Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input variables. On the other hand, the Probabilistic Graphical Models (PGMs) assume an underlying base graph between variables and learns a distribution over them. PGM design choices are carefully made such that the inference \& sampling algorithms are efficient. This brings in certain restrictions and often simplifying assumptions. In this work, we propose Neural Graph Revealers (NGRs), that are an attempt to efficiently merge the sparse graph recovery methods with PGMs into a single flow. The problem setting consists of an input data X with D features and M samples and the task is to recover a sparse graph showing connection between the features and learn a probability distribution over the D at the same time. NGRs view the neural networks as a `glass box' or more specifically as a multitask learning framework. We introduce `Graph-constrained path norm' that NGRs leverage to learn a graphical model that captures complex non-linear functional dependencies between the features in the form of an undirected sparse graph. Furthermore, NGRs can handle multimodal inputs like images, text, categorical data, embeddings etc. which is not straightforward to incorporate in the existing methods. We show experimental results of doing sparse graph recovery and probabilistic inference on data from Gaussian graphical models and a multimodal infant mortality dataset by Centers for Disease Control and Prevention.

Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between categorical variables. We provide a first graphical representation of the equivalence class of a staged tree, by looking only at a specific subset of its underlying independences. We further define a new pre-metric, inspired by the widely used structural intervention distance, to quantify the closeness between two staged trees in terms of their corresponding causal inference statements. A simulation study highlights the efficacy of staged trees in uncovering complexes, asymmetric causal relationships from data, and real-world data applications illustrate their use in practical causal analysis.

Online learning has gained increasing interest due Online optimization methods can directly be applied to update to its capability of tracking real-world streaming models that are fully specified by a certain value of its data. Although it has been widely studied in the parameters. Beyond such models, there is another class of setting of frequentist statistics, few works have models known as Bayesian models that treat the parameters considered online learning with the Bayesian sampling as random variables, thus giving an output also as a random problem. In this paper, we study an Online variable (often the expectation is taken as the final output on Particle-based Variational Inference (OPVI) algorithm par with the conventional case). The stochasticity enables that updates a set of particles to gradually Bayesian models to provide diverse outputs, characterize approximate the Bayesian posterior. To reduce prediction uncertainty, and be more robust to adversarial the gradient error caused by the use of stochastic attacks (Hernández-Lobato and Adams, 2015; Li and Gal, approximation, we include a sublinear increasing 2017; Yoon et al., 2018; Zhang et al., 2019; Tolpin et al., batch-size method to reduce the variance.

Many problems arising in control require the determination of a mathematical model of the application. This has often to be performed starting from input-output data, leading to a task known as system identification in the engineering literature. One emerging topic in this field is estimation of networks consisting of several interconnected dynamic systems. We consider the linear setting assuming that system outputs are the result of many correlated inputs, hence making system identification severely ill-conditioned. This is a scenario often encountered when modeling complex cybernetics systems composed by many sub-units with feedback and algebraic loops. We develop a strategy cast in a Bayesian regularization framework where any impulse response is seen as realization of a zero-mean Gaussian process. Any covariance is defined by the so called stable spline kernel which includes information on smooth exponential decay. We design a novel Markov chain Monte Carlo scheme able to reconstruct the impulse responses posterior by efficiently dealing with collinearity. Our scheme relies on a variation of the Gibbs sampling technique: beyond considering blocks forming a partition of the parameter space, some other (overlapping) blocks are also updated on the basis of the level of collinearity of the system inputs. Theoretical properties of the algorithm are studied obtaining its convergence rate. Numerical experiments are included using systems containing hundreds of impulse responses and highly correlated inputs.

This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that simultaneously incorporates intra-image information to promote sparsity in each individual edge map with inter-image information to promote similarities in any unchanged regions. By treating both the edges as well as the similarity between adjacent images as random variables, there is no need to separately form regions of change. Thus we avoid both additional computational cost as well as any information loss resulting from pre-processing the image. Our numerical examples demonstrate that our new method compares favorably with more standard SBL approaches.

Automatic recommendation systems based on deep neural networks have become extremely popular during the last decade. Some of these systems can however be used for applications which are ranked as High Risk by the European Commission in the A.I. act, as for instance for online job candidate recommendation. When used in the European Union, commercial AI systems for this purpose will then be required to have to proper statistical properties with regard to potential discrimination they could engender. This motivated our contribution, where we present a novel optimal transport strategy to mitigate undesirable algorithmic biases in multi-class neural-network classification. Our stratey is model agnostic and can be used on any multi-class classification neural-network model. To anticipate the certification of recommendation systems using textual data, we then used it on the Bios dataset, for which the learning task consists in predicting the occupation of female and male individuals, based on their LinkedIn biography. Results show that it can reduce undesired algorithmic biases in this context to lower levels than a standard strategy.

