Network topology identification (TI) is an essential function for distributed energy resources management systems (DERMS) to organize and operate widespread distributed energy resources (DERs). In this paper, discriminant analysis (DA) is deployed to develop a network TI function that relies only on the measurements available to DERMS. The propounded method is able to identify the network switching configuration, as well as the status of protective devices. Following, to improve the TI resiliency against the interruption of communication channels, a quadratic programming optimization approach is proposed to recover the missing signals. By deploying the propounded data recovery approach and Bayes' theorem together, a benchmark is developed afterward to identify anomalous measurements. This benchmark can make the TI function resilient against cyber-attacks. Having a low computational burden, this approach is fast-track and can be applied in real-time applications. Sensitivity analysis is performed to assess the contribution of different measurements and the impact of the system load type and loading level on the performance of the proposed approach.

This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks. The proposed neural network-based identification method requires the construction of a database from which an artificial neural network can be trained to learn the nonlinear relationship between the hyperparameters of a prior stochastic model of the random compliance field and some relevant quantities of interest of an ad hoc multiscale computational model. An initial database made up with input and target data is first generated from the computational model, from which a processed database is deduced by conditioning the input data with respect to the target data using the nonparametric statistics. Two-and three-layer feedforward artificial neural networks are then trained from each of the initial and processed databases to construct an algebraic representation of the nonlinear mapping between the hyperparameters (network outputs) and the quantities of interest (network inputs). The performances of the trained artificial neural networks are analyzed in terms of mean squared error, linear regression fit and probability distribution between network outputs and targets for both databases. An ad hoc probabilistic model of the input random vector is finally proposed in order to take into account uncertainties on the network input and to perform a robustness analysis of the network output with respect to the input uncertainties level. The capability of the proposed neural network-based identification method to efficiently solve the underlying statistical inverse problem is illustrated through two numerical examples developed within the framework of 2D plane stress linear elasticity, namely a first validation example on synthetic data obtained through computational simulations and a second application example on real experimental data obtained through a physical experiment monitored by digital image correlation on a real heterogeneous biological material (beef cortical bone).

Deep neural networks have proven extremely efficient at solving a wide range of inverse problems, but most often the uncertainty on the solution they provide is hard to quantify. In this work, we propose a generic Bayesian framework for solving inverse problems, in which we limit the use of deep neural networks to learning a prior distribution on the signals to recover. We adopt recent denoising score matching techniques to learn this prior from data, and subsequently use it as part of an annealed Hamiltonian Monte-Carlo scheme to sample the full posterior of image inverse problems. We apply this framework to Magnetic Resonance Image (MRI) reconstruction and illustrate how this approach not only yields high quality reconstructions but can also be used to assess the uncertainty on particular features of a reconstructed image.

Quality of life assessment represents a key process of deciding treatment success and viability. As such, patients' perceptions of their functional status and well-being are important inputs for impairment assessment. Given that patient completed questionnaires are often used to assess patient status and determine future treatment options, it is important to know the level of agreement of the words used by patients and different groups of medical professionals. In this paper, we propose a measure called the Agreement Ratio which provides a ratio of overall agreement when modelling words through Fuzzy Sets (FSs). The measure has been specifically designed for assessing this agreement in fuzzy sets which are generated from data such as patient responses. The measure relies on using the Jaccard Similarity Measure for comparing the different levels of agreement in the FSs generated.

Noisy labeled data is more a norm than a rarity for crowd sourced contents. It is effective to distill noise and infer correct labels through aggregation results from crowd workers. To ensure the time relevance and overcome slow responses of workers, online label aggregation is increasingly requested, calling for solutions that can incrementally infer true label distribution via subsets of data items. In this paper, we propose a novel online label aggregation framework, BiLA, which employs variational Bayesian inference method and designs a novel stochastic optimization scheme for incremental training. BiLA is flexible to accommodate any generating distribution of labels by the exact computation of its posterior distribution. We also derive the convergence bound of the proposed optimizer. We compare BiLA with the state of the art based on minimax entropy, neural networks and expectation maximization algorithms, on synthetic and real-world data sets. Our evaluation results on various online scenarios show that BiLA can effectively infer the true labels, with an error rate reduction of at least 10 to 1.5 percent points for synthetic and real-world datasets, respectively.

