Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from observational data is a challenging task, especially when individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present the first comprehensive approach for jointly estimating the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we prove that these parameters are identifiable from marginals if and only if the initial distribution is not invariant to a class of generalized rotations, a condition that is satisfied by most distributions. We further prove that the causal graph of any SDE with additive diffusion can be recovered from the SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion, and introduce APPEX (Alternating Projection Parameter Estimation from $X_0$), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals. We show that each of these steps are asymptotically optimal with respect to the Kullback-Leibler divergence, and demonstrate APPEX's effectiveness on simulated data from linear additive noise SDEs.

Determining the reliability of evidence sources is a crucial topic in Dempster-Shafer theory (DST). Previous approaches have addressed high conflicts between evidence sources using discounting methods, but these methods may not ensure the high efficiency of classification models. In this paper, we consider the combination of DS theory and Intuitionistic Fuzzy Sets (IFS) and propose an algorithm for quantifying the reliability of evidence sources, called Fuzzy Reliability Index (FRI). The FRI algorithm is based on decision quantification rules derived from IFS, defining the contribution of different BPAs to correct decisions and deriving the evidential reliability from these contributions. The proposed method effectively enhances the rationality of reliability estimation for evidence sources, making it particularly suitable for classification decision problems in complex scenarios. Subsequent comparisons with DST-based algorithms and classical machine learning algorithms demonstrate the superiority and generalizability of the FRI algorithm. The FRI algorithm provides a new perspective for future decision probability conversion and reliability analysis of evidence sources.

Crime linkage is the process of analyzing criminal behavior data to determine whether a pair or group of crime cases are connected or belong to a series of offenses. This domain has been extensively studied by researchers in sociology, psychology, and statistics. More recently, it has drawn interest from computer scientists, especially with advances in artificial intelligence. Despite this, the literature indicates that work in this latter discipline is still in its early stages. This study aims to understand the challenges faced by machine learning approaches in crime linkage and to support foundational knowledge for future data-driven methods. To achieve this goal, we conducted a comprehensive survey of the main literature on the topic and developed a general framework for crime linkage processes, thoroughly describing each step. Our goal was to unify insights from diverse fields into a shared terminology to enhance the research landscape for those intrigued by this subject.

Diverse computing paradigms have emerged to meet the growing needs for intelligent energy-efficient systems. The Margin Propagation (MP) framework, being one such initiative in the analog computing domain, stands out due to its scalability across biasing conditions, temperatures, and diminishing process technology nodes. However, the lack of digital-like automation tools for designing analog systems (including that of MP analog) hinders their adoption for designing large systems. The inherent scalability and modularity of MP systems present a unique opportunity in this regard. This paper introduces KALAM (toolKit for Automating high-Level synthesis of Analog computing systeMs), which leverages factor graphs as the foundational paradigm for synthesizing MP-based analog computing systems. Factor graphs are the basis of various signal processing tasks and, when coupled with MP, can be used to design scalable and energy-efficient analog signal processors. Using Python scripting language, the KALAM automation flow translates an input factor graph to its equivalent SPICE-compatible circuit netlist that can be used to validate the intended functionality. KALAM also allows the integration of design optimization strategies such as precision tuning, variable elimination, and mathematical simplification. We demonstrate KALAM's versatility for tasks such as Bayesian inference, Low-Density Parity Check (LDPC) decoding, and Artificial Neural Networks (ANN). Simulation results of the netlists align closely with software implementations, affirming the efficacy of our proposed automation tool.

What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring rules and calibration. For the case of imprecise probabilistic forecasts (sets of probabilities), such theory is still lacking. In this work, we therefore generalize proper scoring rules and calibration to the imprecise case. We develop these concepts as relative to data models and decision problems. As a consequence, the imprecision is embedded in a clear context. We establish a close link to the paradigm of (group) distributional robustness and in doing so provide new insights for it. We argue that proper scoring rules and calibration serve two distinct goals, which are aligned in the precise case, but intriguingly are not necessarily aligned in the imprecise case. The concept of decision-theoretic entropy plays a key role for both goals. Finally, we demonstrate the theoretical insights in machine learning practice, in particular we illustrate subtle pitfalls relating to the choice of loss function in distributional robustness.

In pattern recognition, handling uncertainty is a critical challenge that significantly affects decision-making and classification accuracy. Dempster-Shafer Theory (DST) is an effective reasoning framework for addressing uncertainty, and the Random Permutation Set (RPS) extends DST by additionally considering the internal order of elements, forming a more ordered extension of DST. However, there is a lack of a transformation method based on permutation order between RPS and DST, as well as a sequence-based probability transformation method for RPS. Moreover, the reliability of RPS sources remains an issue that requires attention. To address these challenges, this paper proposes an RPS transformation approach and a probability transformation method tailored for RPS. On this basis, a reliability computation method for RPS sources, based on the RPS probability transformation, is introduced and applied to pattern recognition. Experimental results demonstrate that the proposed approach effectively bridges the gap between DST and RPS and achieves superior recognition accuracy in classification problems.

