The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time discrete trajectory data provided by experiments. In many cases second order Langevin models are needed to adequately capture the motility. Additionally, population heterogeneity needs to be taken into account when analyzing data from several individual organisms. In this work, we describe a maximum likelihood approach to infer dynamical, stochastic models and, simultaneously, estimate the heterogeneity in a population of motile active particles from discretely sampled, stochastic trajectories. To this end we propose a new method to approximate the likelihood for non-linear second order Langevin models. We show that this maximum likelihood ansatz outperforms alternative approaches especially for short trajectories. Additionally, we demonstrate how a measure of uncertainty for the heterogeneity estimate can be derived. We thereby pave the way for the systematic, data-driven inference of dynamical models for actively driven entities based on trajectory data, deciphering temporal fluctuations and inter-particle variability.

This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.

The Poisson compound decision problem is a classical problem in statistics, for which parametric and nonparametric empirical Bayes methodologies are available to estimate the Poisson's means in static or batch domains. In this paper, we consider the Poisson compound decision problem in a streaming or online domain. By relying on a quasi-Bayesian approach, often referred to as Newton's algorithm, we obtain sequential Poisson's mean estimates that are of easy evaluation, computationally efficient and with a constant computational cost as data increase, which is desirable for streaming data. Large sample asymptotic properties of the proposed estimates are investigated, also providing frequentist guarantees in terms of a regret analysis. We validate empirically our methodology, both on synthetic and real data, comparing against the most popular alternatives.

Integral projection models (IPMs) are widely used to study population growth and the dynamics of demographic structure (e.g. age and size distributions) within a population.These models use data on individuals' growth, survival, and reproduction to predict changes in the population from one time point to the next and use these in turn to ask about long-term growth rates, the sensitivity of that growth rate to environmental factors, and aspects of the long term population such as how much reproduction concentrates in a few individuals; these quantities are not directly measurable from data and must be inferred from the model. Building IPMs requires us to develop models for individual fates over the next time step -- Did they survive? How much did they grow or shrink? Did they Reproduce? -- conditional on their initial state as well as on environmental covariates in a manner that accounts for the unobservable quantities that are are ultimately interested in estimating.Targeted maximum likelihood estimation (TMLE) methods are particularly well-suited to a framework in which we are largely interested in the consequences of models. These build machine learning-based models that estimate the probability distribution of the data we observe and define a target of inference as a function of these. The initial estimate for the distribution is then modified by tilting in the direction of the efficient influence function to both de-bias the parameter estimate and provide more accurate inference. In this paper, we employ TMLE to develop robust and efficient estimators for properties derived from a fitted IPM. Mathematically, we derive the efficient influence function and formulate the paths for the least favorable sub-models. Empirically, we conduct extensive simulations using real data from both long term studies of Idaho steppe plant communities and experimental Rotifer populations.

Lifting uses a representative of indistinguishable individuals to exploit symmetries in probabilistic relational models, denoted as parametric factor graphs, to speed up inference while maintaining exact answers. In this paper, we show how lifting can be applied to causal inference in partially directed graphs, i.e., graphs that contain both directed and undirected edges to represent causal relationships between random variables. We present partially directed parametric causal factor graphs (PPCFGs) as a generalisation of previously introduced parametric causal factor graphs, which require a fully directed graph. We further show how causal inference can be performed on a lifted level in PPCFGs, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships. Keywords: causal models; probabilistic relational models; lifted inference.

Understanding how individual agents make strategic decisions within collectives is important for advancing fields as diverse as economics, neuroscience, and multi-agent systems. Two complementary approaches can be integrated to this end. The Active Inference framework (AIF) describes how agents employ a generative model to adapt their beliefs about and behaviour within their environment. Game theory formalises strategic interactions between agents with potentially competing objectives. To bridge the gap between the two, we propose a factorisation of the generative model whereby each agent maintains explicit, individual-level beliefs about the internal states of other agents, and uses them for strategic planning in a joint context. We apply our model to iterated general-sum games with 2 and 3 players, and study the ensemble effects of game transitions, where the agents' preferences (game payoffs) change over time. This non-stationarity, beyond that caused by reciprocal adaptation, reflects a more naturalistic environment in which agents need to adapt to changing social contexts. Finally, we present a dynamical analysis of key AIF quantities: the variational free energy (VFE) and the expected free energy (EFE) from numerical simulation data. The ensemble-level EFE allows us to characterise the basins of attraction of games with multiple Nash Equilibria under different conditions, and we find that it is not necessarily minimised at the aggregate level. By integrating AIF and game theory, we can gain deeper insights into how intelligent collectives emerge, learn, and optimise their actions in dynamic environments, both cooperative and non-cooperative.