Let $(X, S, Y) \in \mathbb{R}^p \times \{1, 2\} \times \mathbb{R}$ be a triplet following some joint distribution $\mathbb{P}$ with feature vector $X$, sensitive attribute $S$ , and target variable $Y$. The Bayes optimal prediction $f^*$ which does not produce Disparate Treatment is defined as $f^*(x) = \mathbb{E}[Y | X = x]$. We provide a non-trivial example of a prediction $x \to f(x)$ which satisfies two common group-fairness notions: Demographic Parity \begin{align} (f(X) | S = 1) &\stackrel{d}{=} (f(X) | S = 2) \end{align} and Equal Group-Wise Risks \begin{align} \mathbb{E}[(f^*(X) - f(X))^2 | S = 1] = \mathbb{E}[(f^*(X) - f(X))^2 | S = 2]. \end{align} To the best of our knowledge this is the first explicit construction of a non-constant predictor satisfying the above. We discuss several implications of this result on better understanding of mathematical notions of algorithmic fairness.

We consider the problem of expected risk minimization when the population loss is strongly convex and the target domain of the decision variable is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. We restrict focus to the case that the decision variable belongs to a nonparametric Reproducing Kernel Hilbert Space (RKHS). To solve it, we consider stochastic mirror descent that employs (i) pseudo-gradients and (ii) projections. Compressive projections are executed via kernel orthogonal matching pursuit (KOMP), and overcome the fact that the vanilla RKHS parameterization grows unbounded with time. Moreover, pseudo-gradients are needed, e.g., when stochastic gradients themselves define integrals over unknown quantities that must be evaluated numerically, as in estimating the intensity parameter of an inhomogeneous Poisson Process, and multi-class kernel logistic regression with latent multi-kernels. We establish tradeoffs between accuracy of convergence in mean and the projection budget parameter under constant step-size and compression budget, as well as non-asymptotic bounds on the model complexity. Experiments demonstrate that we achieve state-of-the-art accuracy and complexity tradeoffs for inhomogeneous Poisson Process intensity estimation and multi-class kernel logistic regression.

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. Here we consider sequential algorithms that greedily minimise MMD over a discrete candidate set. We propose a novel non-myopic algorithm and, in order to both improve statistical efficiency and reduce computational cost, we investigate a variant that applies this technique to a mini-batch of the candidate set at each iteration. When the candidate points are sampled from the target, the consistency of these new algorithm - and their mini-batch variants - is established. We demonstrate the algorithms on a range of important computational problems, including optimisation of nodes in Bayesian cubature and the thinning of Markov chain output.

We present Model-Predictive Interaction Primitives -- a robot learning framework for assistive motion in human-machine collaboration tasks which explicitly accounts for biomechanical impact on the human musculoskeletal system. First, we extend Interaction Primitives to enable predictive biomechanics: the prediction of future biomechanical states of a human partner conditioned on current observations and intended robot control signals. In turn, we leverage this capability within a model-predictive control strategy to identify the future ergonomic and biomechanical ramifications of potential robot actions. Optimal control trajectories are selected so as to minimize future physical impact on the human musculoskeletal system. We empirically demonstrate that our approach minimizes knee or muscle forces via generated control actions selected according to biomechanical cost functions. Experiments are performed in synthetic and real-world experiments involving powered prosthetic devices.

Naive Bayes Classifiers are probabilistic models that are used for the classification task. It is based on the Bayes theorem with an assumption of independence among predictors. In the real-world, the independence assumption may or may not be true, but still, Naive Bayes performs well. Naive It is called naive because it assumes that all features in the dataset are mutually independent. Bayes, It is based on Bayes Theorem.