Classic Delphi and Fuzzy Delphi methods are used to test content validity of a data collection tools such as questionnaires. Fuzzy Delphi takes the opinion issued by judges from a linguistic perspective reducing ambiguity in opinions by using fuzzy numbers. We propose an extension named 2-Tuple Fuzzy Linguistic Delphi method to deal with scenarios in which judges show different expertise degrees by using fuzzy multigranular semantics of the linguistic terms and to obtain intermediate and final results expressed by 2-tuple linguistic values. The key idea of our proposal is to validate the full questionnaire by means of the evaluation of its parts, defining the validity of each item as a Decision Making problem. Taking the opinion of experts, we measure the degree of consensus, the degree of consistency, and the linguistic score of each item, in order to detect those items that affect, positively or negatively, the quality of the instrument. Considering the real need to evaluate a b-learning educational experience with a consensual questionnaire, we present a Decision Making model for questionnaire validation that solve it. Additionally, we contribute to this consensus reaching problem by developing an online tool under GPL v3 license. The software visualizes the collective valuations for each iteration and assists to determine which parts of the questionnaire should be modified to reach a consensual solution.

Many state-of-the-art causal discovery methods aim to generate an output graph that encodes the graphical separation and connection statements of the causal graph that underlies the data-generating process. In this work, we argue that an evaluation of a causal discovery method against synthetic data should include an analysis of how well this explicit goal is achieved by measuring how closely the separations/connections of the method's output align with those of the ground truth. We show that established evaluation measures do not accurately capture the difference in separations/connections of two causal graphs, and we introduce three new measures of distance called s/c-distance, Markov distance and Faithfulness distance that address this shortcoming. We complement our theoretical analysis with toy examples, empirical experiments and pseudocode.

Prediction of angler behaviors, such as catch rates and angler pressure, is essential to maintaining fish populations and ensuring angler satisfaction. Angler behavior can partly be tracked by online platforms and mobile phone applications that provide fishing activities reported by recreational anglers. Moreover, angler behavior is known to be driven by local site attributes. Here, the prediction of citizen-reported angler behavior was investigated by machine-learning methods using auxiliary data on the environment, socioeconomics, fisheries management objectives, and events at a freshwater body. The goal was to determine whether auxiliary data alone could predict the reported behavior. Different spatial and temporal extents and temporal resolutions were considered. Accuracy scores averaged 88% for monthly predictions at single water bodies and 86% for spatial predictions on a day in a specific region across Canada. At other resolutions and scales, the models only achieved low prediction accuracy of around 60%. The study represents a first attempt at predicting angler behavior in time and space at a large scale and establishes a foundation for potential future expansions in various directions.

Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their exact localization in the parameter space is challenging, in particular in systems, where the computation of the quantum spectra and resonances is numerically very expensive. We introduce an efficient machine learning algorithm to find exceptional points based on Gaussian process regression (GPR). The GPR-model is trained with an initial set of eigenvalue pairs belonging to an EP and used for a first estimation of the EP position via a numerically cheap root search. The estimate is then improved iteratively by adding selected exact eigenvalue pairs as training points to the GPR-model. The GPR-based method is developed and tested on a simple low-dimensional matrix model and then applied to a challenging real physical system, viz., the localization of EPs in the resonance spectra of excitons in cuprous oxide in external electric and magnetic fields. The precise computation of EPs, by taking into account the complete valence band structure and central-cell corrections of the crystal, can be the basis for the experimental observation of EPs in this system.

An open scientific challenge is how to classify events with reliable measures of uncertainty, when we have a mechanistic model of the data-generating process but the distribution over both labels and latent nuisance parameters is different between train and target data. We refer to this type of distributional shift as generalized label shift (GLS). Direct classification using observed data $\mathbf{X}$ as covariates leads to biased predictions and invalid uncertainty estimates of labels $Y$. We overcome these biases by proposing a new method for robust uncertainty quantification that casts classification as a hypothesis testing problem under nuisance parameters. The key idea is to estimate the classifier's receiver operating characteristic (ROC) across the entire nuisance parameter space, which allows us to devise cutoffs that are invariant under GLS. Our method effectively endows a pre-trained classifier with domain adaptation capabilities and returns valid prediction sets while maintaining high power. We demonstrate its performance on two challenging scientific problems in biology and astroparticle physics with data from realistic mechanistic models.

