The Heckman selection model is one of the most well-renounced econometric models in the analysis of data with sample selection. This model is designed to rectify sample selection biases based on the assumption of bivariate normal error terms. However, real data diverge from this assumption in the presence of heavy tails and/or atypical observations. Recently, this assumption has been relaxed via a more flexible Student's t-distribution, which has appealing statistical properties. This paper introduces a novel Heckman selection model using a bivariate contaminated normal distribution for the error terms. We present an efficient ECM algorithm for parameter estimation with closed-form expressions at the E-step based on truncated multinormal distribution formulas. The identifiability of the proposed model is also discussed, and its properties have been examined. Through simulation studies, we compare our proposed model with the normal and Student's t counterparts and investigate the finite-sample properties and the variation in missing rate. Results obtained from two real data analyses showcase the usefulness and effectiveness of our model. The proposed algorithms are implemented in the R package HeckmanEM.

We present BLINQ, a new model-based algorithm that learns the Whittle indices of an indexable, communicating and unichain Markov Decision Process (MDP). Our approach relies on building an empirical estimate of the MDP and then computing its Whittle indices using an extended version of a state-of-the-art existing algorithm. We provide a proof of convergence to the Whittle indices we want to learn as well as a bound on the time needed to learn them with arbitrary precision. Moreover, we investigate its computational complexity. Our numerical experiments suggest that BLINQ significantly outperforms existing Q-learning approaches in terms of the number of samples needed to get an accurate approximation. In addition, it has a total computational cost even lower than Q-learning for any reasonably high number of samples. These observations persist even when the Q-learning algorithms are speeded up using pre-trained neural networks to predict Q-values.

We show that Restricted Boltzmann Machines (RBMs) provide a flexible generative framework for modeling spin configurations in disordered yet strongly correlated phases of frustrated magnets. As a benchmark, we first demonstrate that an RBM can learn the zero-temperature ground-state manifold of the one-dimensional ANNNI model at its multiphase point, accurately reproducing its characteristic oscillatory and exponentially decaying correlations. We then apply RBMs to kagome spin ice and show that they successfully learn the local ice rules and short-range correlations of the extensively degenerate ice-I manifold. Correlation functions computed from RBM-generated configurations closely match those from direct Monte Carlo simulations. For the partially ordered ice-II phase -- featuring long-range charge order and broken time-reversal symmetry -- accurate modeling requires RBMs with uniform-sign bias fields, mirroring the underlying symmetry breaking. These results highlight the utility of RBMs as generative models for learning constrained and highly frustrated magnetic states.

While recent vision-language models (VLMs) demonstrate strong image understanding, their ability to "think with images", i.e., to reason through multi-step visual interactions, remains limited. We introduce VISTA-Gym, a scalable training environment for incentivizing tool-integrated visual reasoning capabilities in VLMs. VISTA-Gym unifies diverse real-world multimodal reasoning tasks (7 tasks from 13 datasets in total) with a standardized interface for visual tools (e.g., grounding, parsing), executable interaction loops, verifiable feedback signals, and efficient trajectory logging, enabling visual agentic reinforcement learning at scale. While recent VLMs exhibit strong text-only reasoning, both proprietary and open-source models still struggle with tool selection, invocation, and coordination. With VISTA-Gym, we train VISTA-R1 to interleave tool-use with agentic reasoning via multi-turn trajectory sampling and end-to-end reinforcement learning. Extensive experiments across 11 public reasoning-intensive VQA benchmarks show that VISTA-R1-8B outperforms state-of-the-art baselines with similar sizes by 9.51%-18.72%, demonstrating VISTA-Gym as an effective training ground to unlock the tool-integrated reasoning capabilities for VLMs.

Nowadays, social networks are becoming a popular way of analyzing tourist behavior, thanks to the digital traces left by travelers during their stays on these networks. The massive amount of data generated; by the propensity of tourists to share comments and photos during their trip; makes it possible to model their journeys and analyze their behavior. Predicting the next movement of tourists plays a key role in tourism marketing to understand demand and improve decision support. In this paper, we propose a method to understand and to learn tourists' movements based on social network data analysis to predict future movements. The method relies on a machine learning grammatical inference algorithm. A major contribution in this paper is to adapt the grammatical inference algorithm to the context of big data. Our method produces a hidden Markov model representing the movements of a group of tourists. The hidden Markov model is flexible and editable with new data. The capital city of France, Paris is selected to demonstrate the efficiency of the proposed methodology.

