B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto sets/fronts when sample points exactly lie on the Pareto set/front. However, if the sample points scatter away from the Pareto set/front, those methods often likely suffer from over-fitting. To overcome this issue, in this paper, we extend the B\'ezier simplex model to a probabilistic one and propose a new learning algorithm of it, which falls into the framework of approximate Bayesian computation (ABC) based on the Wasserstein distance. We also study the convergence property of the Wasserstein ABC algorithm. An extensive experimental evaluation on publicly available problem instances shows that the new algorithm converges on a finite sample. Moreover, it outperforms the deterministic fitting methods on noisy instances.

Due to the scarcity and often high acquisition cost of labelled data, machine learning methods that make effective use of large quantities of unlabelled data are being increasingly used. One such method is semi-supervised learning (SSL) where, in addition to labelled data, possibly large numbers of unlabelled observations are available at the time of the construction of the classification rule (classifier) to be used. Not surprisingly, semisupervised learning approaches have been gaining much attention in both the application oriented and the theoretical machine learning communities. However, theoretical analysis of SSL has so far been scarce. But last year, Ahfock and McLachlan (2020) provided an asymptotic basis on how to increase in certain situations the accuracy of the commonly used linear discriminant function formed from a partially classified sample as in SSL (Ahfock and McLachlan, 2020). The increase in accuracy can be of sufficient magnitude for this SSL-based classifier to have smaller error rate than that if it were formed from a completely classified sample.

Bayes' theorem is used as foundation Autoencoders are a family of unsupervised learning methods for inference in Bayesian neural networks, and Markov that use neural network architectures and learning algorithms chain Monte Carlo (MCMC) sampling methods [25] are used to learn a lower-dimensional representation (encoding) for constructing the posterior distribution. Variational inference of the data, which can then be used to reconstruct a representation [26] is another way to approximate the posterior distribution, close to the original input. They thus facilitate dimensionality which approximates an intractable posterior distribution by a reduction for prediction and classification [1, 2], and have tractable one. This makes it particularly suited to large data been successfully applied to image classification [3, 4], face sets and models, and so it has been popular for autoencoders recognition [5, 6], geoscience and remote sensing [7], speechbased and neural networks [13, 27].

Languages are powerful solutions to coordination problems: they provide stable, shared expectations about how the words we say correspond to the beliefs and intentions in our heads. Yet language use in a variable and non-stationary social environment requires linguistic representations to be flexible: old words acquire new ad hoc or partner-specific meanings on the fly. In this paper, we introduce a hierarchical Bayesian theory of convention formation that aims to reconcile the long-standing tension between these two basic observations. More specifically, we argue that the central computational problem of communication is not simply transmission, as in classical formulations, but learning and adaptation over multiple timescales. Under our account, rapid learning within dyadic interactions allows for coordination on partner-specific common ground, while social conventions are stable priors that have been abstracted away from interactions with multiple partners. We present new empirical data alongside simulations showing how our model provides a cognitive foundation for explaining several phenomena that have posed a challenge for previous accounts: (1) the convergence to more efficient referring expressions across repeated interaction with the same partner, (2) the gradual transfer of partner-specific common ground to novel partners, and (3) the influence of communicative context on which conventions eventually form.

Patients with Frontotemporal Dementia (FTD) have impaired cognitive abilities, executive and behavioral traits, loss of language ability, and decreased memory capabilities. Based on the distinct patterns of cortical atrophy and symptoms, the FTD spectrum primarily includes three variants: behavioral variant FTD (bvFTD), non-fluent variant primary progressive aphasia (nfvPPA), and semantic variant primary progressive aphasia (svPPA). The purpose of this study is to classify MRI images of every single subject into one of the spectrums of the FTD in a hierarchical order by applying data-driven techniques of Artificial Intelligence (AI) on cortical thickness data. This data is computed by FreeSurfer software. We used the Smallest Univalue Segment Assimilating Nucleus (SUSAN) technique to minimize the noise in cortical thickness data. Specifically, we took 204 subjects from the frontotemporal lobar degeneration neuroimaging initiative (NIFTD) database to validate this approach, and each subject was diagnosed in one of the diagnostic categories (bvFTD, svPPA, nfvPPA and cognitively normal). Our proposed automated classification model yielded classification accuracy of 86.5, 76, and 72.7 with support vector machine (SVM), linear discriminant analysis (LDA), and Naive Bayes methods, respectively, in 10-fold cross-validation analysis, which is a significant improvement on a traditional single multi-class model with an accuracy of 82.7, 73.4, and 69.2.

