We propose an adaptive model-predictive controller that balances driving the system to a goal state and seeking system observations that are informative with respect to the parameters of a nonlinear autoregressive exogenous model. The controller's objective function is derived from an expected free energy functional and contains information-theoretic terms expressing uncertainty over model parameters and output predictions. Experiments illustrate how parameter uncertainty affects the control objective and evaluate the proposed controller for a pendulum swing-up task.

Keywords: carbon fiber reinforced polymer, concrete, confinement effect, strength, particle swarm optimization, grey wolf optimizer, bat algorithm Abstract This article deals with the study of predicting the confinement effect of carbon fiber reinforced polymers (CFRPs) on concrete cylinder strength using metaheuristics-based artificial neural networks. Three metaheuristic models are implemented including particle swarm optimization (PSO), grey wolf optimizer (GWO), and bat algorithm (BA). These algorithms are trained on the data using an objective function of mean square error and their predicted results are validated against the experimental studies and finite element analysis. The study shows that the hybrid model of PSO predicted the strength of CFRP-confined concrete cylinders with maximum accuracy of 99.13% and GWO predicted the results with an accuracy of 98.17%. The high accuracy of axial compressive strength predictions demonstrated that these prediction models are a reliable solution to the empirical methods. The prediction models are especially suitable for avoiding full-scale time-consuming experimental tests that make the process quick and economical. 1 Introduction Fiber-reinforced polymer is a composite material comprising fibers of either glass, aramid, or carbon and a polymer matrix. These fibers improve the properties of the polymer matrix mechanically including its stiffness and strength. The popularity of these composites has increased significantly in civil engineering due to their ability to strengthen concrete structural members. FRPs can be used either as a bar or plates embedded in concrete as an internal reinforcement and can be used as an external reinforcement by wrapping FRP sheets to existing structural members. The FRP bars have significantly higher strength than the steel reinforcement bars. They are highly durable and resistant to chemicals, corrosion (Cousin et al. 2019, Ananthkumar et al. 2020, Zhang et al. 2020), and radiation, their higher strength-to-weight ratio (Zhou et al. 2019) makes them ideal for structures that require high strength but need not be heavy. They can be molded into any required shape that provides higher design flexibility. Moreover, it has a lower environmental impact (Lee and Jain 2009), unlike concrete and timber.

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise, so for typical sample sizes there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over DAGs, but not both. In this paper we leverage the fact that it is possible to estimate the "velocity" of gene expression with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time. Since our objective is to model uncertainty over discrete structures, we leverage Generative Flow Networks (GFlowNets) to estimate the posterior distribution over the combinatorial space of possible sparse dependencies. Our results indicate that our method learns posteriors that better encapsulate the distributions of cyclic structures compared to counterpart state-of-the-art Bayesian structure learning approaches.

We propose a novel Deep Reinforcement Learning (DRL) architecture for sequential decision processes under uncertainty, as encountered in inspection and maintenance (I&M) planning. Unlike other DRL algorithms for (I&M) planning, the proposed +RQN architecture dispenses with computing the belief state and directly handles erroneous observations instead. We apply the algorithm to a basic I&M planning problem for a one-component system subject to deterioration. In addition, we investigate the performance of Monte Carlo tree search for the I&M problem and compare it to the +RQN. The comparison includes a statistical analysis of the two methods' resulting policies, as well as their visualization in the belief space.

Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total ordering. Explicit mixture models have provided some tools for modelling multimodal ranking data, though learning such models from data is often difficult. In this work, we contribute a contextual repeated selection (CRS) model that leverages recent advances in choice modeling to bring a natural multimodality and richness to the rankings space. We provide rigorous theoretical guarantees for maximum likelihood estimation under the model through structure-dependent tail risk and expected risk bounds. As a by-product, we also furnish the first tight bounds on the expected risk of maximum likelihood estimators for the multinomial logit (MNL) choice model and the Plackett-Luce (PL) ranking model, as well as the first tail risk bound on the PL ranking model. The CRS model significantly outperforms existing methods for modeling real world ranking data in a variety of settings, from racing to rank choice voting.

