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.

When designing correct-by-construction controllers for autonomous collectives, three key challenges are the task specification, the modelling, and its use at practical scale. In this paper, we focus on a simple yet useful abstraction for high-level controller synthesis for robot collectives with optimisation goals (e.g., maximum cleanliness, minimum energy consumption) and recurrence (e.g., re-establish contamination and charge thresholds) and safety (e.g., avoid full discharge, mutually exclusive room occupation) constraints. Due to technical limitations (related to scalability and using constraints in the synthesis), we simplify our graph-based setting from a stochastic two-player game into a single-player game on a partially observable Markov decision process (POMDP). Robustness against environmental uncertainty is encoded via partial observability. Linear-time correctness properties are verified separately after synthesising the POMDP strategy. We contribute at-scale guidance on POMDP modelling and controller synthesis for tasked robot collectives exemplified by the scenario of battery-driven robots responsible for cleaning public buildings with utilisation constraints.

Generating large-scale, domain-specific, multilingual multi-turn dialogue datasets remains a significant hurdle for training effective Multi-Turn Intent Classification models in chatbot systems. In this paper, we introduce Chain-of-Intent, a novel mechanism that combines Hidden Markov Models with Large Language Models (LLMs) to generate contextually aware, intent-driven conversations through self-play. By extracting domain-specific knowledge from e-commerce chat logs, we estimate conversation turns and intent transitions, which guide the generation of coherent dialogues. Leveraging LLMs to enhance emission probabilities, our approach produces natural and contextually consistent questions and answers. We also propose MINT-CL, a framework for multi-turn intent classification using multi-task contrastive learning, improving classification accuracy without the need for extensive annotated data. Evaluations show that our methods outperform baselines in dialogue quality and intent classification accuracy, especially in multilingual settings, while significantly reducing data generation efforts. Furthermore, we release MINT-E, a multilingual, intent-aware multi-turn e-commerce dialogue corpus to support future research in this area.

We propose a Bayesian neural network-based continual learning algorithm using Variational Inference, aiming to overcome several drawbacks of existing methods. Specifically, in continual learning scenarios, storing network parameters at each step to retain knowledge poses challenges. This is compounded by the crucial need to mitigate catastrophic forgetting, particularly given the limited access to past datasets, which complicates maintaining correspondence between network parameters and datasets across all sessions. Current methods using Variational Inference with KL divergence risk catastrophic forgetting during uncertain node updates and coupled disruptions in certain nodes. To address these challenges, we propose the following strategies. To reduce the storage of the dense layer parameters, we propose a parameter distribution learning method that significantly reduces the storage requirements. In the continual learning framework employing variational inference, our study introduces a regularization term that specifically targets the dynamics and population of the mean and variance of the parameters. This term aims to retain the benefits of KL divergence while addressing related challenges. To ensure proper correspondence between network parameters and the data, our method introduces an importance-weighted Evidence Lower Bound term to capture data and parameter correlations. This enables storage of common and distinctive parameter hyperspace bases. The proposed method partitions the parameter space into common and distinctive subspaces, with conditions for effective backward and forward knowledge transfer, elucidating the network-parameter dataset correspondence. The experimental results demonstrate the effectiveness of our method across diverse datasets and various combinations of sequential datasets, yielding superior performance compared to existing approaches.