Parametric Bayesian modeling offers a powerful and flexible toolbox for scientific data analysis. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we study nonparametrically perturbed parametric (NPP) Bayesian models, in which a parametric Bayesian model is relaxed via a distortion of its likelihood. We analyze the properties of NPP models when the target of inference is the true data distribution or some functional of it, such as in causal inference. We show that NPP models can offer the robustness of nonparametric models while retaining the data efficiency of parametric models, achieving fast convergence when the parametric model is close to true. To efficiently analyze data with an NPP model, we develop a generalized Bayes procedure to approximate its posterior. We demonstrate our method by estimating causal effects of gene expression from single cell RNA sequencing data. NPP modeling offers an efficient approach to robust Bayesian inference and can be used to robustify any parametric Bayesian model.

Recent techniques in deep generative modeling have leveraged Markov generative processes to learn complex, high-dimensional probability distributions in a more structured and flexible manner [17]. By integrating Markov chain methods with deep neural architectures, these approaches aim to exploit the representational power of deep networks while maintaining a tractable and theoretically grounded training procedure. In contrast to early generative models that relied heavily on direct maximum likelihood estimation or adversarial objectives, this class of methods employs iterative stochastic transformations--often expressed as Markovian updates--to gradually refine initial noise samples into samples drawn from the desired target distribution. Diffusion and flow matching models represent two prominent classes of generative approaches that construct data samples through a sequence of continuous transformations. Diffusion models [6, 13] introduce a forward-noising and reverse-denoising process, progressively refining a simple noise distribution into a complex target distribution by learning to undo incremental noise corruption at each step.

In this paper, we study learning and knowledge acquisition (LKA) of an agent about a proposition that is either true or false. We use a Bayesian approach, where the agent receives data to update his beliefs about the proposition according to a posterior distribution. The LKA is formulated in terms of active information, with data representing external or exogenous information that modifies the agent's beliefs. It is assumed that data provide details about a number of features that are relevant to the proposition. We show that this leads to a Gibbs distribution posterior, which is in maximum entropy relative to the prior, conditioned on the side constraints that the data provide in terms of the features. We demonstrate that full learning is sometimes not possible and full knowledge acquisition is never possible when the number of extracted features is too small. We also distinguish between primary learning (receiving data about features of relevance for the proposition) and secondary learning (receiving data about the learning of another agent). We argue that this type of secondary learning does not represent true knowledge acquisition. Our results have implications for statistical learning algorithms, and we claim that such algorithms do not always generate true knowledge. The theory is illustrated with several examples.

In this paper, a novel classification algorithm that is based on Data Importance (DI) reformatting and Genetic Algorithms (GA) named GADIC is proposed to overcome the issues related to the nature of data which may hinder the performance of the Machine Learning (ML) classifiers. GADIC comprises three phases which are data reformatting phase which depends on DI concept, training phase where GA is applied on the reformatted training dataset, and testing phase where the instances of the reformatted testing dataset are being averaged based on similar instances in the training dataset. GADIC is an approach that utilizes the exiting ML classifiers with involvement of data reformatting, using GA to tune the inputs, and averaging the similar instances to the unknown instance. The averaging of the instances becomes the unknown instance to be classified in the stage of testing. GADIC has been tested on five existing ML classifiers which are Support Vector Machine (SVM), K-Nearest Neighbour (KNN), Logistic Regression (LR), Decision Tree (DT), and Na\"ive Bayes (NB). All were evaluated using seven open-source UCI ML repository and Kaggle datasets which are Cleveland heart disease, Indian liver patient, Pima Indian diabetes, employee future prediction, telecom churn prediction, bank customer churn, and tech students. In terms of accuracy, the results showed that, with the exception of approximately 1% decrease in the accuracy of NB classifier in Cleveland heart disease dataset, GADIC significantly enhanced the performance of most ML classifiers using various datasets. In addition, KNN with GADIC showed the greatest performance gain when compared with other ML classifiers with GADIC followed by SVM while LR had the lowest improvement. The lowest average improvement that GADIC could achieve is 5.96%, whereas the maximum average improvement reached 16.79%.

Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. Similar to other model-based RL approaches, it involves two key components: (1) Inferring the posterior distribution of the data generating process (DGP) modeling the true environment and (2) policy learning using the learned posterior. We propose to model the dynamics of the unknown environment through deep generative models assuming Markov dependence. In absence of likelihood functions for these models we train them by learning a generalized predictive-sequential (or prequential) scoring rule (SR) posterior. We use sequential Monte Carlo (SMC) samplers to draw samples from this generalized Bayesian posterior distribution. In conjunction, to achieve scalability in the high dimensional parameter space of the neural networks, we use the gradient based Markov chain Monte Carlo (MCMC) kernels within SMC. To justify the use of the prequential scoring rule posterior we prove a Bernstein-von Misses type theorem. For policy learning, we propose expected Thompson sampling (ETS) to learn the optimal policy by maximizing the expected value function with respect to the posterior distribution. This improves upon traditional Thompson sampling (TS) and its extensions which utilize only one sample drawn from the posterior distribution. This improvement is studied both theoretically and using simulation studies assuming discrete action and state-space. Finally we successfully extend our setup for a challenging problem with continuous action space without theoretical guarantees.