The adaptation to users' preferences and the ability to infer and interpret humans' beliefs and intents, which is known as the Theory of Mind (ToM), are two crucial aspects for achieving effective human-robot collaboration. Despite its importance, very few studies have investigated the impact of adaptive robots with ToM abilities. In this work, we present an exploratory comparative study to investigate how social robots equipped with ToM abilities impact users' performance and perception. We design a two-layer architecture. The Q-learning agent on the first layer learns the robot's higher-level behaviour. On the second layer, a heuristic-based ToM infers the user's intended strategy and is responsible for implementing the robot's assistance, as well as providing the motivation behind its choice. We conducted a user study in a real-world setting, involving 56 participants who interacted with either an adaptive robot capable of ToM, or with a robot lacking such abilities. Our findings suggest that participants in the ToM condition performed better, accepted the robot's assistance more often, and perceived its ability to adapt, predict and recognise their intents to a higher degree. Our preliminary insights could inform future research and pave the way for designing more complex computation architectures for adaptive behaviour with ToM capabilities.

The acquisition of real-time and accurate traffic arrival information is of vital importance for proactive traffic control systems, especially in partially connected vehicle environments. License plate recognition (LPR) data that record both vehicle departures and identities are proven to be desirable in reconstructing lane-based arrival curves in previous works. Existing LPR databased methods are predominantly designed for reconstructing historical arrival curves. For real-time reconstruction of multi-lane urban roads, it is pivotal to determine the lane choice of real-time link-based arrivals, which has not been exploited in previous studies. In this study, we propose a Bayesian deep learning approach for real-time lane-based arrival curve reconstruction, in which the lane choice patterns and uncertainties of link-based arrivals are both characterized. Specifically, the learning process is designed to effectively capture the relationship between partially observed link-based arrivals and lane-based arrivals, which can be physically interpreted as lane choice proportion. Moreover, the lane choice uncertainties are characterized using Bayesian parameter inference techniques, minimizing arrival curve reconstruction uncertainties, especially in low LPR data matching rate conditions. Real-world experiment results conducted in multiple matching rate scenarios demonstrate the superiority and necessity of lane choice modeling in reconstructing arrival curves.

Humans excel at adapting perceptions and actions to diverse environments, enabling efficient interaction with the external world. This adaptive capability relies on the biological nervous system (BNS), which activates different brain regions for distinct tasks. Meta-learning similarly trains machines to handle multiple tasks but relies on a fixed network structure, not as flexible as BNS. To investigate the role of flexible network structure (FNS) in meta-learning, we conduct extensive empirical and theoretical analyses, finding that model performance is tied to structure, with no universally optimal pattern across tasks. This reveals the crucial role of FNS in meta-learning, ensuring meta-learning to generate the optimal structure for each task, thereby maximizing the performance and learning efficiency of meta-learning. Motivated by this insight, we propose to define, measure, and model FNS in meta-learning. First, we define that an effective FNS should possess frugality, plasticity, and sensitivity. Then, to quantify FNS in practice, we present three measurements for these properties, collectively forming the \emph{structure constraint} with theoretical supports. Building on this, we finally propose Neuromodulated Meta-Learning (NeuronML) to model FNS in meta-learning. It utilizes bi-level optimization to update both weights and structure with the structure constraint. Extensive theoretical and empirical evaluations demonstrate the effectiveness of NeuronML on various tasks. Code is publicly available at \href{https://github.com/WangJingyao07/NeuronML}{https://github.com/WangJingyao07/NeuronML}.

Country instability is a global issue, with unpredictably high levels of instability thwarting socio-economic growth and possibly causing a slew of negative consequences. As a result, uncertainty prediction models for a country are becoming increasingly important in the real world, and they are expanding to provide more input from 'big data' collections, as well as the interconnectedness of global economies and social networks. This has culminated in massive volumes of qualitative data from outlets like television, print, digital, and social media, necessitating the use of artificial intelligence (AI) tools like machine learning to make sense of it all and promote predictive precision [1]. The Global Database of Activities, Voice, and Tone (GDELT Project) records broadcast, print, and web news in over 100 languages every second of every day, identifying the people, locations, organisations, counts, themes, outlets, and events that propel our global community and offering a free open platform for computation on the entire world. The main goal of our research is to investigate how, when our data grows more voluminous and fine-grained, we can conduct a more complex methodological analysis of political conflict. The GDELT dataset, which was released in 2012, is the first and potentially the most technologically sophisticated publicly accessible dataset on political conflict.