This is clearly demonstrated by the performance of BALD. To be specific, the BNNs trained with BALD have accuracies ranging from 70 90%, but for the models-under-test M-FashionMNIST and M-MNIST-ES (average & bad models), the metric estimation accuracies range from 90 100% - which are much higher than the BNNs' accuracies. For our proposed method ALT-MAS, with the models-under-test M-FashionMNIST, M-MNIST-ES, the behaviours are similar to those of BALD. That is, the metric estimation accuracies are always higher than the BNNs accuracies, especially for per-class metrics. It is worth noting that, for the per-class metrics, even though the BNNs accuracies by ALT-MAS are much lower than the BNNs by BALD, but the metric estimations by ALT-MAS are much higher than by BALD. This asserts the motivation of our sampling approach, that is, the BNN only needs to accurately predict the data points that contribute to the metric estimation. On the other hand, with the good model-under-test M-MNIST, due to our data augmentation training strategy, the BNN accuracies by ALT-MAS are much higher than those of BALD, and thus, the metric estimations by ALT-MAS are also more accurate than those by BALD. Figure 2: The accuracy of the BNN, for each combination of model-under-test (M-MNIST, M-FashionMNIST, & M-MNIST-ES) and metric set. Plotting mean and standard error over 3 repetitions (Best seen in color).

Interactions between several features sometimes play an important role in prediction tasks. But taking all the interactions into consideration will lead to an extremely heavy computational burden. For categorical features, the situation is more complicated since the input will be extremely high-dimensional and sparse if one-hot encoding is applied. Inspired by association rule mining, we propose a method that selects interactions of categorical features, called Random Intersection Chains. It uses random intersections to detect frequent patterns, then selects the most meaningful ones among them. At first a number of chains are generated, in which each node is the intersection of the previous node and a random chosen observation. The frequency of patterns in the tail nodes is estimated by maximum likelihood estimation, then the patterns with largest estimated frequency are selected. After that, their confidence is calculated by Bayes' theorem. The most confident patterns are finally returned by Random Intersection Chains. We show that if the number and length of chains are appropriately chosen, the patterns in the tail nodes are indeed the most frequent ones in the data set. We analyze the computation complexity of the proposed algorithm and prove the convergence of the estimators. The results of a series of experiments verify the efficiency and effectiveness of the algorithm.

Parametric statistical models are commonly used in many sub-fields of bioinformatics [1], [2]. For simplicity and computational concerns, bioinformatic scientists prefer to use differentiable and unconstrained statistical models than non-differentiable and constrained ones. For example, in pseudotime analysis (see section 3), in [3], the authors propose to regress gene expression on pseudotime using cubic B-spline so that an analytical solution is available. Other authors suggest to replace B-spline with a generalized linear model and a gradient-based method is applied to find maximum likelihood estimation [4]. In zero imputation problem, the authors construct a Gamma-Normal mixture model so that parameters can be estimated analytically [5]. In [6], the authors propose an unconstrained LASSO-type objective function and optimize it with a convex optimization algorithm. However, in real applications, it is common to impose constraints on parameters for interpretability. Besides, analytically solutions are not always available and the likelihood function is not differentiable or convex if discrete parameters are contained. Thus, constrained models without desirable mathematical properties can be more realistic and interpretable in many cases.

Extra virgin olive oil (EVOO) is the highest quality of olive oil and is characterized by highly beneficial nutritional properties. The large increase in both consumption and fraud, for example through adulteration, creates new challenges and an increasing demand for developing new quality assessment methodologies that are easier and cheaper to perform. As of today, the determination of olive oil quality is performed by producers through chemical analysis and organoleptic evaluation. The chemical analysis requires the advanced equipment and chemical knowledge of certified laboratories, and has therefore a limited accessibility. In this work a minimalist, portable and low-cost sensor is presented, which can perform olive oil quality assessment using fluorescence spectroscopy. The potential of the proposed technology is explored by analyzing several olive oils of different quality levels, EVOO, virgin olive oil (VOO), and lampante olive oil (LOO). The spectral data were analyzed using a large number of machine learning methods, including artificial neural networks. The analysis performed in this work demonstrates the possibility of performing classification of olive oil in the three mentioned classes with an accuracy of 100$\%$. These results confirm that this minimalist low-cost sensor has the potential of substituting expensive and complex chemical analysis.

Following the recent progress in Terahertz (THz) signal generation and radiation methods, joint THz communications and sensing applications are shaping the future of wireless systems. Towards this end, THz spectroscopy is expected to be carried over user equipment devices to identify material and gaseous components of interest. THz-specific signal processing techniques should complement this re-surged interest in THz sensing for efficient utilization of the THz band. In this paper, we present an overview of these techniques, with an emphasis on signal pre-processing (standard normal variate normalization, min-max normalization, and Savitzky-Golay filtering), feature extraction (principal component analysis, partial least squares, t-distributed stochastic neighbor embedding, and nonnegative matrix factorization), and classification techniques (support vector machines, k-nearest neighbor, discriminant analysis, and naive Bayes). We also address the effectiveness of deep learning techniques by exploring their promising sensing capabilities at the THz band. Lastly, we investigate the performance and complexity trade-offs of the studied methods in the context of joint communications and sensing; we motivate the corresponding use-cases, and we present few future research directions in the field.