Minimizing error in prevalence estimates and diagnostic classifiers remains a challenging task in serology. In theory, these problems can be reduced to modeling class-conditional probability densities (PDFs) of measurement outcomes, which control all downstream analyses. However, this task quickly succumbs to the curse of dimensionality, even for assay outputs with only a few dimensions (e.g. target antigens). To address this problem, we propose a technique that uses empirical training data to classify samples and estimate prevalence in arbitrary dimension without direct access to the conditional PDFs. We motivate this method via a lemma that relates relative conditional probabilities to minimum-error classification boundaries. This leads us to formulate an optimization problem that: (i) embeds the data in a parameterized, curved space; (ii) classifies samples based on their position relative to a coordinate axis; and (iii) subsequently optimizes the space by minimizing the empirical classification error of pure training data, for which the classes are known. Interestingly, the solution to this problem requires use of a homotopy-type method to stabilize the optimization. We then extend the analysis to the case of impure training data, for which the classes are unknown. We find that two impure datasets suffice for both prevalence estimation and classification, provided they satisfy a linear independence property. Lastly, we discuss how our analysis unifies discriminative and generative learning techniques in a common framework based on ideas from set and measure theory. Throughout, we validate our methods in the context of synthetic data and a research-use SARS-CoV-2 enzyme-linked immunosorbent (ELISA) assay.

We consider trawl processes, which are stationary and infinitely divisible stochastic processes and can describe a wide range of statistical properties, such as heavy tails and long memory. In this paper, we develop the first likelihood-based methodology for the inference of real-valued trawl processes and introduce novel deterministic and probabilistic forecasting methods. Being non-Markovian, with a highly intractable likelihood function, trawl processes require the use of composite likelihood functions to parsimoniously capture their statistical properties. We formulate the composite likelihood estimation as a stochastic optimization problem for which it is feasible to implement iterative gradient descent methods. We derive novel gradient estimators with variances that are reduced by several orders of magnitude. We analyze both the theoretical properties and practical implementation details of these estimators and release a Python library which can be used to fit a large class of trawl processes. In a simulation study, we demonstrate that our estimators outperform the generalized method of moments estimators in terms of both parameter estimation error and out-of-sample forecasting error. Finally, we formalize a stochastic chain rule for our gradient estimators. We apply the new theory to trawl processes and provide a unified likelihood-based methodology for the inference of both real-valued and integer-valued trawl processes.

Real-world software applications must constantly evolve to remain relevant. This evolution occurs when developing new applications or adapting existing ones to meet new requirements, make corrections, or incorporate future functionality. Traditional methods of software quality control involve software quality models and continuous code inspection tools. These measures focus on directly assessing the quality of the software. However, there is a strong correlation and causation between the quality of the development process and the resulting software product. Therefore, improving the development process indirectly improves the software product, too. To achieve this, effective learning from past processes is necessary, often embraced through post mortem organizational learning. While qualitative evaluation of large artifacts is common, smaller quantitative changes captured by application lifecycle management are often overlooked. In addition to software metrics, these smaller changes can reveal complex phenomena related to project culture and management. Leveraging these changes can help detect and address such complex issues. Software evolution was previously measured by the size of changes, but the lack of consensus on a reliable and versatile quantification method prevents its use as a dependable metric. Different size classifications fail to reliably describe the nature of evolution. While application lifecycle management data is rich, identifying which artifacts can model detrimental managerial practices remains uncertain. Approaches such as simulation modeling, discrete events simulation, or Bayesian networks have only limited ability to exploit continuous-time process models of such phenomena. Even worse, the accessibility and mechanistic insight into such gray- or black-box models are typically very low. To address these challenges, we suggest leveraging objectively [...]

Commonly adopted in the manufacturing and aerospace sectors, digital twin (DT) platforms are increasingly seen as a promising paradigm to control, monitor, and analyze software-based, "open", communication systems. Notably, DT platforms provide a sandbox in which to test artificial intelligence (AI) solutions for communication systems, potentially reducing the need to collect data and test algorithms in the field, i.e., on the physical twin (PT). A key challenge in the deployment of DT systems is to ensure that virtual control optimization, monitoring, and analysis at the DT are safe and reliable, avoiding incorrect decisions caused by "model exploitation". To address this challenge, this paper presents a general Bayesian framework with the aim of quantifying and accounting for model uncertainty at the DT that is caused by limitations in the amount and quality of data available at the DT from the PT. In the proposed framework, the DT builds a Bayesian model of the communication system, which is leveraged to enable core DT functionalities such as control via multi-agent reinforcement learning (MARL), monitoring of the PT for anomaly detection, prediction, data-collection optimization, and counterfactual analysis. To exemplify the application of the proposed framework, we specifically investigate a case-study system encompassing multiple sensing devices that report to a common receiver. Experimental results validate the effectiveness of the proposed Bayesian framework as compared to standard frequentist model-based solutions.

