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.

Bird sound classification is the task of relating any sound recording to those species of bird that can be heard in the recording. Here, we study bird sound clustering, the task of deciding for any pair of sound recordings whether the same species of bird can be heard in both. We address this problem by first learning, from a training set, probabilities of pairs of recordings being related in this way, and then inferring a maximally probable partition of a test set by correlation clustering. We address the following questions: How accurate is this clustering, compared to a classification of the test set? How do the clusters thus inferred relate to the clusters obtained by classification? How accurate is this clustering when applied to recordings of bird species not heard during training? How effective is this clustering in separating, from bird sounds, environmental noise not heard during training?

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at \url{https://github.com/minyoungkim21/niwmeta}.

Identifying the causal variables of an environment and how to intervene on them is of core value in applications such as robotics and embodied AI. While an agent can commonly interact with the environment and may implicitly perturb the behavior of some of these causal variables, often the targets it affects remain unknown. In this paper, we show that causal variables can still be identified for many common setups, e.g., additive Gaussian noise models, if the agent's interactions with a causal variable can be described by an unknown binary variable. This happens when each causal variable has two different mechanisms, e.g., an observational and an interventional one. Using this identifiability result, we propose BISCUIT, a method for simultaneously learning causal variables and their corresponding binary interaction variables. On three robotic-inspired datasets, BISCUIT accurately identifies causal variables and can even be scaled to complex, realistic environments for embodied AI.

Systems based on algorithms and machine learning are increasingly used to guide or outright make decisions which strongly impact human lives; thus it is imperative to take fairness into account when designing such systems. Notions of fairness in computer science can be classified into those that try to capture fairness towards a group (Hardt et al., 2016; Hébert-Johnson et al., 2018; Kearns et al., 2018; Kleinberg et al., 2017) vs. those that try to be fair to each individual Dwork et al. (2012); Kim et al. (2018, 2020). In our work, we focus on the latter notion. The most widely studied notion of individual fairness is due to the seminal work of Dwork et al. (2012): it assumes that a metric space on observable features of individuals captures similarity, and requires that outcomes of a resource allocation mechanism satisfy a certain Lipschitz continuity condition with respect to the given metric. Intuitively, this ensures that individuals who are similar according to the metric will be treated similarly by the mechanism. We consider a setting in which individuals have preferences over the outcomes of the resource allocation mechanism, focusing on the important setting of two-sided markets. Applications of this setting abound: matching students to schools, job fair participants to interviews, doctors to hospitals, patients to treatments, drivers to passengers in ride hailing, or advertisers to ad slots/users in online advertising (Abdulkadiroğlu and Sönmez, 2003; Bronfman et al., 2015; Mehta et al., 2013; Roth, 1986; Roth et al., 2007), to name a

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data as a sparse combination of simpler, more interpretable components. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. The decomposed nature of the dynamics is more expressive than previous switched approaches for a given number of parameters and enables modeling of overlapping and non-stationary dynamics. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system, learn efficient representations, and capture smooth transitions between dynamical modes, focusing on intuitive low-dimensional non-stationary linear and nonlinear systems. Furthermore, we highlight our model's ability to efficiently capture and demix population dynamics generated from multiple independent subnetworks, a task that is computationally impractical for switched models. Finally, we apply our model to neural "full brain" recordings of C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.