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.

In this article, we provide an overview of machine learning (ML) methods, both classical and deep variants, that are used to implement self-healing for cell outages in cellular networks. Self-healing is a promising approach to network management, which aims to detect and compensate for cell outages in an autonomous way. This technology aims to decrease the expenses associated with the installation and maintenance of existing 4G and 5G, i.e. emerging 6G networks by simplifying operational tasks through its ability to heal itself. We provide an overview of the basic concepts and taxonomy for SON, self-healing, and ML techniques, in network management. Moreover, we review the state-of-the-art in literature for cell outages, with a particular emphasis on ML-based approaches.

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.

Reviews and ratings are pervasive in many online platforms. A customer consults reviews/ratings, then chooses a product and then (often) leaves feedback, which is aggregated by the platform and served to future customers. Collectively, customers face a tradeoff between exploration and exploitation, i.e., between acquiring new information while making potentially suboptimal decisions and making optimal decisions using available information. However, individual customers tend to act myopically and favor exploitation, without regards to exploration for the sake of the others. On a high level, we ask whether/how the myopic behavior interferes with efficient exploration. We are particularly interested in learning failures when only a few agents choose an optimal action.

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of probability measures open up new avenues for algorithm development. This paper makes three contributions to this sampling approach by scrutinizing the design components of such gradient flows. Any instantiation of a gradient flow for sampling needs an energy functional and a metric to determine the flow, as well as numerical approximations of the flow to derive algorithms. Our first contribution is to show that the Kullback-Leibler divergence, as an energy functional, has the unique property (among all f-divergences) that gradient flows resulting from it do not depend on the normalization constant of the target distribution. Our second contribution is to study the choice of metric from the perspective of invariance. The Fisher-Rao metric is known as the unique choice (up to scaling) that is diffeomorphism invariant. As a computationally tractable alternative, we introduce a relaxed, affine invariance property for the metrics and gradient flows. In particular, we construct various affine invariant Wasserstein and Stein gradient flows. Affine invariant gradient flows are shown to behave more favorably than their non-affine-invariant counterparts when sampling highly anisotropic distributions, in theory and by using particle methods. Our third contribution is to study, and develop efficient algorithms based on Gaussian approximations of the gradient flows; this leads to an alternative to particle methods. We establish connections between various Gaussian approximate gradient flows, discuss their relation to gradient methods arising from parametric variational inference, and study their convergence properties both theoretically and numerically.

Standard probabilistic sparse coding assumes a Laplace prior, a linear mapping from latents to observables, and Gaussian observable distributions. We here derive a solely entropy-based learning objective for the parameters of standard sparse coding. The novel variational objective has the following features: (A) unlike MAP approximations, it uses non-trivial posterior approximations for probabilistic inference; (B) unlike for previous non-trivial approximations, the novel objective is fully analytical; and (C) the objective allows for a novel principled form of annealing. The objective is derived by first showing that the standard ELBO objective converges to a sum of entropies, which matches similar recent results for generative models with Gaussian priors. The conditions under which the ELBO becomes equal to entropies are then shown to have analytical solutions, which leads to the fully analytical objective. Numerical experiments are used to demonstrate the feasibility of learning with such entropy-based ELBOs. We investigate different posterior approximations including Gaussians with correlated latents and deep amortized approximations. Furthermore, we numerically investigate entropy-based annealing which results in improved learning. Our main contributions are theoretical, however, and they are twofold: (1) for non-trivial posterior approximations, we provide the (to the knowledge of the authors) first analytical ELBO objective for standard probabilistic sparse coding; and (2) we provide the first demonstration on how a recently shown convergence of the ELBO to entropy sums can be used for learning.

The impacts of mass migration, such as crisis induced by climate change, extend beyond environmental concerns and can greatly affect social infrastructure and public services, such as education, healthcare, and security. These crises exacerbate certain elements like cultural barriers, and discrimination by amplifying the challenges faced by these affected communities. This paper proposes an innovative approach to address migration crises in the context of crisis management through a combination of modeling and imbalance assessment tools. By employing deep learning for forecasting and integrating causal reasoning via Bayesian networks, this methodology enables the evaluation of imbalances and risks in the socio-technological landscape, providing crucial insights for informed decision-making. Through this framework, critical systems can be analyzed to understand how fluctuations in migration levels may impact them, facilitating effective crisis governance strategies.

Abstract--This paper considers the adaptation of the e-continuously learn the user's stress pattern in order to adjust The measure of usefulness includes accuracy, among others. As stated in In this paper, two-stage intelligent processing, as seen in [3], e-coaching "may contribute to a better understanding of Figure 1, is used: people's affective responses to the COVID-19 crisis. Stage I is aimed at gathering physiological information legal, and social implications are addressed appropriately, from a subject for human decision-making (reasoning). Stage II is aimed at supporting the human decisionmaker society by monitoring and improving people's mental health". Typical symptoms include anxiety, panic, avoidance, and stress.