This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect of the number of neural networks used in the ensemble, which has been blindly adopted in previous studies, is scrutinized. As a result, an obvious trend towards underestimation of uncertainty as it increases is observed for the first time, and in this context, we propose the deep ensemble framework that applies the post-hoc calibration method to improve its uncertainty quantification performance. It is compared with Gaussian process regression and is shown to have superior performance in terms of regression accuracy ($\uparrow55\sim56\%$), reliability of estimated uncertainty ($\uparrow38\sim77\%$), and training efficiency ($\uparrow78\%$). Finally, the potential impact of the suggested framework on the Bayesian optimization is briefly examined, indicating that deep ensemble without calibration may lead to unintended exploratory behavior. This UQ framework can be seamlessly applied and extended to any regression task, as no special assumptions have been made for the specific problem used in this study.

Our research aims at classifying individuals based on their unique interactions on the touchscreen-based smartphones. In this research, we use'TouchAnalytics' datasets, which include 41 subjects and 30 different behavioral features. Furthermore, we derived new features from the raw data to improve the overall authentication performance. Previous research has already been done on the TouchAnalytics datasets with the state-of-the-art classifiers, including Support Vector Machine (SVM) and k-nearest neighbor (kNN) and achieved equal error rates (EERs) between 0% to 4%. Here, we propose a novel Deep Neural Net (DNN) architecture to classify the individuals correctly. The proposed DNN architecture has three dense layers and used many-to-many mapping techniques. When we combine the new features with the existing ones, SVM and k-NN achieved the classification accuracies of 94.7% and 94.6%, respectively. This research explored seven other classifiers and out of them, decision tree and our proposed DNN classifiers resulted in the highest accuracies with 100%. The others included: Logistic Regression (LR), Linear Discriminant Analysis (LDA), Gaussian Naive Bayes (NB), Neural Network, and VGGNet with the following accuracy scores of 94.7%, 95.9%, 31.9%,

Mutation validation (MV) is a recently proposed approach for model selection, garnering significant interest due to its unique characteristics and potential benefits compared to the widely used cross-validation (CV) method. In this study, we empirically compared MV and $k$-fold CV using benchmark and real-world datasets. By employing Bayesian tests, we compared generalization estimates yielding three posterior probabilities: practical equivalence, CV superiority, and MV superiority. We also evaluated the differences in the capacity of the selected models and computational efficiency. We found that both MV and CV select models with practically equivalent generalization performance across various machine learning algorithms and the majority of benchmark datasets. MV exhibited advantages in terms of selecting simpler models and lower computational costs. However, in some cases MV selected overly simplistic models leading to underfitting and showed instability in hyperparameter selection. These limitations of MV became more evident in the evaluation of a real-world neuroscientific task of predicting sex at birth using brain functional connectivity.

Bayesian inference is a powerful framework for making probabilistic inferences and decisions under uncertainty. Fundamental choices in modern Bayesian workflows concern the specification of the likelihood function and prior distributions, the posterior approximator, and the data. Each choice can significantly influence model-based inference and subsequent decisions, thereby necessitating sensitivity analysis. In this work, we propose a multifaceted approach to integrate sensitivity analyses into amortized Bayesian inference (ABI, i.e., simulation-based inference with neural networks). First, we utilize weight sharing to encode the structural similarities between alternative likelihood and prior specifications in the training process with minimal computational overhead. Second, we leverage the rapid inference of neural networks to assess sensitivity to various data perturbations or pre-processing procedures. In contrast to most other Bayesian approaches, both steps circumvent the costly bottleneck of refitting the model(s) for each choice of likelihood, prior, or dataset. Finally, we propose to use neural network ensembles to evaluate variation in results induced by unreliable approximation on unseen data. We demonstrate the effectiveness of our method in applied modeling problems, ranging from the estimation of disease outbreak dynamics and global warming thresholds to the comparison of human decision-making models. Our experiments showcase how our approach enables practitioners to effectively unveil hidden relationships between modeling choices and inferential conclusions.

Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. Additionally, we demonstrate how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method.