In this work, we study the problem of aggregation in the context of Bayesian Federated Learning (BFL). Using an information geometric perspective, we interpret the BFL aggregation step as finding the barycenter of the trained posteriors for a pre-specified divergence metric. We study the barycenter problem for the parametric family of $\alpha$-divergences and, focusing on the standard case of independent and Gaussian distributed parameters, we recover the closed-form solution of the reverse Kullback-Leibler barycenter and develop the analytical form of the squared Wasserstein-2 barycenter. Considering a non-IID setup, where clients possess heterogeneous data, we analyze the performance of the developed algorithms against state-of-the-art (SOTA) Bayesian aggregation methods in terms of accuracy, uncertainty quantification (UQ), model calibration (MC), and fairness. Finally, we extend our analysis to the framework of Hybrid Bayesian Deep Learning (HBDL), where we study how the number of Bayesian layers in the architecture impacts the considered performance metrics. Our experimental results show that the proposed methodology presents comparable performance with the SOTA while offering a geometric interpretation of the aggregation phase.

Generative networks are an exciting tool for fast LHC event generation. Usually, they are used to generate configurations with a fixed number of particles. Autoregressive transformers allow us to generate events with variable numbers of particles, very much in line with the physics of QCD jet radiation. We show how they can learn a factorized likelihood for jet radiation and extrapolate in terms of the number of generated jets. For this extrapolation, bootstrapping training data and training with modifications of the likelihood loss can be used.

In two-player cooperative games, agents can play together effectively when they have accurate assumptions about how their teammate will behave, but may perform poorly when these assumptions are inaccurate. In language games, failure may be due to disagreement in the understanding of either the semantics or pragmatics of an utterance. We model coarse uncertainty in semantics using a prior distribution of language models and uncertainty in pragmatics using the cognitive hierarchy, combining the two aspects into a single prior distribution over possible partner types. Fine-grained uncertainty in semantics is modeled using noise that is added to the embeddings of words in the language. To handle all forms of uncertainty we construct agents that learn the behavior of their partner using Bayesian inference and use this information to maximize the expected value of a heuristic function. We test this approach by constructing Bayesian agents for the game of Codenames, and show that they perform better in experiments where semantics is uncertain

Extracting anomaly causality facilitates diagnostics once monitoring systems detect system faults. Identifying anomaly causes in large systems involves investigating a more extensive set of monitoring variables across multiple subsystems. However, learning causal graphs comes with a significant computational burden that restrains the applicability of most existing methods in real-time and large-scale deployments. In addition, modern monitoring applications for large systems often generate large amounts of binary alarm flags, and the distinct characteristics of binary anomaly data -- the meaning of state transition and data sparsity -- challenge existing causality learning mechanisms. This study proposes an anomaly causal discovery approach (AnomalyCD), addressing the accuracy and computational challenges of generating causal graphs from binary flag data sets. The AnomalyCD framework presents several strategies, such as anomaly flag characteristics incorporating causality testing, sparse data and link compression, and edge pruning adjustment approaches. We validate the performance of this framework on two datasets: monitoring sensor data of the readout-box system of the Compact Muon Solenoid experiment at CERN, and a public data set for information technology monitoring. The results demonstrate the considerable reduction of the computation overhead and moderate enhancement of the accuracy of temporal causal discovery on binary anomaly data sets.

In recent years, Geospatial Artificial Intelligence (GeoAI) has gained traction in the most relevant research works and industrial applications, while also becoming involved in various fields of use. This paper offers a comprehensive review of GeoAI as a synergistic concept applying Artificial Intelligence (AI) methods and models to geospatial data. A preliminary study is carried out, identifying the methodology of the work, the research motivations, the issues and the directions to be tracked, followed by exploring how GeoAI can be used in various interesting fields of application, such as precision agriculture, environmental monitoring, disaster management and urban planning. Next, a statistical and semantic analysis is carried out, followed by a clear and precise presentation of the challenges facing GeoAI. Then, a concrete exploration of the future prospects is provided, based on several informations gathered during the census. To sum up, this paper provides a complete overview of the correlation between AI and the geospatial domain, while mentioning the researches conducted in this context, and emphasizing the close relationship linking GeoAI with other advanced concepts such as geographic information systems (GIS) and large-scale geospatial data, known as big geodata. This will enable researchers and scientific community to assess the state of progress in this promising field, and will help other interested parties to gain a better understanding of the issues involved.