Approaches based on computing with words find good applicability in decision making systems. Predominantly finding their basis in type-1 fuzzy sets, computing with words approaches employ type-1 fuzzy sets as semantics of the linguistic terms. However, type-2 fuzzy sets have been proven to be scientifically more appropriate to represent linguistic information in practical systems. They take into account both the intra-uncertainty as well as the inter-uncertainty in cases where the linguistic information comes from a group of experts. Hence in this paper, we propose to introduce linguistic terms whose semantics are denoted by interval type-2 fuzzy sets within the hesitant fuzzy linguistic term set framework, resulting in type-2 fuzzy sets based hesitant fuzzy linguistic term sets. We also introduce a novel method of computing type-2 fuzzy envelopes out of multiple interval type-2 fuzzy sets with trapezoidal membership functions. Furthermore, the proposed framework with interval type-2 fuzzy sets is applied on a supplier performance evaluation scenario. Since humans are predominantly involved in the entire process of supply chain, their feedback is crucial while deciding many factors. Towards the end of the paper, we compare our presented model with various existing models and demonstrate the advantages of the former.

Modelling exchangeable relational data can be described by \textit{graphon theory}. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we introduce a smoothing procedure to piecewise-constant graphons to form {\em smoothing graphons}, which permit continuous intensity values for describing relations, but without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We initially propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. We then develop the Latent Feature Smoothing Graphon (LFSG), which improves on the ISG by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.

Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted, and in order to support safety critical systems, we require such systems to give an indication of the training sample related uncertainty associated with their output. Some readers may think that this is a well known issue which is already covered by the basic principles of pattern recognition. We will explain below how this is not the case and how the conventional (Likelihood estimate of) conditional probability of classification does not correctly assess this uncertainty. We provide a discussion of the standard interpretations of this problem and show how a quantitative approach based upon long standing methods can be practically applied. The methods are illustrated on the task of early diagnosis of dementing diseases using Magnetic Resonance Imaging.

Normalizing flows (Rezende & Mohamed, 2015) are probabilistic models constructed as a sequence of successive transformations applied to some initial distribution. A key strength of normalizing flows is their expressive power as generative models, while enjoying an explicitly computable form of the likelihood function evaluated on the transformed space. This makes them especially well-equipped for variational inference (VI). Neural networks are often used as inspiration for finding effective transformations (Dinh et al., 2015; van den Berg et al., 2018). Continuous normalizing flows were later developed in Chen et al. (2018) as a means to perform maximum likelihood estimation and VI for large-scale probabilistic models derived from ordinary differential equations (ODEs).

Neural networks with binary weights are computation-efficient and hardware-friendly, but their training is challenging because it involves a discrete optimization problem. Surprisingly, ignoring the discrete nature of the problem and using gradient-based methods, such as Straight-Through Estimator, still works well in practice. This raises the question: are there principled approaches which justify such methods? In this paper, we propose such an approach using the Bayesian learning rule. The rule, when applied to estimate a Bernoulli distribution over the binary weights, results in an algorithm which justifies some of the algorithmic choices made by the previous approaches. The algorithm not only obtains state-of-the-art performance, but also enables uncertainty estimation for continual learning to avoid catastrophic forgetting. Our work provides a principled approach for training binary neural networks which justifies and extends existing approaches.

Imputation of missing data is a common application in various classification problems where the feature training matrix has missingness. A widely used solution to this imputation problem is based on the lazy learning technique, $k$-nearest neighbor (kNN) approach. However, most of the previous work on missing data does not take into account the presence of the class label in the classification problem. Also, existing kNN imputation methods use variants of Minkowski distance as a measure of distance, which does not work well with heterogeneous data. In this paper, we propose a novel iterative kNN imputation technique based on class weighted grey distance between the missing datum and all the training data. Grey distance works well in heterogeneous data with missing instances. The distance is weighted by Mutual Information (MI) which is a measure of feature relevance between the features and the class label. This ensures that the imputation of the training data is directed towards improving classification performance. This class weighted grey kNN imputation algorithm demonstrates improved performance when compared to other kNN imputation algorithms, as well as standard imputation algorithms such as MICE and missForest, in imputation and classification problems. These problems are based on simulated scenarios and UCI datasets with various rates of missingness.

The ability to leverage large-scale hardware parallelism has been one of the key enablers of the accelerated recent progress in machine learning. Consequently, there has been considerable effort invested into developing efficient parallel variants of classic machine learning algorithms. However, despite the wealth of knowledge on parallelization, some classic machine learning algorithms often prove hard to parallelize efficiently while maintaining convergence. In this paper, we focus on efficient parallel algorithms for the key machine learning task of inference on graphical models, in particular on the fundamental belief propagation algorithm. We address the challenge of efficiently parallelizing this classic paradigm by showing how to leverage scalable relaxed schedulers in this context. We present an extensive empirical study, showing that our approach outperforms previous parallel belief propagation implementations both in terms of scalability and in terms of wall-clock convergence time, on a range of practical applications.

Multi-task reinforcement learning (RL) aims to simultaneously learn policies for solving many tasks. Several prior works have found that relabeling past experience with different reward functions can improve sample efficiency. Relabeling methods typically ask: if, in hindsight, we assume that our experience was optimal for some task, for what task was it optimal? In this paper, we show that hindsight relabeling is inverse RL, an observation that suggests that we can use inverse RL in tandem for RL algorithms to efficiently solve many tasks. We use this idea to generalize goal-relabeling techniques from prior work to arbitrary classes of tasks. Our experiments confirm that relabeling data using inverse RL accelerates learning in general multi-task settings, including goal-reaching, domains with discrete sets of rewards, and those with linear reward functions.

In the previous article, we studied Artificial Intelligence, its functions, and its python implementations. In this article, we will be studying Machine Learning. One thing that I believe is that if we are able to correlate anything with us or our life, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans.

Accurate predictions of reactive mixing are critical for many Earth and environmental science problems. To investigate mixing dynamics over time under different scenarios, a high-fidelity, finite-element-based numerical model is built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations are performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast, and molecular diffusion. Outputs comprise concentration profiles of the reactants and products. The inputs and outputs of these simulations are concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) emulators to approximate system behavior. The 20 ML emulators based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptron (MLP), are compared to assess these models. The ML emulators are specifically trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay, and degree of mixing. Linear classifiers and regressors fail to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP accurately classify the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predict the QoIs. At run time, trained ML emulators are $\approx10^5$ times faster than the high-fidelity numerical simulations. Speed and accuracy of the ensemble and MLP models facilitate uncertainty quantification, which usually requires 1,000s of model run, to estimate the uncertainty bounds on the QoIs.