This paper proposes a novel analytical framework: Transition Network Analysis (TNA), an approach that integrates Stochastic Process Mining and probabilistic graph representation to model, visualize, and identify transition patterns in the learning process data. Combining the relational and temporal aspects into a single lens offers capabilities beyond either framework, including centralities to capture important learning events, community finding to identify patterns of behavior, and clustering to reveal temporal patterns. This paper introduces the theoretical and mathematical foundations of TNA. To demonstrate the functionalities of TNA, we present a case study with students (n=191) engaged in small-group collaboration to map patterns of group dynamics using the theories of co-regulation and socially-shared regulated learning. The analysis revealed that TNA could reveal the regulatory processes and identify important events, temporal patterns and clusters. Bootstrap validation established the significant transitions and eliminated spurious transitions. In doing so, we showcase TNA's utility to capture learning dynamics and provide a robust framework for investigating the temporal evolution of learning processes. Future directions include advancing estimation methods, expanding reliability assessment, exploring longitudinal TNA, and comparing TNA networks using permutation tests.

Bayesian Optimization (BO) is widely used for optimising black-box functions but requires us to specify the length scale hyperparameter, which defines the smoothness of the functions the optimizer will consider. Most current BO algorithms choose this hyperparameter by maximizing the marginal likelihood of the observed data, albeit risking misspecification if the objective function is less smooth in regions we have not yet explored. The only prior solution addressing this problem with theoretical guarantees was A-GP-UCB, proposed by Berkenkamp et al. (2019). This algorithm progressively decreases the length scale, expanding the class of functions considered by the optimizer. However, A-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow convergence. To overcome this, we introduce Length scale Balancing (LB) - a novel approach, aggregating multiple base surrogate models with varying length scales. LB intermittently adds smaller length scale candidate values while retaining longer scales, balancing exploration and exploitation. We formally derive a cumulative regret bound of LB and compare it with the regret of an oracle BO algorithm using the optimal length scale. Denoting the factor by which the regret bound of A-GP-UCB was away from oracle as $g(T)$, we show that LB is only $\log g(T)$ away from oracle regret. We also empirically evaluate our algorithm on synthetic and real-world benchmarks and show it outperforms A-GP-UCB, maximum likelihood estimation and MCMC.

As the availability of financial services online continues to grow, the incidence of fraud has surged correspondingly. Fraudsters continually seek new and innovative ways to circumvent the detection algorithms in place. Traditionally, fraud detection relied on rule-based methods, where rules were manually created based on transaction data features. However, these techniques soon became ineffective due to their reliance on manual rule creation and their inability to detect complex data patterns. Today, a significant portion of the financial services sector employs various machine learning algorithms, such as XGBoost, Random Forest, and neural networks, to model transaction data. While these techniques have proven more efficient than rule-based methods, they still fail to capture interactions between different transactions and their interrelationships. Recently, graph-based techniques have been adopted for financial fraud detection, leveraging graph topology to aggregate neighborhood information of transaction data using Graph Neural Networks (GNNs). Despite showing improvements over previous methods, these techniques still struggle to keep pace with the evolving camouflaging tactics of fraudsters and suffer from information loss due to over-smoothing. In this paper, we propose a novel algorithm that employs an efficient neighborhood sampling method, effective for camouflage detection and preserving crucial feature information from non-similar nodes. Additionally, we introduce a novel GNN architecture that utilizes attention mechanisms and preserves holistic neighborhood information to prevent information loss. We test our algorithm on financial data to show that our method outperforms other state-of-the-art graph algorithms.

We show that deep neural networks achieve dimension-independent rates of convergence for learning structured densities such as those arising in image, audio, video, and text applications. More precisely, we demonstrate that neural networks with a simple $L^2$-minimizing loss achieve a rate of $n^{-1/(4+r)}$ in nonparametric density estimation when the underlying density is Markov to a graph whose maximum clique size is at most $r$, and we provide evidence that in the aforementioned applications, this size is typically constant, i.e., $r=O(1)$. We then establish that the optimal rate in $L^1$ is $n^{-1/(2+r)}$ which, compared to the standard nonparametric rate of $n^{-1/(2+d)}$, reveals that the effective dimension of such problems is the size of the largest clique in the Markov random field. These rates are independent of the data's ambient dimension, making them applicable to realistic models of image, sound, video, and text data. Our results provide a novel justification for deep learning's ability to circumvent the curse of dimensionality, demonstrating dimension-independent convergence rates in these contexts.

In the last decade, the free energy principle (FEP) and active inference (AIF) have achieved many successes connecting conceptual models of learning and cognition to mathematical models of perception and action. This effort is driven by a multidisciplinary interest in understanding aspects of self-organizing complex adaptive systems, including elements of agency. Various reinforcement learning (RL) models performing active inference have been proposed and trained on standard RL tasks using deep neural networks. Recent work has focused on improving such agents' performance in complex environments by incorporating the latest machine learning techniques. In this paper, we take an alternative approach. Within the constraints imposed by the FEP and AIF, we attempt to model agents in an interpretable way without deep neural networks by introducing Free Energy Projective Simulation (FEPS). Using internal rewards only, FEPS agents build a representation of their partially observable environments with which they interact. Following AIF, the policy to achieve a given task is derived from this world model by minimizing the expected free energy. Leveraging the interpretability of the model, techniques are introduced to deal with long-term goals and reduce prediction errors caused by erroneous hidden state estimation. We test the FEPS model on two RL environments inspired from behavioral biology: a timed response task and a navigation task in a partially observable grid. Our results show that FEPS agents fully resolve the ambiguity of both environments by appropriately contextualizing their observations based on prediction accuracy only. In addition, they infer optimal policies flexibly for any target observation in the environment.