In recent years, there has been a significant transformation in medical research methodologies towards the adoption of Deep Learning (DL) techniques for predicting critical events, such as disease development and patient mortality. Despite their potential to handle complex data, practical applications in this domain remain limited, with most studies still relying on traditional statistical methods. Survival Analysis (SA), or time-to-event analysis, is an essential tool for studying specific events in various disciplines, not only in medicine but also in fields such as recommendation systems [1], employee retention [2], market modeling [3], and financial risk assessment [4]. According to the existing literature, the Cox proportional hazards model (Cox-PH) [5] is the dominant SA method that offers a semiparametric regression solution to the non-parametric Kaplan-Meier estimator problem [6]. Unlike the Kaplan-Meier method, which uses a single covariate, Cox-PH incorporates multiple covariates to predict event times and assess their impact on the hazard rate at specific time points. However, it is crucial to acknowledge that the Cox-PH model is built on certain strong assumptions. One of these is the proportional hazards assumption, which posits that different individuals have hazard functions that remain constant over time. Furthermore, the model assumes a linear relation between the natural logarithm of the relative hazard (the ratio of the hazard at time t to the baseline hazard) and the covariates. Furthermore, it assumes the absence of interactions among these covariates.

The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the desired data distribution. We show that the time-reversal argument, common to all denoising diffusion probabilistic modeling proposals, is not necessary. We obtain diffusion processes targeting the desired data distribution by taking appropriate mixtures of diffusion bridges. The resulting transport is exact by construction, allows for greater flexibility in choosing the dynamics of the underlying diffusion, and can be approximated by means of a neural network via novel training objectives. We develop a unifying view of the drift adjustments corresponding to our and to time-reversal approaches and make use of this representation to inspect the inner workings of diffusion-based generative models. Finally, we leverage on scalable simulation and inference techniques common in spatial statistics to move beyond fully factorial distributions in the underlying diffusion dynamics. The methodological advances contained in this work contribute toward establishing a general framework for generative modeling based on diffusion processes.

The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a reference process. We propose a novel sampling-based iterative algorithm, the iterated diffusion bridge mixture (IDBM) procedure, aimed at solving the dynamic Schr\"odinger bridge problem. The IDBM procedure exhibits the attractive property of realizing a valid transport between the target probability measures at each iteration. We perform an initial theoretical investigation of the IDBM procedure, establishing its convergence properties. The theoretical findings are complemented by numerical experiments illustrating the competitive performance of the IDBM procedure. Recent advancements in generative modeling employ the time-reversal of a diffusion process to define a generative process that approximately transports a simple distribution to the data distribution. As an alternative, we propose utilizing the first iteration of the IDBM procedure as an approximation-free method for realizing this transport. This approach offers greater flexibility in selecting the generative process dynamics and exhibits accelerated training and superior sample quality over larger discretization intervals. In terms of implementation, the necessary modifications are minimally intrusive, being limited to the training loss definition.

The polyhedral method by Lee et al. (2016) introduced confidence intervals for exact selective inference in Gaussian regression models. This method provides valid inferences for selected parameters by conditioning on the outcome of selection. A pivot is obtained for each selected parameter from a truncated Gaussian distribution, provided the outcome of selection can be described by linear constraints, also known as polyhedral constraints. However, as shown by Kivaranovic and Leeb (2021), confidence intervals based on this pivot can have infinite length in expectation. Randomizing data at the time of selection and conditioning on the outcome of randomized selection produces narrower confidence intervals than the polyhedral method.

Meta-Learning aims to speed up the learning process on new tasks by acquiring useful inductive biases from datasets of related learning tasks. While, in practice, the number of related tasks available is often small, most of the existing approaches assume an abundance of tasks; making them unrealistic and prone to overfitting. A central question in the meta-learning literature is how to regularize to ensure generalization to unseen tasks. In this work, we provide a theoretical analysis using the PAC-Bayesian theory and present a generalization bound for meta-learning, which was first derived by Rothfuss et al. (2021a). Crucially, the bound allows us to derive the closed form of the optimal hyper-posterior, referred to as PACOH, which leads to the best performance guarantees. We provide a theoretical analysis and empirical case study under which conditions and to what extent these guarantees for meta-learning improve upon PAC-Bayesian per-task learning bounds. The closed-form PACOH inspires a practical meta-learning approach that avoids the reliance on bi-level optimization, giving rise to a stochastic optimization problem that is amenable to standard variational methods that scale well. Our experiments show that, when instantiating the PACOH with Gaussian processes and Bayesian Neural Networks models, the resulting methods are more scalable, and yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates.