Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the Cramér-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.

Coverage Path Planning (CPP) is vital in precision agriculture to improve efficiency and resource utilization. In irregular and dispersed plantations, traditional grid-based CPP often causes redundant coverage over non-vegetated areas, leading to waste and pollution. To overcome these limitations, we propose CPP-DIP, a multi-objective CPP framework designed for Micro Air Vehicles (MAVs). The framework transforms the CPP task into a Traveling Salesman Problem (TSP) and optimizes flight paths by minimizing travel distance, turning angles, and intersection counts. Unlike conventional approaches, our method does not rely on GPS-based environmental modeling. Instead, it uses aerial imagery and a Histogram of Oriented Gradients (HOG)-based approach to detect trees and extract image coordinates. A density-aware waypoint strategy is applied: Kernel Density Estimation (KDE) is used to reduce redundant waypoints in dense regions, while a greedy algorithm ensures complete coverage in sparse areas. To verify the generality of the framework, we solve the resulting TSP using three different methods: Greedy Heuristic Insertion (GHI), Ant Colony Optimization (ACO), and Monte Carlo Reinforcement Learning (MCRL). Then an object-based optimization is applied to further refine the resulting path. Additionally, CPP-DIP integrates ForaNav, our insect-inspired navigation method, for accurate tree localization and tracking. The experimental results show that MCRL offers a balanced solution, reducing the travel distance by 16.9 % compared to ACO while maintaining a similar performance to GHI. It also improves path smoothness by reducing turning angles by 28.3 % and 59.9 % relative to ACO and GHI, respectively, and effectively eliminates intersections. These results confirm the robustness and effectiveness of CPP-DIP in different TSP solvers.

Diffusion probabilistic models (DPMs), widely recognized for their potential to generate high-quality samples, tend to go unnoticed in representation learning. While recent progress has highlighted their potential for capturing visual semantics, adapting DPMs to graph representation learning remains in its infancy. In this paper, we introduce Graffe, a self-supervised diffusion model proposed for graph representation learning. It features a graph encoder that distills a source graph into a compact representation, which, in turn, serves as the condition to guide the denoising process of the diffusion decoder. To evaluate the effectiveness of our model, we first explore the theoretical foundations of applying diffusion models to representation learning, proving that the denoising objective implicitly maximizes the conditional mutual information between data and its representation. Specifically, we prove that the negative logarithm of the denoising score matching loss is a tractable lower bound for the conditional mutual information. Empirically, we conduct a series of case studies to validate our theoretical insights. In addition, Graffe delivers competitive results under the linear probing setting on node and graph classification tasks, achieving state-of-the-art performance on 9 of the 11 real-world datasets. These findings indicate that powerful generative models, especially diffusion models, serve as an effective tool for graph representation learning.

Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a comprehensive account of IFNs, covering their theoretical foundations, construction methodologies, and diverse applications. Tracing their origins from early network-based models to advanced formulations such as the Triangulated Maximally Filtered Graph (TMFG) and the Maximally Filtered Clique Forest (MFCF), the paper highlights how IFNs address key challenges in high-dimensional data-driven modeling. IFNs and their construction methodologies are intrinsically higher-order networks that generate simplicial complexes-structures that are only now becoming popular in the broader literature. Applications span fields including finance, biology, psychology, and artificial intelligence, where IFNs improve interpretability, computational efficiency, and predictive performance. Special attention is given to their role in graphical modeling, where IFNs enable the estimation of sparse inverse covariance matrices with greater accuracy and scalability than traditional approaches like Graphical LASSO. Finally, the review discusses recent developments that integrate IFNs with machine learning and deep learning, underscoring their potential not only to bridge classical network theory with contemporary data-driven paradigms, but also to shape the architectures of deep learning models themselves.

In this note research and publications by Zdzisław Pawlak and his collaborators from 1970s and 1981 are recalled. Focus is placed on the sources of inspiration which one can identify on the basis of those publications. Finally, developments from 1981 related to rough sets and information systems are outlined.

This paper provides a formulation of the particle flow particle filter from the perspective of variational inference. We show that the transient density used to derive the particle flow particle filter follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density.

Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile estimate should, on average, reflect the desired probability of exceedance. In this research, we show that for unconditional distributions isomorphic to the exponential, a Bayesian quantile estimate results in zero coverage error. This compares to the traditional maximum likelihood method, where the coverage error can be significant under small sample sizes even though the quantile estimate is unbiased. More generally, we prove a sufficient condition for an unbiased quantile estimator to result in coverage error. Interestingly, our results hold by virtue of using a Jeffreys prior for the unknown parameters and is independent of the true prior. We also derive an expression for the distribution, and moments, of future exceedances which is vital for risk assessment. We extend our results to the conditional tail of distributions with asymptotic Paretian tails and, in particular, those in the Fréchet maximum domain of attraction. We illustrate our results using simulations for a variety of light and heavy-tailed distributions.

This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as a main target task. These basic ideas include loss formulation, backpropagation, stochastic gradient descent, generalization, model selection as well as fundamental blocks of artificial neural networks. Based on these basic ideas, the lecture note explores in depth the probablistic approach to unsupervised learning, covering directed latent variable models, product of experts, generative adversarial networks and autoregressive models. Finally, the note ends by covering a diverse set of further topics, such as reinforcement learning, ensemble methods and meta-learning. After reading this lecture note, a student should be ready to embark on studying and researching more advanced topics in machine learning and more broadly artificial intelligence.

When the likelihood is analytically unavailable and computationally intractable, approximate Bayesian computation (ABC) has emerged as a widely used methodology for approximate posterior inference; however, it suffers from severe computational inefficiency in high-dimensional settings or under diffuse priors. To overcome these limitations, we propose Adaptive Bayesian Inference (ABI), a framework that bypasses traditional data-space discrepancies and instead compares distributions directly in posterior space through nonparametric distribution matching. By leveraging a novel Marginally-augmented Sliced Wasserstein (MSW) distance on posterior measures and exploiting its quantile representation, ABI transforms the challenging problem of measuring divergence between posterior distributions into a tractable sequence of one-dimensional conditional quantile regression tasks. Moreover, we introduce a new adaptive rejection sampling scheme that iteratively refines the posterior approximation by updating the proposal distribution via generative density estimation. Theoretically, we establish parametric convergence rates for the trimmed MSW distance and prove that the ABI posterior converges to the true posterior as the tolerance threshold vanishes. Through extensive empirical evaluation, we demonstrate that ABI significantly outperforms data-based Wasserstein ABC, summary-based ABC, and state-of-the-art likelihood-free simulators, especially in high-dimensional or dependent observation regimes.

We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics, considered in depth in the forthcoming book \cite{LMPT2024}.