We consider the problem of sequentially maximising an unknown function over a set of actions while ensuring that every sampled point has a function value below a given safety threshold. We model the function using kernel-based and Gaussian process methods, while differing from previous works in our assumption that the function is monotonically increasing with respect to a \emph{safety variable}. This assumption is motivated by various practical applications such as adaptive clinical trial design and robotics. Taking inspiration from the \textsc{\sffamily GP-UCB} and \textsc{\sffamily SafeOpt} algorithms, we propose an algorithm, monotone safe {\sffamily UCB} (\textsc{\sffamily M-SafeUCB}) for this task. We show that \textsc{\sffamily M-SafeUCB} enjoys theoretical guarantees in terms of safety, a suitably-defined regret notion, and approximately finding the entire safe boundary. In addition, we illustrate that the monotonicity assumption yields significant benefits in terms of the guarantees obtained, as well as algorithmic simplicity and efficiency. We support our theoretical findings by performing empirical evaluations on a variety of functions, including a simulated clinical trial experiment.

MCMC algorithms offer empirically efficient tools for sampling from a target distribution $\pi(x) \propto \exp(-V(x))$. However, on the theory side, MCMC algorithms suffer from slow mixing rate when $\pi(x)$ is non-log-concave. Our work examines this gap and shows that when Poincar\'e-style inequality holds on a subset $\mathcal{X}$ of the state space, the conditional distribution of MCMC iterates over $\mathcal{X}$ mixes fast to the true conditional distribution. This fast mixing guarantee can hold in cases when global mixing is provably slow. We formalize the statement and quantify the conditional mixing rate. We further show that conditional mixing can have interesting implications for sampling from mixtures of Gaussians, parameter estimation for Gaussian mixture models and Gibbs-sampling with well-connected local minima.

In the field of out-of-distribution (OOD) detection, a previous method that use auxiliary data as OOD data has shown promising performance. However, the method provides an equal loss to all auxiliary data to differentiate them from inliers. However, based on our observation, in various tasks, there is a general imbalance in the distribution of the auxiliary OOD data across classes. We propose a balanced energy regularization loss that is simple but generally effective for a variety of tasks. Our balanced energy regularization loss utilizes class-wise different prior probabilities for auxiliary data to address the class imbalance in OOD data. The main concept is to regularize auxiliary samples from majority classes, more heavily than those from minority classes. Our approach performs better for OOD detection in semantic segmentation, long-tailed image classification, and image classification than the prior energy regularization loss. Furthermore, our approach achieves state-of-the-art performance in two tasks: OOD detection in semantic segmentation and long-tailed image classification. Code is available at https://github.com/hyunjunChhoi/Balanced_Energy.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift -- a prevalent issue in practice -- poses a serious unsolved challenge. In this paper, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is \textit{asymptotically probably approximately correct}, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.

We introduce variational sequential Optimal Experimental Design (vsOED), a new method for optimally designing a finite sequence of experiments under a Bayesian framework and with information-gain utilities. Specifically, we adopt a lower bound estimator for the expected utility through variational approximation to the Bayesian posteriors. The optimal design policy is solved numerically by simultaneously maximizing the variational lower bound and performing policy gradient updates. We demonstrate this general methodology for a range of OED problems targeting parameter inference, model discrimination, and goal-oriented prediction. These cases encompass explicit and implicit likelihoods, nuisance parameters, and physics-based partial differential equation models. Our vsOED results indicate substantially improved sample efficiency and reduced number of forward model simulations compared to previous sequential design algorithms.

In real-life decision-making problems, determining the influences of the factors on the decision attribute is one of the primary tasks. To affect the decision attribute most, finding a proper hierarchy among the factors and determining their importance values in the system becomes quite important. Interpretive structural modeling (ISM) is a widely used hierarchy-building method that mines factor inter-influences based on expert opinions. This paper discusses one of the main drawbacks of the conventional ISM method in systems where the factors are densely interrelated. We refer to such systems as "dense systems". We propose a novel iterative hierarchy-building technique, called 'Iterative Hierarchy and Ranking Process'(IHRP) which performs effectively in such dense systems. To take the vagueness of the expert opinions into account, intuitionistic fuzzy linguistics has been used in the research work. In this paper, we propose a two-stage calculation of the relative importance of the factors in the system based on their hierarchical positions and rank the factors accordingly. We have performed a case study on student performance assessment by taking up novel Indian high-school administrative factors' data collected by surveying the experts in this field. A comparative study has been conducted in terms of the correlation of the factor ranking achieved by the proposed method and conventional ISM method with that of standard outranking methods like TOPSIS, and VIKOR. Our proposed IHRP framework achieves an 85-95% correlation compared to a 50-60% correlation for the conventional ISM method. This proves the effectiveness of the proposed method in determining a better hierarchy than the conventional method, especially in dense systems.

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming.

This paper introduces \textsc{FuzzyLogic.jl}, a Julia library to perform fuzzy inference. The library is fully open-source and released under a permissive license. The core design principles of the library are: user-friendliness, flexibility, efficiency and interoperability. Particularly, our library is easy to use, allows to specify fuzzy systems in an expressive yet concise domain specific language, has several visualization tools, supports popular inference systems like Mamdani, Sugeno and Type-2 systems, can be easily expanded with custom user settings or algorithms and can perform fuzzy inference efficiently. It also allows reading fuzzy models from other formats such as Matlab .fis, FCL or FML. In this paper, we describe the library main features and benchmark it with a few examples, showing it achieves significant speedup compared to the Matlab fuzzy toolbox.

Molecular dynamics (MD) enables the study of physical systems with excellent spatiotemporal resolution but suffers from severe time-scale limitations. To address this, enhanced sampling methods have been developed to improve exploration of configurational space. However, implementing these is challenging and requires domain expertise. In recent years, integration of machine learning (ML) techniques in different domains has shown promise, prompting their adoption in enhanced sampling as well. Although ML is often employed in various fields primarily due to its data-driven nature, its integration with enhanced sampling is more natural with many common underlying synergies. This review explores the merging of ML and enhanced MD by presenting different shared viewpoints. It offers a comprehensive overview of this rapidly evolving field, which can be difficult to stay updated on. We highlight successful strategies like dimensionality reduction, reinforcement learning, and flow-based methods. Finally, we discuss open problems at the exciting ML-enhanced MD interface.