Sequential Monte Carlo methods can characterize arbitrary distributions using sequential importance sampling and resampling, but typically require very large sample sizes to mitigate weight collapse [Snyder et al., 2008, 2015]. By contrast, ensemble Kalman-type methods avoid the use of weights, but are based on affine prior-to-posterior updates that are consistent only if all distributions involved are Gaussian. In the context of smoothing, such methods include the ensemble Kalman smoother (EnKS) [Evensen and Van Leeuwen, 2000], which has inspired numerous algorithmic variations such as the ensemble smoother with multiple data assimilation [Emerick and Reynolds, 2013] and the iterative ensemble Kalman smoother (iEnKS) [Bocquet and Sakov, 2014, Evensen et al., 2019], as well as backwards smoothers such as the ensemble Rauch-Tung-Striebel smoother (EnRTSS) [Raanes, 2016]. These two classes of methods occupy opposite ends of a spectrum that ranges from an emphasis on statistical generality at one end to an emphasis on computational efficiency at the other. This trade-off complicates design decisions for smoothing problems that are at once non-Gaussian and computationally expensive.

Smoothers are algorithms for Bayesian time series re-analysis. Most operational smoothers rely either on affine Kalman-type transformations or on sequential importance sampling. These strategies occupy opposite ends of a spectrum that trades computational efficiency and scalability for statistical generality and consistency: non-Gaussianity renders affine Kalman updates inconsistent with the true Bayesian solution, while the ensemble size required for successful importance sampling can be prohibitive. This paper revisits the smoothing problem from the perspective of measure transport, which offers the prospect of consistent prior-to-posterior transformations for Bayesian inference. We leverage this capacity by proposing a general ensemble framework for transport-based smoothing. Within this framework, we derive a comprehensive set of smoothing recursions based on nonlinear transport maps and detail how they exploit the structure of state-space models in fully non-Gaussian settings. We also describe how many standard Kalman-type smoothing algorithms emerge as special cases of our framework. A companion paper (Ramgraber et al., 2023) explores the implementation of nonlinear ensemble transport smoothers in greater depth.

The concept of creating a virtual copy of a complete Cyber-Physical System opens up numerous possibilities, including real-time assessments of the physical environment and continuous learning from the system to provide reliable and precise information. This process, known as the twinning process or the development of a digital twin (DT), has been widely adopted across various industries. However, challenges arise when considering the computational demands of implementing AI models, such as those employed in digital twins, in real-time information exchange scenarios. This work proposes a digital twin framework for optimal and autonomous decision-making applied to a gas-lift process in the oil and gas industry, focusing on enhancing the robustness and adaptability of the DT. The framework combines Bayesian inference, Monte Carlo simulations, transfer learning, online learning, and novel strategies to confer cognition to the DT, including model hyperdimensional reduction and cognitive tack. Consequently, creating a framework for efficient, reliable, and trustworthy DT identification was possible. The proposed approach addresses the current gap in the literature regarding integrating various learning techniques and uncertainty management in digital twin strategies. This digital twin framework aims to provide a reliable and efficient system capable of adapting to changing environments and incorporating prediction uncertainty, thus enhancing the overall decision-making process in complex, real-world scenarios. Additionally, this work lays the foundation for further developments in digital twins for process systems engineering, potentially fostering new advancements and applications across various industrial sectors.

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

The posterior covariance matrix W defined by the log-likelihood of each observation plays important roles both in the sensitivity analysis and frequencist's evaluation of the Bayesian estimators. This study focused on the matrix W and its principal space; we term the latter as an essential subspace. First, it is shown that they appear in various statistical settings, such as the evaluation of the posterior sensitivity, assessment of the frequencist's uncertainty from posterior samples, and stochastic expansion of the loss; a key tool to treat frequencist's properties is the recently proposed Bayesian infinitesimal jackknife approximation (Giordano and Broderick (2023)). In the following part, we show that the matrix W can be interpreted as a reproducing kernel; it is named as W-kernel. Using the W-kernel, the essential subspace is expressed as a principal space given by the kernel PCA. A relation to the Fisher kernel and neural tangent kernel is established, which elucidates the connection to the classical asymptotic theory; it also leads to a sort of Bayesian-frequencist's duality. Finally, two applications, selection of a representative set of observations and dimensional reduction in the approximate bootstrap, are discussed. In the former, incomplete Cholesky decomposition is introduced as an efficient method to compute the essential subspace. In the latter, different implementations of the approximate bootstrap for posterior means are compared.