While the application of Artificial Intelligence in Finance has a long tradition, its potential in Entrepreneurship has been intensively explored only recently. In this context, Entrepreneurial Finance is a particularly fertile ground for future Artificial Intelligence proliferation. To support the latter, the study provides a bibliometric review of Artificial Intelligence applications in (1) entrepreneurial finance literature, and (2) corporate finance literature with implications for Entrepreneurship. Rigorous search and screening procedures of the scientific database Web of Science Core Collection resulted in the identification of 1890 relevant journal articles subjected to analysis. The bibliometric analysis gives a rich insight into the knowledge field's conceptual, intellectual, and social structure, indicating nascent and underdeveloped research directions. As far as we were able to identify, this is the first study to map and bibliometrically analyze the academic field concerning the relationship between Artificial Intelligence, Entrepreneurship, and Finance, and the first review that deals with Artificial Intelligence methods in Entrepreneurship. According to the results, Artificial Neural Network, Deep Neural Network and Support Vector Machine are highly represented in almost all identified topic niches. At the same time, applying Topic Modeling, Fuzzy Neural Network and Growing Hierarchical Self-organizing Map is quite rare. As an element of the research, and before final remarks, the article deals as well with a discussion of certain gaps in the relationship between Computer Science and Economics. These gaps do represent problems in the application of Artificial Intelligence in Economic Science. As a way to at least in part remedy this situation, the foundational paradigm and the bespoke demonstration of the Monte Carlo randomized algorithm are presented.

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational challenges. In this work, we propose the covariance alignment model to study and compare various alignment methods and establish a minimax lower bound for covariance alignment that has a non-standard dimension scaling because of the presence of a nuisance parameter. This lower bound is in fact minimax optimal and is achieved by a natural quasi MLE. However, this estimator involves a search over all permutations which is computationally infeasible even when the problem has moderate size. To overcome this limitation, we show that the celebrated Gromov-Wasserstein algorithm from optimal transport which is more amenable to fast implementation even on large-scale problems is also minimax optimal. These results give the first statistical justification for the deployment of the Gromov-Wasserstein algorithm in practice.

Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. $\overline{X|Y}$ as random variable containing information from $X$, but with removed information about $Y$, by using $(x,y) \leftrightarrow (\bar{x}=\textrm{CDF}_{X|Y=y}(x),y)$ reversible normalization. One application can be decoupling of individual information of variables: reversibly transform $(X_1,\ldots,X_n)\leftrightarrow(\tilde{X}_1,\ldots \tilde{X}_n)$ together containing the same information, but being independent: $\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$. It requires detailed models of complex conditional probability distributions - it is generally a difficult task, but here can be done through multiple dependency reducing iterations, using imperfect methods (here HCR: Hierarchical Correlation Reconstruction). It could be also used for direct mutual information - evaluating direct information transfer: without use of intermediate variables. For causality direction there is discussed multi-feature Granger causality, e.g. to trace various types of individual information transfers between such decoupled variables, including propagation time (delay).

While deep learning has achieved remarkable success, there is no clear explanation about why it works so well. In order to discuss this question quantitatively, we need a mathematical framework that explains what learning is in the first place. After several considerations, we succeeded in constructing a mathematical framework that can provide a unified understanding of all types of learning, including deep learning and learning in the brain. We call it learning principle, and it follows that all learning is equivalent to estimating the probability of input data. We not only derived this principle, but also mentioned its application to actual machine learning models. For example, we found that conventional supervised learning is equivalent to estimating conditional probabilities, and succeeded in making supervised learning more effective and generalized. We also proposed a new method of defining the values of estimated probability using differentiation, and showed that unsupervised learning can be performed on arbitrary dataset without any prior knowledge. Namely, this method is a general-purpose machine learning in the true sense. Moreover, we succeeded in describing the learning mechanism in the brain by considering the time evolution of a fully or partially connected model and applying this new method. The learning principle provides solutions to many unsolved problems in deep learning and cognitive neuroscience.

This study employs Bayesian methodologies to explore the influence of player or positional factors in predicting the probability of a shot resulting in a goal, measured by the expected goals (xG) metric. Utilising publicly available data from StatsBomb, Bayesian hierarchical logistic regressions are constructed, analysing approximately 10,000 shots from the English Premier League to ascertain whether positional or player-level effects impact xG. The findings reveal positional effects in a basic model that includes only distance to goal and shot angle as predictors, highlighting that strikers and attacking midfielders exhibit a higher likelihood of scoring. However, these effects diminish when more informative predictors are introduced. Nevertheless, even with additional predictors, player-level effects persist, indicating that certain players possess notable positive or negative xG adjustments, influencing their likelihood of scoring a given chance. The study extends its analysis to data from Spain's La Liga and Germany's Bundesliga, yielding comparable results. Additionally, the paper assesses the impact of prior distribution choices on outcomes, concluding that the priors employed in the models provide sound results but could be refined to enhance sampling efficiency for constructing more complex and extensive models feasibly.