It has long been posited that there is a connection between the dynamical equations describing evolutionary processes in biology and sequential Bayesian learning methods. This manuscript describes new research in which this precise connection is rigorously established in the continuous time setting. Here we focus on a partial differential equation known as the Kushner-Stratonovich equation describing the evolution of the posterior density in time. Of particular importance is a piecewise smooth approximation of the observation path from which the discrete time filtering equations, which are shown to converge to a Stratonovich interpretation of the Kushner-Stratonovich equation. This smooth formulation will then be used to draw precise connections between nonlinear stochastic filtering and replicator-mutator dynamics. Additionally, gradient flow formulations will be investigated as well as a form of replicator-mutator dynamics which is shown to be beneficial for the misspecified model filtering problem. It is hoped this work will spur further research into exchanges between sequential learning and evolutionary biology and to inspire new algorithms in filtering and sampling.

Understanding the inner mechanisms of black-box foundation models (FMs) is essential yet challenging in artificial intelligence and its applications. Over the last decade, the long-running focus has been on their explainability, leading to the development of post-hoc explainable methods to rationalize the specific decisions already made by black-box FMs. However, these explainable methods have certain limitations in terms of faithfulness and resource requirement. Consequently, a new class of interpretable methods should be considered to unveil the underlying mechanisms of FMs in an accurate, comprehensive, heuristic, and resource-light way. This survey aims to review those interpretable methods that comply with the aforementioned principles and have been successfully applied to FMs. These methods are deeply rooted in machine learning theory, covering the analysis of generalization performance, expressive capability, and dynamic behavior. They provide a thorough interpretation of the entire workflow of FMs, ranging from the inference capability and training dynamics to their ethical implications. Ultimately, drawing upon these interpretations, this review identifies the next frontier research directions for FMs.

Large-scale generative models have achieved remarkable success in a number of domains. However, for sequential decision-making problems, such as robotics, action-labelled data is often scarce and therefore scaling-up foundation models for decision-making remains a challenge. A potential solution lies in leveraging widely-available unlabelled videos to train world models that simulate the consequences of actions. If the world model is accurate, it can be used to optimize decision-making in downstream tasks. Image-to-video diffusion models are already capable of generating highly realistic synthetic videos. However, these models are not action-conditioned, and the most powerful models are closedsource which means they cannot be finetuned. In this work, we propose to adapt pretrained video diffusion models to action-conditioned world models, without access to the parameters of the pretrained model. Our approach, AVID, trains an adapter on a small domain-specific dataset of action-labelled videos. AVID uses a learned mask to modify the intermediate outputs of the pretrained model and generate accurate action-conditioned videos. We evaluate AVID on video game and real-world robotics data, and show that it outperforms existing baselines for diffusion model adaptation. Our results demonstrate that if utilized correctly, pretrained video models have the potential to be powerful tools for embodied AI. Large generative models trained on web-scale data have driven rapid improvement in natural language processing (Brown, 2020; Touvron et al., 2023; Achiam et al., 2023), image generation (Rombach et al., 2022), and video generation (OpenAI, 2024).

Phishing is one of the most effective ways in which cybercriminals get sensitive details such as credentials for online banking, digital wallets, state secrets, and many more from potential victims. They do this by spamming users with malicious URLs with the sole purpose of tricking them into divulging sensitive information which is later used for various cybercrimes. In this research, we did a comprehensive review of current state-of-the-art machine learning and deep learning phishing detection techniques to expose their vulnerabilities and future research direction. For better analysis and observation, we split machine learning techniques into Bayesian, non-Bayesian, and deep learning. We reviewed the most recent advances in Bayesian and non-Bayesian-based classifiers before exploiting their corresponding weaknesses to indicate future research direction. While exploiting weaknesses in both Bayesian and non-Bayesian classifiers, we also compared each performance with a deep learning classifier. For a proper review of deep learning-based classifiers, we looked at Recurrent Neural Networks (RNN), Convolutional Neural Networks (CNN), and Long Short Term Memory Networks (LSTMs). We did an empirical analysis to evaluate the performance of each classifier along with many of the proposed state-of-the-art anti-phishing techniques to identify future research directions, we also made a series of proposals on how the performance of the under-performing algorithm can improved in addition to a two-stage prediction model

In the big data era, integrating information from multiple heterogeneous sources has become increasingly crucial for achieving larger sample sizes and more diverse study populations. The applications of data integration are in a variety of fields, including but not limited to, causal inference on heterogeneous populations (Shi et al., 2023), survey sampling (Yang et al., 2020), health policy (Paddock et al., 2024), retrospective psychometrics (Howe and Brown, 2023), and multi-omics biological science (Du et al., 2022). Data integration methods have been proposed to mitigate the unwanted effects of heterogeneous datasets and unmeasured covariates, recovering the common variation across datasets. However, a critical and often overlooked question is whether reliable statistical inference can be made from integrated data. Directly performing statistical inference on integrated outcomes and covariates of interests fails to account for the complex correlation structures introduced by the data integration process, often leading to improper analyses that incorrectly assume the corrected data points are independent (Li et al., 2023). While data integration is broadly utilized in various fields, our paper focuses on a challenging scenario with the presence of high-dimensional outcomes.

