Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrated variant of expectation propagation. This method resembles standard EP with an additional factor that "tilts" the posterior towards higher-utility decisions. We show applications to Gaussian process classification under binary utility functions with asymmetric penalties on False Negative and False Positive errors, and show how this asymmetry can have dramatic consequences on what information is "useful" to capture in an approximation.

We develop a structural econometric model to capture the decision dynamics of human evaluators on an online micro-lending platform, and estimate the model parameters using a real-world dataset. We find two types of biases in gender, preference-based bias and belief-based bias, are present in human evaluators' decisions. Both types of biases are in favor of female applicants. Through counterfactual simulations, we quantify the effect of gender bias on loan granting outcomes and the welfare of the company and the borrowers. Our results imply that both the existence of the preference-based bias and that of the belief-based bias reduce the company's profits. When the preference-based bias is removed, the company earns more profits. When the belief-based bias is removed, the company's profits also increase. Both increases result from raising the approval probability for borrowers, especially male borrowers, who eventually pay back loans. For borrowers, the elimination of either bias decreases the gender gap of the true positive rates in the credit risk evaluation. We also train machine learning algorithms on both the real-world data and the data from the counterfactual simulations. We compare the decisions made by those algorithms to see how evaluators' biases are inherited by the algorithms and reflected in machine-based decisions. We find that machine learning algorithms can mitigate both the preference-based bias and the belief-based bias.

As stated in the general overview, we need to calculate the summary statistics for each class (and feature) as well as the prior. First of all, we need to gather some basic information about the dataset and create three zero-matrices to store the mean, the variance, and the prior for each class. Next, we iterate over all the classes, compute the statistics and update our zero-matrices accordingly. For example, assume we have two unique classes (0,1) and two features in our dataset. The matrix storing the mean values, therefore will have a two rows and two columns (2x2). The prior is just a single vector (1x2), containing the ratio of a single classes' samples divided by the total sample size.

Humans ability to transfer knowledge through teaching is one of the essential aspects for human intelligence. A human teacher can track the knowledge of students to customize the teaching on students needs. With the rise of online education platforms, there is a similar need for machines to track the knowledge of students and tailor their learning experience. This is known as the Knowledge Tracing (KT) problem in the literature. Effectively solving the KT problem would unlock the potential of computer-aided education applications such as intelligent tutoring systems, curriculum learning, and learning materials' recommendation. Moreover, from a more general viewpoint, a student may represent any kind of intelligent agents including both human and artificial agents. Thus, the potential of KT can be extended to any machine teaching application scenarios which seek for customizing the learning experience for a student agent (i.e., a machine learning model). In this paper, we provide a comprehensive and systematic review for the KT literature. We cover a broad range of methods starting from the early attempts to the recent state-of-the-art methods using deep learning, while highlighting the theoretical aspects of models and the characteristics of benchmark datasets. Besides these, we shed light on key modelling differences between closely related methods and summarize them in an easy-to-understand format. Finally, we discuss current research gaps in the KT literature and possible future research and application directions.

Instead of using current deep-learning segmentation models (like the UNet and variants), we approach the segmentation problem using trained Convolutional Neural Network (CNN) classifiers, which automatically extract important features from classified targets for image classification. Those extracted features can be visualized and formed heatmaps using Gradient-weighted Class Activation Mapping (Grad-CAM). This study tested whether the heatmaps could be used to segment the classified targets. We also proposed an evaluation method for the heatmaps; that is, to re-train the CNN classifier using images filtered by heatmaps and examine its performance. We used the mean-Dice coefficient to evaluate segmentation results. Results from our experiments show that heatmaps can locate and segment partial tumor areas. But only use of the heatmaps from CNN classifiers may not be an optimal approach for segmentation. In addition, we have verified that the predictions of CNN classifiers mainly depend on tumor areas, and dark regions in Grad-CAM's heatmaps also contribute to classification.

Classification models are a fundamental component of physical-asset management technologies such as structural health monitoring (SHM) systems and digital twins. Previous work introduced \textit{risk-based active learning}, an online approach for the development of statistical classifiers that takes into account the decision-support context in which they are applied. Decision-making is considered by preferentially querying data labels according to \textit{expected value of perfect information} (EVPI). Although several benefits are gained by adopting a risk-based active learning approach, including improved decision-making performance, the algorithms suffer from issues relating to sampling bias as a result of the guided querying process. This sampling bias ultimately manifests as a decline in decision-making performance during the later stages of active learning, which in turn corresponds to lost resource/utility. The current paper proposes two novel approaches to counteract the effects of sampling bias: \textit{semi-supervised learning}, and \textit{discriminative classification models}. These approaches are first visualised using a synthetic dataset, then subsequently applied to an experimental case study, specifically, the Z24 Bridge dataset. The semi-supervised learning approach is shown to have variable performance; with robustness to sampling bias dependent on the suitability of the generative distributions selected for the model with respect to each dataset. In contrast, the discriminative classifiers are shown to have excellent robustness to the effects of sampling bias. Moreover, it was found that the number of inspections made during a monitoring campaign, and therefore resource expenditure, could be reduced with the careful selection of the statistical classifiers used within a decision-supporting monitoring system.

Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep networks in the limit of infinite layer width, $n\to\infty$. Here we present a unified and systematic derivation of the mean-field theory for both architectures that starts from first principles by employing established methods from statistical physics of disordered systems. The theory elucidates that while the mean-field equations are different with regard to their temporal structure, they yet yield identical Gaussian kernels when readouts are taken at a single time point or layer, respectively. Bayesian inference applied to classification then predicts identical performance and capabilities for the two architectures. Numerically, we find that convergence towards the mean-field theory is typically slower for recurrent networks than for deep networks and the convergence speed depends non-trivially on the parameters of the weight prior as well as the depth or number of time steps, respectively. Our method exposes that Gaussian processes are but the lowest order of a systematic expansion in $1/n$. The formalism thus paves the way to investigate the fundamental differences between recurrent and deep architectures at finite widths $n$.

AI and humans bring complementary skills to group deliberations. Modeling this group decision making is especially challenging when the deliberations include an element of risk and an exploration-exploitation process of appraising the capabilities of the human and AI agents. To investigate this question, we presented a sequence of intellective issues to a set of human groups aided by imperfect AI agents. A group's goal was to appraise the relative expertise of the group's members and its available AI agents, evaluate the risks associated with different actions, and maximize the overall reward by reaching consensus. We propose and empirically validate models of human-AI team decision making under such uncertain circumstances, and show the value of socio-cognitive constructs of prospect theory, influence dynamics, and Bayesian learning in predicting the behavior of human-AI groups.

This paper proposes an efficient approach to learning disentangled representations with causal mechanisms based on the difference of conditional probabilities in original and new distributions. We approximate the difference with models' generalization abilities so that it fits in the standard machine learning framework and can be efficiently computed. In contrast to the state-of-the-art approach, which relies on the learner's adaptation speed to new distribution, the proposed approach only requires evaluating the model's generalization ability. We provide a theoretical explanation for the advantage of the proposed method, and our experiments show that the proposed technique is 1.9-11.0 Causal reasoning is a fundamental tool that has shown significant impact in different disciplines (Rubin & Waterman, 2006; Ramsey et al., 2010; Rotmensch et al., 2017; Schölkopf et al., 2021), and it has roots in work by David Hume in the eighteenth century (Hume, 2003) and classical AI (Pearl, 2003). Causality has been mainly studied from a statistical perspective (Pearl, 2009; Peters et al., 2016; Greenland et al., 1999; Pearl, 2018) with Judea Pearl's work on the causal calculus leading its statistical development. More recently, there has been a growing interest in integrating statistical techniques into machine learning to leverage their benefits. Welling raises a particular question about how to disentangle correlation from causation in machine learning settings to take advantage of the sample efficiency and generalization abilities of causal reasoning (Welling, 2015). Although machine learning has achieved important results on a variety of tasks like computer vision and games over the past decade (e.g., Mnih et al. (2015); Silver et al. (2017); Szegedy et al. (2017); Hudson & Manning (2018)), current approaches can struggle to generalize when the test data distribution is much different from the training distribution (common in real applications). Further, these successful methods are typically "data-hungry", requiring an abundance of labeled examples to perform well across data distributions. In statistical settings, encoding the causal structure in models has been shown to have significant efficiency advantages.

The paper describes the use of Bayesian regression for building time series models and stacking different predictive models for time series. Using Bayesian regression for time series modeling with nonlinear trend was analyzed. This approach makes it possible to estimate an uncertainty of time series prediction and calculate value at risk characteristics. A hierarchical model for time series using Bayesian regression has been considered. In this approach, one set of parameters is the same for all data samples, other parameters can be different for different groups of data samples. Such an approach allows using this model in the case of short historical data for specified time series, e.g. in the case of new stores or new products in the sales prediction problem. In the study of predictive models stacking, the models ARIMA, Neural Network, Random Forest, Extra Tree were used for the prediction on the first level of model ensemble. On the second level, time series predictions of these models on the validation set were used for stacking by Bayesian regression. This approach gives distributions for regression coefficients of these models. It makes it possible to estimate the uncertainty contributed by each model to stacking result. The information about these distributions allows us to select an optimal set of stacking models, taking into account the domain knowledge. The probabilistic approach for stacking predictive models allows us to make risk assessment for the predictions that are important in a decision-making process.