We present a sound and complete algorithm for recovering causal graphs from observed, non-interventional data, in the possible presence of latent confounders and selection bias. We rely on the causal Markov and faithfulness assumptions and recover the equivalence class of the underlying causal graph by performing a series of conditional independence (CI) tests between observed variables. We propose a single step that is applied iteratively, such that the independence and causal relations entailed from the resulting graph, after any iteration, is correct and becomes more informative with successive iteration. Essentially, we tie the size of the CI condition set to its distance from the tested nodes on the resulting graph. Each iteration refines the skeleton and orientation by performing CI tests having condition sets that are larger than in the preceding iteration. In an iteration, condition sets of CI tests are constructed from nodes that are within a specified search distance, and the sizes of these condition sets is equal to this search distance. The algorithm then iteratively increases the search distance along with the condition set sizes. Thus, each iteration refines a graph, that was recovered by previous iterations having smaller condition sets---having a higher statistical power. We demonstrate that our algorithm requires significantly fewer CI tests and smaller condition sets compared to the FCI algorithm. This is evident for both recovering the true underlying graph using a perfect CI oracle, and accurately estimating the graph using limited observed data.

A key task for speech recognition systems is to reduce the mismatch between the training and evaluation data that is often attributable to speaker differences. To this end, speaker adaptation techniques play a vital role to reduce the mismatch. Model-based speaker adaptation approaches often require sufficient amounts of target speaker data to ensure robustness. When the amount of speaker level data is limited, speaker adaptation is prone to overfitting and poor generalization. To address the issue, this paper proposes a full Bayesian learning based DNN speaker adaptation framework to model speaker-dependent (SD) parameter uncertainty given limited speaker specific adaptation data. This framework is investigated in three forms of model based DNN adaptation techniques: Bayesian learning of hidden unit contributions (BLHUC), Bayesian parameterized activation functions (BPAct), and Bayesian hidden unit bias vectors (BHUB). In all three Bayesian adaptation methods, deterministic SD parameters are replaced by latent variable posterior distributions to be learned for each speaker, whose parameters are efficiently estimated using a variational inference based approach. Experiments conducted on 300-hour speed perturbed Switchboard corpus trained LF-MMI factored TDNN/CNN-TDNN systems featuring i-vector speaker adaptation suggest the proposed Bayesian adaptation approaches consistently outperform the adapted systems using deterministic parameters on the NIST Hub5'00 and RT03 evaluation sets in both unsupervised test time speaker adaptation and speaker adaptive training. The efficacy of the proposed Bayesian adaptation techniques is further demonstrated in a comparison against the state-of-the-art performance obtained on the same task using the most recent hybrid and end-to-end systems reported in the literature.

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.

For multimode processes, one has to establish local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is built. It would result in an abrupt performance decrease. Is it possible to make local monitoring model remember the features of previous modes? Choosing the principal component analysis (PCA) as a basic monitoring model, we try to resolve this problem. A modified PCA algorithm is built with continual learning ability for monitoring multimode processes, which adopts elastic weight consolidation (EWC) to overcome catastrophic forgetting of PCA for successive modes. It is called PCA-EWC, where the significant features of previous modes are preserved when a PCA model is established for the current mode. The computational complexity and key parameters are discussed to further understand the relationship between PCA and the proposed algorithm. Numerical case study and a practical industrial system in China are employed to illustrate the effectiveness of the proposed algorithm.

In a report published in Nature Communications, Hongliang Xin, associate professor of chemical engineering at Virginia Tech, and his team of researchers developed a Bayesian learning model of chemisorption, or Bayeschem for short, aiming to use artificial intelligence to unlock the nature of chemical bonding at catalyst surfaces. "It all comes down to how catalysts bind with molecules," said Xin. "The interaction has to be strong enough to break some chemical bonds at reasonably low temperatures, but not too strong that catalysts would be poisoned by reaction intermediates. This rule is known as the Sabatier principle in catalysis." Understanding how catalysts interact with different intermediates and determining how to control their bond strengths so that they are within that "goldilocks zone" is the key to designing efficient catalytic processes, Xin said. The research provides a tool for that purpose. Bayeschem works using Bayesian learning, a specific machine learning algorithm for inferring models from data.