Identifying causality is a challenging task in many data-intensive scenarios. Many algorithms have been proposed for this critical task. However, most of them consider the learning algorithms for directed acyclic graph (DAG) of Bayesian network (BN). These BN-based models only have limited causal explainability because of the issue of Markov equivalence class. Moreover, they are dependent on the assumption of stationarity, whereas many sampling time series from complex system are nonstationary. The nonstationary time series bring dataset shift problem, which leads to the unsatisfactory performances of these algorithms. To fill these gaps, a novel causation model named Unique Causal Network (UCN) is proposed in this paper. Different from the previous BN-based models, UCN considers the influence of time delay, and proves the uniqueness of obtained network structure, which addresses the issue of Markov equivalence class. Furthermore, based on the decomposability property of UCN, a higher-order causal entropy (HCE) algorithm is designed to identify the structure of UCN in a distributed way. HCE algorithm measures the strength of causality by using nearest-neighbors entropy estimator, which works well on nonstationary time series. Finally, lots of experiments validate that HCE algorithm achieves state-of-the-art accuracy when time series are nonstationary, compared to the other baseline algorithms.

Sentiment analysis is the process of identifying and categorizing people's emotions or opinions regarding various topics. The analysis of Twitter sentiment has become an increasingly popular topic in recent years. In this paper, we present several machine learning and a deep learning model to analysis sentiment of Persian political tweets. Our analysis was conducted using Bag of Words and ParsBERT for word representation. We applied Gaussian Naive Bayes, Gradient Boosting, Logistic Regression, Decision Trees, Random Forests, as well as a combination of CNN and LSTM to classify the polarities of tweets. The results of this study indicate that deep learning with ParsBERT embedding performs better than machine learning. The CNN-LSTM model had the highest classification accuracy with 89 percent on the first dataset and 71 percent on the second dataset. Due to the complexity of Persian, it was a difficult task to achieve this level of efficiency. The main objective of our research was to reduce the training time while maintaining the model's performance. As a result, several adjustments were made to the model architecture and parameters. In addition to achieving the objective, the performance was slightly improved as well.

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based methods have been proposed. As these methods need a great number of forward and backward computations, they become costly in computation, in particular, when the forward or generative models are complex and the evaluation of the likelihood becomes very costly. Using Deep Neural Network surrogate models and approximate computation can become very helpful. However, accounting for the uncertainties, we need first understand the Bayesian Deep Learning and then, we can see how we can use them for inverse problems. In this work, we focus on NN, DL and more specifically the Bayesian DL particularly adapted for inverse problems. We first give details of Bayesian DL approximate computations with exponential families, then we will see how we can use them for inverse problems. We consider two cases: First the case where the forward operator is known and used as physics constraint, the second more general data driven DL methods. keyword: Neural Network, Variational Bayesian inference, Bayesian Deep Learning (DL), Inverse problems, Physics based DL.

Cluster analysis is about finding groups in data. Robust statistics is about methods that are not affected strongly by deviations from the statistical model assumptions or moderate changes in a data set. Particular attention has been paid in the robustness literature to the effect of outliers. Outliers and other model deviations can have a strong effect on cluster analysis methods as well. There is now much work on robust cluster analysis, see [1, 19, 9] for overviews.

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method of choice. Indeed, kernel distribution regression is both computationally favorable, and supported by a recent learning theory. This theory also tackles the two-stage sampling setting, where only samples from the input distributions are available. In this paper, we improve the learning theory of kernel distribution regression. We address kernels based on Hilbertian embeddings, that encompass most, if not all, of the existing approaches. We introduce the novel near-unbiased condition on the Hilbertian embeddings, that enables us to provide new error bounds on the effect of the two-stage sampling, thanks to a new analysis. We show that this near-unbiased condition holds for three important classes of kernels, based on optimal transport and mean embedding. As a consequence, we strictly improve the existing convergence rates for these kernels. Our setting and results are illustrated by numerical experiments.

Recent years have witnessed the widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models. Despite their tremendous success, a number of vital problems like ML model brittleness, their fairness, and the lack of interpretability warrant the need for the active developments in explainable artificial intelligence (XAI) and formal ML model verification. The two major lines of work in XAI include feature selection methods, e.g. Anchors, and feature attribution techniques, e.g. LIME and SHAP. Despite their promise, most of the existing feature selection and attribution approaches are susceptible to a range of critical issues, including explanation unsoundness and out-of-distribution sampling. A recent formal approach to XAI (FXAI) although serving as an alternative to the above and free of these issues suffers from a few other limitations. For instance and besides the scalability limitation, the formal approach is unable to tackle the feature attribution problem. Additionally, a formal explanation despite being formally sound is typically quite large, which hampers its applicability in practical settings. Motivated by the above, this paper proposes a way to apply the apparatus of formal XAI to the case of feature attribution based on formal explanation enumeration. Formal feature attribution (FFA) is argued to be advantageous over the existing methods, both formal and non-formal. Given the practical complexity of the problem, the paper then proposes an efficient technique for approximating exact FFA. Finally, it offers experimental evidence of the effectiveness of the proposed approximate FFA in comparison to the existing feature attribution algorithms not only in terms of feature importance and but also in terms of their relative order.