Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means of performing imputation of missing values using a probabilistic framework. While the present Gaussian copula models have shown to yield state of the art performance, they have two limitations: they are based on an approximation that is fast but may be imprecise and they do not support unordered multinomial variables. We address the first limitation using direct and arbitrarily precise approximations both for model estimation and imputation by using randomized quasi-Monte Carlo procedures. The method we provide has lower errors for the estimated model parameters and the imputed values, compared to previously proposed methods. We also extend the previous Gaussian copula models to include unordered multinomial variables in addition to the present support of ordinal, binary, and continuous variables.

Local approximations are popular methods to scale Gaussian processes (GPs) to big data. Local approximations reduce time complexity by dividing the original dataset into subsets and training a local expert on each subset. Aggregating the experts' prediction is done assuming either conditional dependence or independence between the experts. Imposing the \emph{conditional independence assumption} (CI) between the experts renders the aggregation of different expert predictions time efficient at the cost of poor uncertainty quantification. On the other hand, modeling dependent experts can provide precise predictions and uncertainty quantification at the expense of impractically high computational costs. By eliminating weak experts via a theory-guided expert selection step, we substantially reduce the computational cost of aggregating dependent experts while ensuring calibrated uncertainty quantification. We leverage techniques from the literature on undirected graphical models, using sparse precision matrices that encode conditional dependencies between experts to select the most important experts. Moreov

Probabilistic graphical models [KF09] provide a rich and unifying framework to model structured high-dimensional distributions in terms of the local dependencies between the input variables. The problem of inference in graphical models arises in many applications across scientific disciplines, see, e.g., [WJ08]. In this work, we study the inverse problem of learning graphical models from data. Various formalizations of this general learning problem have been studied during the past five decades, see, e.g., [CL68, Das97, AKN06, WRL06, AHHK12, SW12, LW12, BMS13, BGS14, Bre15, KM17], resulting in general theory and algorithms for various settings. In this work, we focus on learning Ising models [Isi25], the prototypical family of binary undirected graphical models with applications in computer vision, computational biology, and statistical physics [Li09, JEMF06, Fel04, Cha05].

Mathematical modelling of unemployment dynamics attempts to predict the probability of a job seeker finding a job as a function of time. This is typically achieved by using information in unemployment records. These records are right censored, making survival analysis a suitable approach for parameter estimation. The proposed model uses a deep artificial neural network (ANN) as a non-linear hazard function. Through embedding, high-cardinality categorical features are analysed efficiently. The posterior distribution of the ANN parameters are estimated using a variational Bayes method. The model is evaluated on a time-to-employment data set spanning from 2011 to 2020 provided by the Slovenian public employment service. It is used to determine the employment probability over time for each individual on the record. Similar models could be applied to other questions with multi-dimensional, high-cardinality categorical data including censored records. Such data is often encountered in personal records, for example in medical records.

Federated learning (FL) allows multiple clients to collaboratively learn a globally shared model through cycles of model aggregation and local model training without the need to share data. In this paper, we comprehensively study a new problem named aggregation error (AE), arising from the model aggregation stage on a server, which is mainly induced by the heterogeneity of the client data. Due to the large discrepancies between local models, the accompanying large AE generally results in a slow convergence and an expected reduction of accuracy for FL. In order to reduce AE, we propose a novel federated learning framework from a Bayesian perspective, in which a multivariate Gaussian product mechanism is employed to aggregate the local models. It is worth noting that the product of Gaussians is still a Gaussian. This property allows us to directly aggregate local expectations and covariances in a definitely convex form, thereby greatly reducing the AE. Accordingly, on the clients, we develop a new Federated Online Laplace Approximation (FOLA) method, which can estimate the parameters of the local posterior by repeatedly accumulating priors. Specifically, in every round, the global posterior distributed from the server can be treated as the priors, and thus the local posterior can also be effectively approximated by a Gaussian using FOLA. Experimental results on benchmarks reach state-of-the-arts performance and clearly demonstrate the advantages of the proposed method.