Inter-agent communication serves as an effective mechanism for enhancing performance in collaborative multi-agent reinforcement learning(MARL) systems. However, the inherent communication latency in practical systems induces both action decision delays and outdated information sharing, impeding MARL performance gains, particularly in time-critical applications like autonomous driving. In this work, we propose a V alue-of-Information aware Low-latency Communication(VIL2C) scheme that proactively adjusts the latency distribution to mitigate its effects in MARL systems. Specifically, we define a V alue of Information (VOI) metric to quantify the importance of delayed message transmission based on each delayed message's importance. Moreover, we propose a progressive message reception mechanism to adap-tively adjust the reception duration based on received messages. We derive the optimized V oI aware resource allocation and theoretically prove the performance advantage of the proposed VIL2C scheme. Extensive experiments demonstrate that VIL2C outperforms existing approaches under various communication conditions. These gains are attributed to the low-latency transmission of high-V oI messages via resource allocation and the elimination of unnecessary waiting periods via adaptive reception duration.

Decoded Neurofeedback (DecNef) is a flourishing non-invasive approach to brain modulation with wide-ranging applications in neuromedicine and cognitive neuroscience. However, progress in DecNef research remains constrained by subject-dependent learning variability, reliance on indirect measures to quantify progress, and the high cost and time demands of experimentation. We present DecNefLab, a modular and interpretable simulation framework that formalizes DecNef as a machine learning problem. Beyond providing a virtual laboratory, DecNefLab enables researchers to model, analyze and understand neurofeedback dynamics. Using latent variable generative models as simulated participants, DecNefLab allows direct observation of internal cognitive states and systematic evaluation of how different protocol designs and subject characteristics influence learning. We demonstrate how this approach can (i) reproduce empirical phenomena of DecNef learning, (ii) identify conditions under which DecNef feedback fails to induce learning, and (iii) guide the design of more robust and reliable DecNef protocols in silico before human implementation. In summary, DecNefLab bridges computational modeling and cognitive neuroscience, offering a principled foundation for methodological innovation, robust protocol design, and ultimately, a deeper understanding of DecNef-based brain modulation.

Reinforcement-based learning has attracted considerable attention both in modeling human behavior as well as in engineering, for designing measurement- or payoff-based optimization schemes. Such learning schemes exhibit several advantages, especially in relation to filtering out noisy observations. However, they may exhibit several limitations when applied in a distributed setup. In multi-player weakly-acyclic games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. To address this main limitation, this paper introduces a novel payoff-based learning scheme for distributed optimization, namely aspiration-based perturbed learning automata (APLA). In this class of dynamics, and contrary to standard reinforcement-based learning schemes, each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility games under the presence of noisy observations. This is the first part of the paper that characterizes stochastic stability in generic non-zero-sum games by establishing equivalence of the induced infinite-dimensional Markov chain with a finite dimensional one. In the second part, stochastic stability is further specialized to weakly acyclic games.

Modern large language models (LLMs) demonstrate exceptional performance on knowledge-intensive tasks, yet the theoretical mechanisms underlying knowledge acquisition (storage and memorization) during pre-training and extraction (retrieval and recall) during inference after fine-tuning remain poorly understood. Although prior theoretical studies have explored these processes through analyses of training dynamics, they overlook critical components essential for a comprehensive theory: (1) the multi-layer perceptron (MLP), empirically identified as the primary module for knowledge storage; (2) out-of-distribution (OOD) adaptivity, which enables LLMs to generalize to unseen scenarios post-pre-training; and (3) next-token prediction, the standard autoregressive objective that encodes knowledge as conditional probabilities. In this work, we introduce, to the best of our knowledge, the first theoretical framework that addresses these limitations by examining the training dynamics of one-layer transformers. Under regularity assumptions, we establish that: (i) transformers attain near-optimal training loss during pre-training, demonstrating effective knowledge acquisition; (ii) given a sufficiently large fine-tuning dataset and appropriate data multiplicity conditions, transformers achieve low generalization error on factual knowledge acquired during pre-training but not revisited in fine-tuning, indicating robust knowledge extraction; and (iii) violation of these conditions leads to elevated generalization error, manifesting as hallucinations. Our analysis encompasses both full fine-tuning and low-rank fine-tuning, yielding insights into the efficacy of practical low-rank adaptation methods. We validate our theoretical findings through experiments on synthetic datasets and the real-world PopQA benchmark, employing GPT-2 and Llama-3.2-1B models.

-- In this work we introduce a novel adaptive anomaly detection framework specifically designed for monitoring sequential random finite set (RFS) observations. Our approach effectively distinguishes between In-Control data (normal) and Out-Of-Control data (anomalies) by detecting deviations from the expected statistical behavior of the process. The primary contributions of this study include the development of an innovative RFS-based framework that not only learns the normal behavior of the data-generating process online but also dynamically adapts to behavioral shifts to accurately identify abnormal point patterns. T o achieve this, we introduce a new class of RFS-based posterior distributions, named Power Discounting Posteriors (PD), which facilitate adaptation to systematic changes in data while enabling anomaly detection of point pattern data through a novel predictive posterior density function. The effectiveness of the proposed approach is demonstrated by extensive qualitative and quantitative simulation experiments.