In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes ill-conditioned, provided the sampling locations are fairly evenly distributed. This condition poses significant challenges to numerical algorithms used in prediction and estimation computations and necessitates an approximation to prediction and the Gaussian likelihood. A review of current methodologies for managing large spatial data indicates that some fail to address this ill-conditioning problem. Such ill-conditioning often results in low-rank approximations of the stochastic processes. This paper introduces various optimality criteria and provides solutions for each.

In biomedical applications it is often necessary to estimate a physiological response to a treatment consisting of multiple components, and learn the separate effects of the components in addition to the joint effect. Here, we extend existing probabilistic nonparametric approaches to explicitly address this problem. We also develop a new convolution-based model for composite treatment-response curves that is more biologically interpretable. We validate our models by estimating the impact of carbohydrate and fat in meals on blood glucose. By differentiating treatment components, incorporating their dosages, and sharing statistical information across patients via a hierarchical multi-output Gaussian process, our method improves prediction accuracy over existing approaches, and allows us to interpret the different effects of carbohydrates and fat on the overall glucose response.

Like many optimizers, Bayesian optimization often falls short of gaining user trust due to opacity. While attempts have been made to develop human-centric optimizers, they typically assume user knowledge is well-specified and error-free, employing users mainly as supervisors of the optimization process. We relax these assumptions and propose a more balanced human-AI partnership with our Collaborative and Explainable Bayesian Optimization (CoExBO) framework. Instead of explicitly requiring a user to provide a knowledge model, CoExBO employs preference learning to seamlessly integrate human insights into the optimization, resulting in algorithmic suggestions that resonate with user preference. CoExBO explains its candidate selection every iteration to foster trust, empowering users with a clearer grasp of the optimization. Furthermore, CoExBO offers a no-harm guarantee, allowing users to make mistakes; even with extreme adversarial interventions, the algorithm converges asymptotically to a vanilla Bayesian optimization. We validate CoExBO's efficacy through human-AI teaming experiments in lithium-ion battery design, highlighting substantial improvements over conventional 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.

Reconstructing a continuous surface from an unoritented 3D point cloud is a fundamental task in 3D shape processing. In recent years, several methods have been proposed to address this problem using implicit neural representations (INRs). In this study, we propose a method to optimize INRs using energy-based models (EBMs). By employing the absolute value of the coordinate-based neural networks as the energy function, the INR can be optimized through the estimation of the point cloud distribution by the EBM. In addition, appropriate parameter settings of the EBM enable the model to consider the magnitude of point cloud noise. Our experiments confirmed that the proposed method is more robust against point cloud noise than conventional surface reconstruction methods.

We propose a straightforward solution for detecting scarce topics in unbalanced short-text datasets. Our approach, named CWUTM (Topic model based on co-occurrence word networks for unbalanced short text datasets), Our approach addresses the challenge of sparse and unbalanced short text topics by mitigating the effects of incidental word co-occurrence. This allows our model to prioritize the identification of scarce topics (Low-frequency topics). Unlike previous methods, CWUTM leverages co-occurrence word networks to capture the topic distribution of each word, and we enhanced the sensitivity in identifying scarce topics by redefining the calculation of node activity and normalizing the representation of both scarce and abundant topics to some extent. Moreover, CWUTM adopts Gibbs sampling, similar to LDA, making it easily adaptable to various application scenarios. Our extensive experimental validation on unbalanced short-text datasets demonstrates the superiority of CWUTM compared to baseline approaches in discovering scarce topics. According to the experimental results the proposed model is effective in early and accurate detection of emerging topics or unexpected events on social platforms.

Test log-likelihood, also known as predictive log-likelihood or test log-predictive, is computed as the log-predictive density averaged over a set of held-out data. It is often used to compare different models of the same data or to compare different algorithms used to fit the same probabilistic model. Although there are compelling reasons for this practice (Section 2.1), we provide examples that falsify the following, usually implicit, claims: Claim: The higher the test log-likelihood, the more accurately an approximate inference algorithm recovers the Bayesian posterior distribution of latent model parameters (Section 3). Claim: The higher the test log-likelihood, the better the predictive performance on held-out data according to other measurements, like root mean squared error (Section 4). Our examples demonstrate that test log-likelihood is not always a good proxy for posterior approximation error. They further demonstrate that forecast evaluations based on test log-likelihood may not agree with forecast evaluations based on root mean squared error. We are not the first to highlight discrepancies between test log-likelihood and other analysis objectives. For instance, Quiñonero-Candela et al. (2005) and Kohonen and Suomela (2005) showed that when predicting discrete data with continuous distributions, test log-likelihood can be made arbitrarily large by concentrating probability into vanishingly small intervals. Chang et al. (2009) observed

Brain network discovery aims to find nodes and edges from the spatio-temporal signals obtained by neuroimaging data, such as fMRI scans of human brains. Existing methods tend to derive representative or average brain networks, assuming observed signals are generated by only a single brain activity state. However, the human brain usually involves multiple activity states, which jointly determine the brain activities. The brain regions and their connectivity usually exhibit intricate patterns that are difficult to capture with only a single-state network. Recent studies find that brain parcellation and connectivity change according to the brain activity state. We refer to such brain networks as multi-state, and this mixture can help us understand human behavior. Thus, compared to a single-state network, a multi-state network can prevent us from losing crucial information of cognitive brain network. To achieve this, we propose a new model called MNGL (Multi-state Network Graphical Lasso), which successfully models multi-state brain networks by combining CGL (coherent graphical lasso) with GMM (Gaussian Mixture Model). Using both synthetic and real world ADHD 200 fMRI datasets, we demonstrate that MNGL outperforms recent state-of-the-art alternatives by discovering more explanatory and realistic results.

Despite the remarkable performance of text-to-image diffusion models in image generation tasks, recent studies have raised the issue that generated images sometimes cannot capture the intended semantic contents of the text prompts, which phenomenon is often called semantic misalignment. To address this, here we present a novel energy-based model (EBM) framework for adaptive context control by modeling the posterior of context vectors. Specifically, we first formulate EBMs of latent image representations and text embeddings in each cross-attention layer of the denoising autoencoder. Then, we obtain the gradient of the log posterior of context vectors, which can be updated and transferred to the subsequent cross-attention layer, thereby implicitly minimizing a nested hierarchy of energy functions. Our latent EBMs further allow zero-shot compositional generation as a linear combination of cross-attention outputs from different contexts. Using extensive experiments, we demonstrate that the proposed method is highly effective in handling various image generation tasks, including multi-concept generation, text-guided image inpainting, and real and synthetic image editing.

Over the past few years, significant advancements have been made in the field of machine learning (ML) to address resource management, interference management, autonomy, and decision-making in wireless networks. Traditional ML approaches rely on centralized methods, where data is collected at a central server for training. However, this approach poses a challenge in terms of preserving the data privacy of devices. To address this issue, federated learning (FL) has emerged as an effective solution that allows edge devices to collaboratively train ML models without compromising data privacy. In FL, local datasets are not shared, and the focus is on learning a global model for a specific task involving all devices. However, FL has limitations when it comes to adapting the model to devices with different data distributions. In such cases, meta learning is considered, as it enables the adaptation of learning models to different data distributions using only a few data samples. In this tutorial, we present a comprehensive review of FL, meta learning, and federated meta learning (FedMeta). Unlike other tutorial papers, our objective is to explore how FL, meta learning, and FedMeta methodologies can be designed, optimized, and evolved, and their applications over wireless networks. We also analyze the relationships among these learning algorithms and examine their advantages and disadvantages in real-world applications.