect of federated models has been largely disregarded. In this study, we conduct extensive experiments to investigate the reliability of both generic and personalized federated models. Our exploration uncovers a significant finding: \textbf{federated models exhibit unreliability when faced with heterogeneous data}, demonstrating poor calibration on in-distribution test data and low uncertainty levels on out-of-distribution data. This unreliability is primarily attributed to the presence of biased projection heads, which introduce miscalibration into the federated models. Inspired by this observation, we propose the "Assembled Projection Heads" (APH) method for enhancing the reliability of federated models. By treating the existing projection head parameters as priors, APH randomly samples multiple initialized parameters of projection heads from the prior and further performs targeted fine-tuning on locally available data under varying learning rates. Such a head ensemble introduces parameter diversity into the deterministic model, eliminating the bias and producing reliable predictions via head averaging. We evaluate the effectiveness of the proposed APH method across three prominent federated benchmarks. Experimental results validate the efficacy of APH in model calibration and uncertainty estimation. Notably, APH can be seamlessly integrated into various federated approaches but only requires less than 30\% additional computation cost for 100$\times$ inferences within large models.

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.

Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compensate for bias or noise in the low-fidelity samples. Deep Gaussian processes (GPs) are attractive for multifidelity modelling as they are non-parametric, robust to overfitting, perform well for small datasets, and, critically, can capture nonlinear and input-dependent relationships between data of different fidelities. Many datasets naturally contain gradient data, especially when they are generated by computational models that are compatible with automatic differentiation or have adjoint solutions. Principally, this work extends deep GPs to incorporate gradient data. We demonstrate this method on an analytical test problem and a realistic partial differential equation problem, where we predict the aerodynamic coefficients of a hypersonic flight vehicle over a range of flight conditions and geometries. In both examples, the gradient-enhanced deep GP outperforms a gradient-enhanced linear GP model and their non-gradient-enhanced counterparts.

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.

We explore the sampling problem within the framework where parallel evaluations of the gradient of the log-density are feasible. Our investigation focuses on target distributions characterized by smooth and strongly log-concave densities. We revisit the parallelized randomized midpoint method and employ proof techniques recently developed for analyzing its purely sequential version. Leveraging these techniques, we derive upper bounds on the Wasserstein distance between the sampling and target densities. These bounds quantify the runtime improvement achieved by utilizing parallel processing units, which can be considerable.