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare a wide range of Markov Chain Monte Carlo (MCMC) and nested sampling techniques to determine their relative efficacy on functions that resemble those encountered most frequently in the particle astrophysics literature. Our first series of tests explores a series of high-dimensional analytic test functions that exemplify particular challenges, for example highly multimodal posteriors or posteriors with curving degeneracies. We then investigate two real physics examples, the first being a global fit of the $\Lambda$CDM model using cosmic microwave background data from the Planck experiment, and the second being a global fit of the Minimal Supersymmetric Standard Model using a wide variety of collider and astrophysics data. We show that several examples widely thought to be most easily solved using nested sampling approaches can in fact be more efficiently solved using modern MCMC algorithms, but the details of the implementation matter. Furthermore, we also provide a series of useful insights for practitioners of particle astrophysics and cosmology.

The Bayesian paradigm offers the possibility to incorporate prior knowledge into a statistical model through the specification of prior distributions. This possibility is a central advantage of the Bayesian paradigm (Mikkola et al 2023), yet it also presents one of its most challenging aspects (Simpson et al 2017; lgorzata Roos et al 2015; Van Dongen 2006). In the following, we define prior knowledge as the expertise provided by a domain expert -- an individual with extensive knowledge of a specific subject matter (Falconer et al 2022). This knowledge can be represented in various forms, but to integrate it into a Bayesian model, we need to translate it into a formal mathematical language that can be expressed as a prior distribution over the model parameters (Perepolkin et al 2023; O'Hagan 2019; Martin et al 2012; Garthwaite et al 2005). A whole field of research, commonly referred to as (expert) prior elicitation, has emerged around the question of how to gather expert knowledge and translate it into appropriate prior distributions (Stefan et al 2022; Mikkola et al 2023; Falconer et al 2022).

Effective extraction of the world knowledge in LLMs for complex decision-making tasks remains a challenge. We propose a framework PIANIST for decomposing the world model into seven intuitive components conducive to zero-shot LLM generation. Given only the natural language description of the game and how input observations are formatted, our method can generate a working world model for fast and efficient MCTS simulation. We show that our method works well on two different games that challenge the planning and decision making skills of the agent for both language and non-language based action taking, without any training on domain-specific training data or explicitly defined world model.

Precision matrix estimation is essential in various fields, yet it is challenging when samples for the target study are limited. Transfer learning can enhance estimation accuracy by leveraging data from related source studies. We propose Trans-Glasso, a two-step transfer learning method for precision matrix estimation. First, we obtain initial estimators using a multi-task learning objective that captures shared and unique features across studies. Then, we refine these estimators through differential network estimation to adjust for structural differences between the target and source precision matrices. Under the assumption that most entries of the target precision matrix are shared with source matrices, we derive non-asymptotic error bounds and show that Trans-Glasso achieves minimax optimality under certain conditions. Extensive simulations demonstrate Trans Glasso's superior performance compared to baseline methods, particularly in small-sample settings. We further validate Trans-Glasso in applications to gene networks across brain tissues and protein networks for various cancer subtypes, showcasing its effectiveness in biological contexts. Additionally, we derive the minimax optimal rate for differential network estimation, representing the first such guarantee in this area.

Multimodal Learning Analytics (MMLA) leverages advanced sensing technologies and artificial intelligence to capture complex learning processes, but integrating diverse data sources into cohesive insights remains challenging. This study introduces a novel methodology for integrating latent class analysis (LCA) within MMLA to map monomodal behavioural indicators into parsimonious multimodal ones. Using a high-fidelity healthcare simulation context, we collected positional, audio, and physiological data, deriving 17 monomodal indicators. LCA identified four distinct latent classes: Collaborative Communication, Embodied Collaboration, Distant Interaction, and Solitary Engagement, each capturing unique monomodal patterns. Epistemic network analysis compared these multimodal indicators with the original monomodal indicators and found that the multimodal approach was more parsimonious while offering higher explanatory power regarding students' task and collaboration performances. The findings highlight the potential of LCA in simplifying the analysis of complex multimodal data while capturing nuanced, cross-modality behaviours, offering actionable insights for educators and enhancing the design of collaborative learning interventions. This study proposes a pathway for advancing MMLA, making it more parsimonious and manageable, and aligning with the principles of learner-centred education.