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. The encouraging results combined with advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). We contribute to this development by presenting a probabilistic VFM based on a Bayesian neural network. We consider homoscedastic and heteroscedastic measurement noise, and show how to train the models using maximum a posteriori estimation and variational inference. We study the methods by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where we achieve an average error of 5-6% and 9-13% for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. The difference in prediction performance and uncertainty on historical and future data is explored in detail, and the findings motivate the development of alternative strategies for data-driven VFM.

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a simple generalization of the adaptive interpolation method in Bayesian inference for linear regimes to sub-linear ones. A modification of the well-known approximate message passing algorithm to approach the MMSE fundamental limit is also proposed. Our results show that the traditional linear assumption between the signal dimension and number of observations in the replica and adaptive interpolation methods is not necessary for sparse signals. They also show how to modify the existing well-known AMP algorithms for linear regimes to sub-linear ones.

There is a clear need to involve patients in medical decisions. However, cognitive psychological research has highlighted the cognitive limitations of humans with respect to 1. Probabilistic assessment of the patient state and of potential outcomes of various decisions, 2. Elicitation of the patient utility function, and 3. Integration of the probabilistic knowledge and of patient preferences to determine the optimal strategy. Therefore, without adequate computational support, current shared decision models have severe ethical deficiencies. An informed consent model unfairly transfers the responsibility to a patient who does not have the necessary knowledge, nor the integration capability. A paternalistic model endows with exaggerated power a physician who might not be aware of the patient preferences, is prone to multiple cognitive biases, and whose computational integration capability is bounded. Recent progress in Artificial Intelligence suggests adding a third agent: a computer, in all deliberative medical decisions: Non emergency medical decisions in which more than one alternative exists, the patient preferences can be elicited, the therapeutic alternatives might be influenced by these preferences, medical knowledge exists regarding the likelihood of the decision outcomes, and there is sufficient decision time. Ethical physicians should exploit computational decision support technologies, neither making the decisions solely on their own, nor shirking their duty and shifting the responsibility to patients in the name of informed consent. The resulting three way (patient, care provider, computer) human machine model that we suggest emphasizes the patient preferences, the physician knowledge, and the computational integration of both aspects, does not diminish the physician role, but rather brings out the best in human and machine.

We present a framework for analysing agent incentives using causal influence diagrams. We establish that a well-known criterion for value of information is complete. We propose a new graphical criterion for value of control, establishing its soundness and completeness. We also introduce two new concepts for incentive analysis: response incentives indicate which changes in the environment affect an optimal decision, while instrumental control incentives establish whether an agent can influence its utility via a variable X. For both new concepts, we provide sound and complete graphical criteria. We show by example how these results can help with evaluating the safety and fairness of an AI system.

The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would otherwise remain unknown. However, these algorithms are less effective when the input data are limited in terms of sample size, which is often the case when working with real data. This paper focuses on purely machine learned and purely knowledge-based BNs and investigates their differences in terms of graphical structure and how well the implied statistical models explain the data. The tests are based on four previous case studies whose BN structure was determined by domain knowledge. Using various metrics, we compare the knowledge-based graphs to the machine learned graphs generated from various algorithms implemented in TETRAD spanning all three classes of learning. The results show that, while the algorithms produce graphs with much higher model selection score, the knowledge-based graphs are more accurate predictors of variables of interest. Maximising score fitting is ineffective in the presence of limited sample size because the fitting becomes increasingly distorted with limited data, guiding algorithms towards graphical patterns that share higher fitting scores and yet deviate considerably from the true graph. This highlights the value of causal knowledge in these cases, as well as the need for more appropriate fitting scores suitable for limited data. Lastly, the experiments also provide new evidence that support the notion that results from simulated data tell us little about actual real-world performance.