We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - \lambda^{\ast}) g_0(Y| X)+ \lambda^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast} f(Y|(a_{i}^{\ast})^{\top}X+b_i^{\ast},\sigma_{i}^{\ast})$, where $X, Y$ are respectively a covariate vector and a response variable, $g_{0}(Y|X)$ is a known function, $\lambda^{\ast} \in [0, 1]$ is true but unknown mixing proportion, and $(p_{i}^{\ast}, a_{i}^{\ast}, b_{i}^{\ast}, \sigma_{i}^{\ast})$ for $1 \leq i \leq k^{\ast}$ are unknown parameters of the Gaussian mixture of experts. This problem arises from the goodness-of-fit test when we would like to test whether the data are generated from $g_{0}(Y|X)$ (null hypothesis) or they are generated from the whole mixture (alternative hypothesis). Based on the algebraic structure of the expert functions and the distinguishability between $g_0$ and the mixture part, we construct novel Voronoi-based loss functions to capture the convergence rates of maximum likelihood estimation (MLE) for our models. We further demonstrate that our proposed loss functions characterize the local convergence rates of parameter estimation more accurately than the generalized Wasserstein, a loss function being commonly used for estimating parameters in the Gaussian mixture of experts.

We propose a novel white-box approach to hyper-parameter optimization. Motivated by recent work establishing a relationship between flat minima and generalization, we first establish a relationship between the strong convexity of the loss and its flatness. Based on this, we seek to find hyper-parameter configurations that improve flatness by minimizing the strong convexity of the loss. By using the structure of the underlying neural network, we derive closed-form equations to approximate the strong convexity parameter, and attempt to find hyper-parameters that minimize it in a randomized fashion. Through experiments on 14 classification datasets, we show that our method achieves strong performance at a fraction of the runtime.

A filter for inertial-based odometry is a recursive method used to estimate the pose from measurements of ego-motion and relative pose. Currently, there is no known filter that guarantees the computation of a globally optimal solution for the non-linear measurement model. In this paper, we demonstrate that an innovative filter, with the state being $SE_2(3)$ and the $\sqrt{n}$-\textit{consistent} pose as the initialization, efficiently achieves \textit{asymptotic optimality} in terms of minimum mean square error. This approach is tailored for real-time SLAM and inertial-based odometry applications. Our first contribution is that we propose an iterative filtering method based on the Gauss-Newton method on Lie groups which is numerically to solve the estimation of states from a priori and non-linear measurements. The filtering stands out due to its iterative mechanism and adaptive initialization. Second, when dealing with environmental measurements of the surroundings, we utilize a $\sqrt{n}$-consistent pose as the initial value for the update step in a single iteration. The solution is closed in form and has computational complexity $O(n)$. Third, we theoretically show that the approach can achieve asymptotic optimality in the sense of minimum mean square error from the a priori and virtual relative pose measurements (see Problem~\ref{prob:new update problem}). Finally, to validate our method, we carry out extensive numerical and experimental evaluations. Our results consistently demonstrate that our approach outperforms other state-of-the-art filter-based methods, including the iterated extended Kalman filter and the invariant extended Kalman filter, in terms of accuracy and running time.

In these settings, such as communicable disease management (Tuldrà et al., the underlying transition dynamics are often unknown 1999; Killian et al., 2019), prenatal and infant care (Hegde a priori, requiring online reinforcement & Doshi, 2016; Ope, 2020; Bashingwa et al., 2021), and learning (RL). However, existing methods in online cancer prevention (Wells et al., 2011; Lee et al., 2019), beneficiaries RL for RMABs cannot incorporate properties may at any time enter an adhering (e.g., following often present in real-world public health applications, their treatment regimen) or non-adhering (e.g., missing a such as contextual information and treatment) state. As adherence is often vital for ensuring non-stationarity. We present Bayesian Learning certain health outcomes, programs may allocate resources for Contextual RMABs (BCoR), an online or interventions to patients at risk of drop-out from the program RL approach for RMABs that novelly combines due to continued non-adherence. We can model this techniques in Bayesian modeling with Thompson problem as an RMAB by representing each beneficiary as an sampling to flexibly model a wide range of arm, their adherence status as the state of the corresponding complex RMAB settings, such as contextual and MDP, and the allocation of an intervention as the action.

However, the complexity and versatility of modern AI systems calls for a unified framework to assess their trustworthiness, which cannot The probabilistic formal verification (PFV) of be captured by a single evaluation metric or formal property. AI systems is in its infancy. So far, approaches This papers aims to introduce such a framework. We have been limited to ad-hoc algorithms for specific show how by leveraging the Weighted Model Integration classes of models and/or properties. We propose (WMI) [Belle et al., 2015] formalism, it is possible to devise a unifying framework for the PFV of AI systems a unified formulation for the probabilistic verification of based on Weighted Model Integration (WMI), combinatorial AI systems. Broadly speaking, WMI is the which allows to frame the problem in very general task of computing probabilities of arbitrary combinations terms. Crucially, this reduction enables the verification of logical and algebraic constraints given a structured joint of many properties of interest, like fairness, distribution over both continuous and discrete variables.