The digital factory provides undoubtedly a great potential for future production systems in terms of efficiency and effectivity. A key aspect on the way to realize the digital copy of a real factory is the understanding of complex indoor environments on the basis of 3D data. In order to generate an accurate factory model including the major components, i.e. building parts, product assets and process details, the 3D data collected during digitalization can be processed with advanced methods of deep learning. In this work, we propose a fully Bayesian and an approximate Bayesian neural network for point cloud segmentation. This allows us to analyze how different ways of estimating uncertainty in these networks improve segmentation results on raw 3D point clouds. We achieve superior model performance for both, the Bayesian and the approximate Bayesian model compared to the frequentist one. This performance difference becomes even more striking when incorporating the networks' uncertainty in their predictions. For evaluation we use the scientific data set S3DIS as well as a data set, which was collected by the authors at a German automotive production plant. The methods proposed in this work lead to more accurate segmentation results and the incorporation of uncertainty information makes this approach especially applicable to safety critical applications.

Explainable components in XAI algorithms often come from a familiar set of models, such as linear models or decision trees. We formulate an approach where the type of explanation produced is guided by a specification. Specifications are elicited from the user, possibly using interaction with the user and contributions from other areas. Areas where a specification could be obtained include forensic, medical, and scientific applications. Providing a menu of possible types of specifications in an area is an exploratory knowledge representation and reasoning task for the algorithm designer, aiming at understanding the possibilities and limitations of efficiently computable modes of explanations. Two examples are discussed: explanations for Bayesian networks using the theory of argumentation, and explanations for graph neural networks. The latter case illustrates the possibility of having a representation formalism available to the user for specifying the type of explanation requested, for example, a chemical query language for classifying molecules. The approach is motivated by a theory of explanation in the philosophy of science, and it is related to current questions in the philosophy of science on the role of machine learning.

Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also represent asymmetric distributions. In a recent contribution we showed that SkewGP and probit likelihood are conjugate, which allows us to compute the exact posterior for non-parametric binary classification and preference learning. In this paper, we generalize previous results and we prove that SkewGP is conjugate with both the normal and affine probit likelihood, and more in general, with their product. This allows us to (i) handle classification, preference, numeric and ordinal regression, and mixed problems in a unified framework; (ii) derive closed-form expression for the corresponding posterior distributions. We show empirically that the proposed framework based on SkewGP provides better performance than Gaussian processes in active learning and Bayesian (constrained) optimization.

Machine learning algorithms have been successfully used to approximate nonlinear maps under weak assumptions on the structure and properties of the maps. We present deep neural networks using dense and convolutional layers to solve an inverse problem, where we seek to estimate parameters in a FitzHugh-Nagumo model, which consists of a nonlinear system of ordinary differential equations (ODEs). We employ the neural networks to approximate reconstruction maps for model parameter estimation from observational data, where the data comes from the solution of the ODE and takes the form of a time series representing dynamically spiking membrane potential of a (biological) neuron. We target this dynamical model because of the computational challenges it poses in an inference setting, namely, having a highly nonlinear and nonconvex data misfit term and permitting only weakly informative priors on parameters. These challenges cause traditional optimization to fail and alternative algorithms to exhibit large computational costs. We quantify the predictability of model parameters obtained from the neural networks with statistical metrics and investigate the effects of network architectures and presence of noise in observational data. Our results demonstrate that deep neural networks are capable of very accurately estimating parameters in dynamical models from observational data.

Reliably quantifying the confidence of deep neural classifiers is a challenging yet fundamental requirement for deploying such models in safety-critical applications. In this paper, we introduce a novel target criterion for model confidence, namely the true class probability (TCP). We show that TCP offers better properties for confidence estimation than standard maximum class probability (MCP). Since the true class is by essence unknown at test time, we propose to learn TCP criterion from data with an auxiliary model, introducing a specific learning scheme adapted to this context. We evaluate our approach on the task of failure prediction and of self-training with pseudo-labels for domain adaptation, which both necessitate effective confidence estimates. Extensive experiments are conducted for validating the relevance of the proposed approach in each task. We study various network architectures and experiment with small and large datasets for image classification and semantic segmentation. In every tested benchmark, our approach outperforms strong baselines.