In principle, Bayesian learning directly applies to this setting, since recursive and one-off Bayesian updates yield the same result. In practice, however, recursive updating often leads to poor trade-off solutions across tasks because approximate inference is necessary for most models of interest. Here, we describe an alternative Bayesian approach where task-conditioned parameter distributions are continually inferred from data. We offer a practical deep learning implementation of our framework based on probabilistic task-conditioned hypernetworks, an approach we term posterior meta-replay. Experiments on standard benchmarks show that our probabilistic hypernetworks compress sequences of posterior parameter distributions with virtually no forgetting.

Motivated by decentralized approaches to machine learning, we propose a collaborative Bayesian learning algorithm taking the form of decentralized Langevin dynamics in a non-convex setting. Our analysis show that the initial KL-divergence between the Markov Chain and the target posterior distribution is exponentially decreasing while the error contributions to the overall KL-divergence from the additive noise is decreasing in polynomial time. We further show that the polynomial-term experiences speed-up with number of agents and provide sufficient conditions on the time-varying step-sizes to guarantee convergence to the desired distribution. The performance of the proposed algorithm is evaluated on a wide variety of machine learning tasks. The empirical results show that the performance of individual agents with locally available data is on par with the centralized setting with considerable improvement in the convergence rate.

Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning.

Suppose an online platform wants to compare a treatment and control policy (e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site). Standard experimental approaches to this problem are biased (due to temporal interference between the policies), and not sample efficient. We study optimal experimental design for this setting. We view testing the two policies as the problem of estimating the steady state difference in reward between two unknown Markov chains (i.e., policies). We assume estimation of the steady state reward for each chain proceeds via nonparametric maximum likelihood, and search for consistent (i.e., asymptotically unbiased) experimental designs that are efficient (i.e., asymptotically minimum variance).

Learning binary classifiers only from positive and unlabeled (PU) data is an important and challenging task in many real-world applications, including web text classification, disease gene identification and fraud detection, where negative samples are difficult to verify experimentally. Most recent PU learning methods are developed based on the misclassification risk of the supervised learning type, and they may suffer from inaccurate estimates of class prior probabilities. In this paper, we introduce a variational principle for PU learning that allows us to quantitatively evaluate the modeling error of the Bayesian classifier directly from given data. This leads to a loss function which can be efficiently calculated without involving class prior estimation or any other intermediate estimation problems, and the variational learning method can then be employed to optimize the classifier under general conditions. We illustrate the effectiveness of the proposed variational method on a number of benchmark examples.

Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if data is incomplete, the latent states of the CTBN have to be estimated by laboriously simulating the intractable dynamics of the assumed CTBN. This is a problem, especially for structure learning tasks, where this has to be done for each element of a super-exponentially growing set of possible structures. In order to circumvent this notorious bottleneck, we develop a novel gradient-based approach to structure learning.

The bias-variance trade-off is a well-known problem in machine learning that only gets more pronounced the less available data there is. In active learning, where labeled data is scarce or difficult to obtain, neglecting this trade-off can cause inefficient and non-optimal querying, leading to unnecessary data labeling. In this paper, we focus on active learning with Gaussian Processes (GPs). For the GP, the bias-variance trade-off is made by optimization of the two hyperparameters: the length scale and noise-term. Considering that the optimal mode of the joint posterior of the hyperparameters is equivalent to the optimal bias-variance trade-off, we approximate this joint posterior and utilize it to design two new acquisition functions.

Recent advancements in edge computing have significantly enhanced the AI capabilities of Internet of Things (IoT) devices. However, these advancements introduce new challenges in knowledge exchange and resource management, particularly addressing the spatiotemporal data locality in edge computing environments. This study examines algorithms and methods for deploying distributed machine learning within autonomous, network-capable, AI-enabled edge devices. We focus on determining confidence levels in learning outcomes considering the spatial variability of data encountered by independent agents. Using collaborative mapping as a case study, we explore the application of the Distributed Neural Network Optimization (DiNNO) algorithm extended with Bayesian neural networks (BNNs) for uncertainty estimation. We implement a 3D environment simulation using the Webots platform to simulate collaborative mapping tasks, decouple the DiNNO algorithm into independent processes for asynchronous network communication in distributed learning, and integrate distributed uncertainty estimation using BNNs. Our experiments demonstrate that BNNs can effectively support uncertainty estimation in a distributed learning context, with precise tuning of learning hyperparameters crucial for effective uncertainty assessment. Notably, applying Kullback-Leibler divergence for parameter regularization resulted in a 12-30% reduction in validation loss during distributed BNN training compared to other regularization strategies.

In this paper, we investigate the use of N-gram models and Large Pre-trained Multilingual models for Language Identification (LID) across 11 South African languages. For N-gram models, this study shows that effective data size selection remains crucial for establishing effective frequency distributions of the target languages, that efficiently model each language, thus, improving language ranking. For pre-trained multilingual models, we conduct extensive experiments covering a diverse set of massively pre-trained multilingual (PLM) models -- mBERT, RemBERT, XLM-r, and Afri-centric multilingual models -- AfriBERTa, Afro-XLMr, AfroLM, and Serengeti. We further compare these models with available large-scale Language Identification tools: Compact Language Detector v3 (CLD V3), AfroLID, GlotLID, and OpenLID to highlight the importance of focused-based LID. From these, we show that Serengeti is a superior model across models: N-grams to Transformers on average. Moreover, we propose a lightweight BERT-based LID model (za_BERT_lid) trained with NHCLT + Vukzenzele corpus, which performs on par with our best-performing Afri-centric models.

Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support embodied, adaptable, and energy-efficient autonomous agents. A central theory in this domain is predictive coding, which posits that learning and behaviour are driven by hierarchical probabilistic inferences about the causes of sensory inputs. Biological realism constrains these networks to rely on simple local computations in the form of precision-weighted predictions and prediction errors. This can make this framework highly efficient, but its implementation comes with unique challenges on the software development side. Embedding such models in standard neural network libraries often becomes limiting, as these libraries' compilation and differentiation backends can force a conceptual separation between optimization algorithms and the systems being optimized. This critically departs from other biological principles such as self-monitoring, self-organisation, cellular growth and functional plasticity. In this paper, we introduce \texttt{pyhgf}: a Python package backed by JAX and Rust for creating, manipulating and sampling dynamic networks for predictive coding. We improve over other frameworks by enclosing the network components as transparent, modular and malleable variables in the message-passing steps. The resulting graphs can implement arbitrary computational complexities as beliefs propagation. But the transparency of core variables can also translate into inference processes that leverage self-organisation principles, and express structure learning, meta-learning or causal discovery as the consequence of network structural adaptation to surprising inputs. The code, tutorials and documentation are hosted at: https://github.com/ilabcode/pyhgf.