Understanding human mobility behavior is crucial for numerous applications, including crowd management, location-based recommendations, and the estimation of pandemic spread. Machine learning models can predict the Points of Interest (POIs) that individuals are likely to visit in the future by analyzing their historical visit patterns. Previous studies address this problem by learning a POI classifier, where each class corresponds to a POI. However, this limits their applicability to predict a new POI that was not in the training data, such as the opening of new restaurants. To address this challenge, we propose a model designed to predict a new POI outside the training data as long as its context is aligned with the user's interests. Unlike existing approaches that directly predict specific POIs, our model first forecasts the semantic context of potential future POIs, then combines this with a proximity-based prior probability distribution to determine the exact POI. Experimental results on real-world visit data demonstrate that our model outperforms baseline methods that do not account for semantic contexts, achieving a 17% improvement in accuracy. Notably, as new POIs are introduced over time, our model remains robust, exhibiting a lower decline rate in prediction accuracy compared to existing methods.

Named Entity Recognition (NER) is a machine learning task that traditionally relies on supervised learning and annotated data. Acquiring such data is often a challenge, particularly in specialized fields like medical, legal, and financial sectors. Those are commonly referred to as low-resource domains, which comprise long-tail entities, due to the scarcity of available data. To address this, data augmentation techniques are increasingly being employed to generate additional training instances from the original dataset. In this study, we evaluate the effectiveness of two prominent text augmentation techniques, Mention Replacement and Contextual Word Replacement, on two widely-used NER models, Bi-LSTM+CRF and BERT. We conduct experiments on four datasets from low-resource domains, and we explore the impact of various combinations of training subset sizes and number of augmented examples. We not only confirm that data augmentation is particularly beneficial for smaller datasets, but we also demonstrate that there is no universally optimal number of augmented examples, i.e., NER practitioners must experiment with different quantities in order to fine-tune their projects.

Multiple linear regression provides a simple, but widely used, method to find associations between outcomes (responses) and a set of predictors (explanatory variables). It has been actively studied over more than a century, and there is a rich and vast literature on the subject [1]. In practical situations the number of predictor variables is often large, and it becomes desirable to induce sparsity in the regression coefficients to avoid overfitting [2, 3]. Sparse linear regression also serves as the foundation for non-linear techniques, such as trendfiltering [4, 5], which can estimate an underlying non-linear trend from time series data. Applications of sparse multiple linear regression and trendfiltering arise in a wide range of applications in modern science and engineering, including astronomy [6], atmospheric sciences [7], biology [8], economics [9, 10], genetics [11-15], geophysics [16], medical sciences [17, 18], social sciences [19] and text analysis [20]. Approaches to sparse linear regression can be broadly classified into two groups: (a) penalized linear regressions (PLR), which add a penalty term to the likelihood to penalize the magnitude of its parameters [21-23], and (b) Bayesian approaches [11-14, 24-29], which use a prior probability distribution on the model parameters to induce sparsity.

We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. The method leverages latent variables within variational autoencoders to efficiently estimate complex posterior distributions arising from stochastic simulations. We explore two variations of this approach distinguished by their treatment of the prior distribution. The first model adapts the prior based on observed data using a multivariate prior network, enhancing generalization across various posterior queries. In contrast, the second model utilizes a standard Gaussian prior, offering simplicity while still effectively capturing complex posterior distributions. We demonstrate the efficacy of these models on well-established benchmark problems, achieving results comparable to flow-based approaches while maintaining computational efficiency and scalability.

When human operators of cyber-physical systems encounter surprising behavior, they often consider multiple hypotheses that might explain it. In some cases, taking information-gathering actions such as additional measurements or control inputs given to the system can help resolve uncertainty and determine the most accurate hypothesis. The task of optimizing these actions can be formulated as a belief-space Markov decision process that we call a hypothesis-driven belief MDP. Unfortunately, this problem suffers from the curse of history similar to a partially observable Markov decision process (POMDP). To plan in continuous domains, an agent needs to reason over countlessly many possible action-observation histories, each resulting in a different belief over the unknown state. The problem is exacerbated in the hypothesis-driven context because each action-observation pair spawns a different belief for each hypothesis, leading to additional branching. This paper considers the case in which each hypothesis corresponds to a different dynamic model in an underlying POMDP. We present a new belief MDP formulation that: (i) enables reasoning over multiple hypotheses, (ii) balances the goals of determining the (most likely) correct hypothesis and performing well in the underlying POMDP, and (iii) can be solved with sparse tree search.