Counterfactual Explanations (CEs) are an important tool in Algorithmic Recourse for addressing two questions: 1. What are the crucial factors that led to an automated prediction/decision? 2. How can these factors be changed to achieve a more favorable outcome from a user's perspective? Thus, guiding the user's interaction with AI systems by proposing easy-to-understand explanations and easy-to-attain feasible changes is essential for the trustworthy adoption and long-term acceptance of AI systems. In the literature, various methods have been proposed to generate CEs, and different quality measures have been suggested to evaluate these methods. However, the generation of CEs is usually computationally expensive, and the resulting suggestions are unrealistic and thus non-actionable. In this paper, we introduce a new method to generate CEs for a pre-trained binary classifier by first shaping the latent space of an autoencoder to be a mixture of Gaussian distributions. CEs are then generated in latent space by linear interpolation between the query sample and the centroid of the target class. We show that our method maintains the characteristics of the input sample during the counterfactual search. In various experiments, we show that the proposed method is competitive based on different quality measures on image and tabular datasets -- efficiently returns results that are closer to the original data manifold compared to three state-of-the-art methods, which are essential for realistic high-dimensional machine learning applications.

Policy Mirror Descent (PMD) is a general family of algorithms that covers a wide range of novel and fundamental methods in reinforcement learning. Motivated by the instability of policy iteration (PI) with inexact policy evaluation, PMD algorithmically regularises the policy improvement step of PI. With exact policy evaluation, PI is known to converge linearly with a rate given by the discount factor $\gamma$ of a Markov Decision Process. In this work, we bridge the gap between PI and PMD with exact policy evaluation and show that the dimension-free $\gamma$-rate of PI can be achieved by the general family of unregularised PMD algorithms under an adaptive step-size. We show that both the rate and step-size are unimprovable for PMD: we provide matching lower bounds that demonstrate that the $\gamma$-rate is optimal for PMD methods as well as PI, and that the adaptive step-size is necessary for PMD to achieve it. Our work is the first to relate PMD to rate-optimality and step-size necessity. Our study of the convergence of PMD avoids the use of the performance difference lemma, which leads to a direct analysis of independent interest. We also extend the analysis to the inexact setting and establish the first dimension-optimal sample complexity for unregularised PMD under a generative model, improving upon the best-known result.

People rely heavily on context to enrich meaning beyond what is literally said, enabling concise but effective communication. To interact successfully and naturally with people, user-facing artificial intelligence systems will require similar skills in pragmatics: relying on various types of context -- from shared linguistic goals and conventions, to the visual and embodied world -- to use language effectively. We survey existing grounded settings and pragmatic modeling approaches and analyze how the task goals, environmental contexts, and communicative affordances in each work enrich linguistic meaning. We present recommendations for future grounded task design to naturally elicit pragmatic phenomena, and suggest directions that focus on a broader range of communicative contexts and affordances.

In this paper, we propose a reinforcement learning algorithm to solve a multi-agent Markov decision process (MMDP). The goal, inspired by Blackwell's Approachability Theorem, is to lower the time average cost of each agent to below a pre-specified agent-specific bound. For the MMDP, we assume the state dynamics to be controlled by the joint actions of agents, but the per-stage costs to only depend on the individual agent's actions. We combine the Q-learning algorithm for a weighted combination of the costs of each agent, obtained by a gossip algorithm with the Metropolis-Hastings or Multiplicative Weights formalisms to modulate the averaging matrix of the gossip. We use multiple timescales in our algorithm and prove that under mild conditions, it approximately achieves the desired bounds for each of the agents. We also demonstrate the empirical performance of this algorithm in the more general setting of MMDPs having jointly controlled per-stage costs.

In our case, we employed a traditional approach to define the automatic system, in other words, a system based on Hidden During a conversation, our brain is responsible for combining Markov Models combined with Gaussian Mixture Models information obtained from multiple senses in order (GMM-HMM), an approach that has been widely used in to improve our ability to understand the message we are Acoustic Speech Recognition (ASR) [6]. Although this is not perceiving. Different studies have shown the importance of the state-of-the-art for speech-related signal recognition, it is presenting visual information in these situations. Nevertheless, an appropriate option for comparing the different possibilities lipreading is a complex task whose objective is to interpret for feature extraction. Unlike in ASR, when we deal with Visual speech when audio is not available. By dispensing with a sense Speech Recognition (VSR) our basic speech unit is not the as crucial as hearing, it will be necessary to be aware of the phoneme, but the one known as the viseme, which is associated challenge that this lack presents. In this paper, we propose an with the representation of the phoneme on the visual domain analysis of different speech visual features with the intention [7]. Unfortunately, there is not direct or one-to-one correspondence of identifying which of them is the best approach to capture between them, which causes visual ambiguities.