Particle-based methods include a variety of techniques, such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC), for approximating a probabilistic target distribution with a set of weighted particles. In this paper, we prove that for any set of particles, there is a unique weighting mechanism that minimizes the Kullback-Leibler (KL) divergence of the (particle-based) approximation from the target distribution, when that distribution is discrete -- any other weighting mechanism (e.g. MCMC weighting that is based on particles' repetitions in the Markov chain) is sub-optimal with respect to this divergence measure. Our proof does not require any restrictions either on the target distribution, or the process by which the particles are generated, other than the discreteness of the target. We show that the optimal weights can be determined based on values that any existing particle-based method already computes; As such, with minimal modifications and no extra computational costs, the performance of any particle-based method can be improved. Our empirical evaluations are carried out on important applications of discrete distributions including Bayesian Variable Selection and Bayesian Structure Learning. The results illustrate that our proposed reweighting of the particles improves any particle-based approximation to the target distribution consistently and often substantially.

The Tweedie exponential dispersion family is a popular choice among many to model insurance losses that consist of zero-inflated semicontinuous data. In such data, it is often important to obtain credibility (inference) of the most important features that describe the endogenous variables. Post-selection inference is the standard procedure in statistics to obtain confidence intervals of model parameters after performing a feature extraction procedure. For a linear model, the lasso estimate often has non-negligible estimation bias for large coefficients corresponding to exogenous variables. To have valid inference on those coefficients, it is necessary to correct the bias of the lasso estimate. Traditional statistical methods, such as hypothesis testing or standard confidence interval construction might lead to incorrect conclusions during post-selection, as they are generally too optimistic. Here we discuss a few methodologies for constructing confidence intervals of the coefficients after feature selection in the Generalized Linear Model (GLM) family with application to insurance data.

The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which involves forecasting wireless spectrum availability, is an older field where many "classical" tools were considered around the 2010s, such as Markov models. This work revisits high-order Markov models for spectrum prediction in dynamic wireless environments. We introduce a framework to address mismatches between sensing length and model order as well as state-space complexity arising with large order. Furthermore, we extend this Markov framework by enabling fine-tuning of the probability transition matrix through gradient-based supervised learning, offering a hybrid approach that bridges probabilistic modeling and modern machine learning. Simulations on real-world Wi-Fi traffic demonstrate the competitive performance of high-order Markov models compared to deep learning methods, particularly in scenarios with constrained datasets containing outliers.

Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the precise measurement in computer networks because of the high measurement cost, and the unavoidable transmission loss. Although some methods proposed in recent years allowed estimating network traffic from partial flow-level or link-level measurements, they often perform poorly for traffic matrix estimation nowadays. Despite strong assumptions like low-rank structure and the prior distribution, existing techniques are usually task-specific and tend to be significantly worse as modern network communication is extremely complicated and dynamic. To address the dilemma, this paper proposed a diffusion-based traffic matrix analysis framework named Diffusion-TM, which leverages problem-agnostic diffusion to notably elevate the estimation performance in both traffic distribution and accuracy. The novel framework not only takes advantage of the powerful generative ability of diffusion models to produce realistic network traffic, but also leverages the denoising process to unbiasedly estimate all end-to-end traffic in a plug-and-play manner under theoretical guarantee. Moreover, taking into account that compiling an intact traffic dataset is usually infeasible, we also propose a two-stage training scheme to make our framework be insensitive to missing values in the dataset. With extensive experiments with real-world datasets, we illustrate the effectiveness of Diffusion-TM on several tasks. Moreover, the results also demonstrate that our method can obtain promising results even with $5\%$ known values left in the datasets.

In settings where the application of reinforcement learning (RL) requires running real-world trials, including the optimization of adaptive health interventions, the number of episodes available for learning can be severely limited due to cost or time constraints. In this setting, the bias-variance trade-off of contextual bandit methods can be significantly better than that of more complex full RL methods. However, Thompson sampling bandits are limited to selecting actions based on distributions of immediate rewards. In this paper, we extend the linear Thompson sampling bandit to select actions based on a state-action utility function consisting of the Thompson sampler's estimate of the expected immediate reward combined with an action bias term. We use batch Bayesian optimization over episodes to learn the action bias terms with the goal of maximizing the expected return of the extended Thompson sampler. The proposed approach is able to learn optimal policies for a strictly broader class of Markov decision processes (MDPs) than standard Thompson sampling. Using an adaptive intervention simulation environment that captures key aspects of behavioral dynamics, we show that the proposed method can significantly out-perform standard Thompson sampling in terms of total return, while requiring significantly fewer episodes than standard value function and policy gradient methods.