PET imaging is widely employed for observing biological metabolic activities within the human body. However, numerous benign conditions can cause increased uptake of radiopharmaceuticals, confounding differentiation from malignant tumors. Several studies have indicated that dual-time PET imaging holds promise in distinguishing between malignant and benign tumor processes. Nevertheless, the hour-long distribution period of radiopharmaceuticals post-injection complicates the determination of optimal timing for the second scan, presenting challenges in both practical applications and research. Notably, we have identified that delay time PET imaging can be framed as an image-to-image conversion problem. Motivated by this insight, we propose a novel spatial-temporal guided diffusion transformer probabilistic model (st-DTPM) to solve dual-time PET imaging prediction problem. Specifically, this architecture leverages the U-net framework that integrates patch-wise features of CNN and pixel-wise relevance of Transformer to obtain local and global information. And then employs a conditional DDPM model for image synthesis. Furthermore, on spatial condition, we concatenate early scan PET images and noisy PET images on every denoising step to guide the spatial distribution of denoising sampling. On temporal condition, we convert diffusion time steps and delay time to a universal time vector, then embed it to each layer of model architecture to further improve the accuracy of predictions. Experimental results demonstrated the superiority of our method over alternative approaches in preserving image quality and structural information, thereby affirming its efficacy in predictive task.

Sequential learning in deep models often suffers from challenges such as catastrophic forgetting and loss of plasticity, largely due to the permutation dependence of gradient-based algorithms, where the order of training data impacts the learning outcome. In this work, we introduce a novel permutation-invariant learning framework based on high-dimensional particle filters. We theoretically demonstrate that particle filters are invariant to the sequential ordering of training minibatches or tasks, offering a principled solution to mitigate catastrophic forgetting and loss-of-plasticity. We develop an efficient particle filter for optimizing high-dimensional models, combining the strengths of Bayesian methods with gradient-based optimization. Through extensive experiments on continual supervised and reinforcement learning benchmarks, including SplitMNIST, SplitCIFAR100, and ProcGen, we empirically show that our method consistently improves performance, while reducing variance compared to standard baselines.

Mobile health (mHealth) programs face a critical challenge in optimizing the timing of automated health information calls to beneficiaries. This challenge has been formulated as a collaborative multi-armed bandit problem, requiring online learning of a low-rank reward matrix. Existing solutions often rely on heuristic combinations of offline matrix completion and exploration strategies. In this work, we propose a principled Bayesian approach using Thompson Sampling for this collaborative bandit problem. Our method leverages prior information through efficient Gibbs sampling for posterior inference over the low-rank matrix factors, enabling faster convergence. We demonstrate significant improvements over state-of-the-art baselines on a real-world dataset from the world's largest maternal mHealth program. Our approach achieves a $16\%$ reduction in the number of calls compared to existing methods and a $47$\% reduction compared to the deployed random policy. This efficiency gain translates to a potential increase in program capacity by $0.5-1.4$ million beneficiaries, granting them access to vital ante-natal and post-natal care information. Furthermore, we observe a $7\%$ and $29\%$ improvement in beneficiary retention (an extremely hard metric to impact) compared to state-of-the-art and deployed baselines, respectively. Synthetic simulations further demonstrate the superiority of our approach, particularly in low-data regimes and in effectively utilizing prior information. We also provide a theoretical analysis of our algorithm in a special setting using Eluder dimension.

Disease progression models infer group-level temporal trajectories of change in patients' features as a chronic degenerative condition plays out. They provide unique insight into disease biology and staging systems with individual-level clinical utility. Discrete models consider disease progression as a latent permutation of events, where each event corresponds to a feature becoming measurably abnormal. However, permutation inference using traditional maximum likelihood approaches becomes prohibitive due to combinatoric explosion, severely limiting model dimensionality and utility. Here we leverage ideas from optimal transport to model disease progression as a latent permutation matrix of events belonging to the Birkhoff polytope, facilitating fast inference via optimisation of the variational lower bound. This enables a factor of 1000 times faster inference than the current state of the art and, correspondingly, supports models with several orders of magnitude more features than the current state of the art can consider. Experiments demonstrate the increase in speed, accuracy and robustness to noise in simulation. Further experiments with real-world imaging data from two separate datasets, one from Alzheimer's disease patients, the other age-related macular degeneration, showcase, for the first time, pixel-level disease progression events in the brain and eye, respectively. Our method is low compute, interpretable and applicable to any progressive condition and data modality, giving it broad potential clinical utility.