Within this study, we propose a new approach for natural language processing using Bayesian networks to predict and analyze the context and how this approach can be applied to the Community Question Answering domain. We discuss how Bayesian networks can detect semantic relationships and dependencies between entities, and this is connected to different score-based approaches of structure-learning. We compared the Bayesian networks with different score metrics, such as the BIC, BDeu, K2 and Chow-Liu trees. Our proposed approach out-performs the baseline model at the precision metric. We also discuss the influence of penalty terms on the structure of Bayesian networks and how they can be used to analyze the relationships between entities. In addition, we examine the visualization of directed acyclic graphs to analyze semantic relationships. The article further identifies issues with detecting certain semantic classes that are separated in the structure of directed acyclic graphs. Finally, we evaluate potential improvements for the Bayesian network approach.

Recent decades have witnessed great advancements in multiobjective evolutionary algorithms (MOEAs) for multiobjective optimization problems (MOPs). However, these progressively improved MOEAs have not necessarily been equipped with scalable and learnable problem-solving strategies for new and grand challenges brought by the scaling-up MOPs with continuously increasing complexity from diverse aspects, mainly including expensive cost of function evaluations, many objectives, large-scale search space, time-varying environments, and multi-task. Under different scenarios, divergent thinking is required in designing new powerful MOEAs for solving them effectively. In this context, research studies on learnable MOEAs with machine learning techniques have received extensive attention in the field of evolutionary computation. This paper begins with a general taxonomy of scaling-up MOPs and learnable MOEAs, followed by an analysis of the challenges that these MOPs pose to traditional MOEAs. Then, we synthetically overview recent advances of learnable MOEAs in solving various scaling-up MOPs, focusing primarily on four attractive directions (i.e., learnable evolutionary discriminators for environmental selection, learnable evolutionary generators for reproduction, learnable evolutionary evaluators for function evaluations, and learnable evolutionary transfer modules for sharing or reusing optimization experience). The insight of learnable MOEAs is offered to readers as a reference to the general track of the efforts in this field.

Autonomous Experimentation Platforms (AEPs) are advanced manufacturing platforms that, under intelligent control, can sequentially search the material design space (MDS) and identify parameters with the desired properties. At the heart of the intelligent control of these AEPs is the policy guiding the sequential experiments, which is to choose the location to carry out the next experiment. In such cases, a balance between exploitation and exploration must be achieved. A Bayesian Optimization (BO) framework with Expected Improvement based (EI-based) acquisition function can effectively search the MDS and guide where to conduct the next experiments so that the underlying relationship can be identified with a smaller number of experiments. The traditional BO framework tries to optimize a black box objective function in a sequential manner by relying on a single model. However, this single-model approach does not account for model uncertainty. Bayesian Model Averaging (BMA) addresses this issue by working with multiple models and thus considering the uncertainty in the models. In this work, we first apply the conventional BO algorithm with the most popular EI-based experiment policy in a real-life fatigue dataset for steel to predict the fatigue strength of steel. Afterward, we apply BMA to the same dataset by working with a set of predictive models and compare the performance of BMA with the traditional BO algorithm, which relies on a single model for approximation. We compare the results in terms of RMSE and find that BMA performs better than EI-based BO in the prediction task by considering the model uncertainty in its framework.

The standard paradigm of neural language generation adopts maximum likelihood estimation (MLE) as the optimizing method. From a distributional view, MLE in fact minimizes the Kullback-Leibler divergence (KLD) between the distribution of the real data and that of the model. However, this approach forces the model to distribute non-zero (sometimes large) probability mass to all training samples regardless of their quality. Moreover, in the attempt to cover the low-probability regions in the data distribution, the model systematically overestimates the probability of corrupted text sequences, which we conjecture is one of the main reasons for text degeneration during autoregressive decoding. To remedy this problem, we leverage the total variation distance (TVD) with its robustness to outliers, and develop practical bounds to apply it to language generation. Then, we introduce the TaiLr objective that balances the tradeoff of estimating TVD. Intuitively, TaiLr downweights real data samples that have low model probabilities with tunable penalization intensity. Experimental results show that our method alleviates the overestimation of degenerated sequences without sacrificing diversity and improves generation quality on a wide range of text generation tasks.