In recent years, model-based reinforcement learning (MBRL) has emerged as a solution to address sample complexity in multi-agent reinforcement learning (MARL) by modeling agent-environment dynamics to improve sample efficiency. However, most MBRL methods assume complete and continuous observations from each agent during the inference stage, which can be overly idealistic in practical applications. A novel model-based MARL approach called RMIO is introduced to address this limitation, specifically designed for scenarios where observation is lost in some agent. RMIO leverages the world model to reconstruct missing observations, and further reduces reconstruction errors through inter-agent information integration to ensure stable multi-agent decision-making. Secondly, unlike CTCE methods such as MAMBA, RMIO adopts the CTDE paradigm in standard environment, and enabling limited communication only when agents lack observation data, thereby reducing reliance on communication. Additionally, RMIO improves asymptotic performance through strategies such as reward smoothing, a dual-layer experience replay buffer, and an RNN-augmented policy model, surpassing previous work. Our experiments conducted in both the SMAC and MaMuJoCo environments demonstrate that RMIO outperforms current state-of-the-art approaches in terms of asymptotic convergence performance and policy robustness, both in standard mission settings and in scenarios involving observation loss.

This paper presents a novel method to quantify Trust in HRI. It proposes an HRI framework for estimating the Robot Trust towards the Human in the context of a narrow and specified task. The framework produces a real-time estimation of an AI agent's Artificial Trust towards a Human partner interacting with a mobile teleoperation robot. The approach for the framework is based on principles drawn from Theory of Mind, including information about the human state, action, and intent. The framework creates the ATTUNE model for Artificial Trust Towards Human Operators. The model uses metrics on the operator's state of attention, navigational intent, actions, and performance to quantify the Trust towards them. The model is tested on a pre-existing dataset that includes recordings (ROSbags) of a human trial in a simulated disaster response scenario. The performance of ATTUNE is evaluated through a qualitative and quantitative analysis. The results of the analyses provide insight into the next stages of the research and help refine the proposed approach.

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of nonlinear latent hierarchical causal models, relaxing previous assumptions in literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for nonlinear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. We demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks.

Semi-supervised learning (SSL) is a machine learning methodology that leverages unlabeled data in conjunction with a limited amount of labeled data. Although SSL has been applied in various applications and its effectiveness has been empirically demonstrated, it is still not fully understood when and why SSL performs well. Some existing theoretical studies have attempted to address this issue by modeling classification problems using the so-called Gaussian Mixture Model (GMM). These studies provide notable and insightful interpretations. However, their analyses are focused on specific purposes, and a thorough investigation of the properties of GMM in the context of SSL has been lacking. In this paper, we conduct such a detailed analysis of the properties of the high-dimensional GMM for binary classification in the SSL setting. To this end, we employ the approximate message passing and state evolution methods, which are widely used in high-dimensional settings and originate from statistical mechanics. We deal with two estimation approaches: the Bayesian one and the l2-regularized maximum likelihood estimation (RMLE). We conduct a comprehensive comparison between these two approaches, examining aspects such as the global phase diagram, estimation error for the parameters, and prediction error for the labels. A specific comparison is made between the Bayes-optimal (BO) estimator and RMLE, as the BO setting provides optimal estimation performance and is ideal as a benchmark. Our analysis shows that with appropriate regularizations, RMLE can achieve near-optimal performance in terms of both the estimation error and prediction error, especially when there is a large amount of unlabeled data. These results demonstrate that the l2 regularization term plays an effective role in estimation and prediction in SSL approaches.

In this paper, we explore how to optimize task allocation for robot swarms in dynamic environments, emphasizing the necessity of formulating robust, flexible, and scalable strategies for robot cooperation. We introduce a novel framework using a decentralized partially observable Markov decision process (Dec_POMDP), specifically designed for distributed robot swarm networks. At the core of our methodology is the Local Information Aggregation Multi-Agent Deep Deterministic Policy Gradient (LIA_MADDPG) algorithm, which merges centralized training with distributed execution (CTDE). During the centralized training phase, a local information aggregation (LIA) module is meticulously designed to gather critical data from neighboring robots, enhancing decision-making efficiency. In the distributed execution phase, a strategy improvement method is proposed to dynamically adjust task allocation based on changing and partially observable environmental conditions. Our empirical evaluations show that the LIA module can be seamlessly integrated into various CTDE-based MARL methods, significantly enhancing their performance. Additionally, by comparing LIA_MADDPG with six conventional reinforcement learning algorithms and a heuristic algorithm, we demonstrate its superior scalability, rapid adaptation to environmental changes, and ability to maintain both stability and convergence speed. These results underscore LIA_MADDPG's outstanding performance and its potential to significantly improve dynamic task allocation in robot swarms through enhanced local collaboration and adaptive strategy execution.