This paper is concerned with regularized extensions of hierarchical non-stationary temporal Gaussian processes (NSGPs) in which the parameters (e.g., length-scale) are modeled as GPs. In particular, we consider two commonly used NSGP constructions which are based on explicitly constructed non-stationary covariance functions and stochastic differential equations, respectively. We extend these NSGPs by including $L^1$-regularization on the processes in order to induce sparseness. To solve the resulting regularized NSGP (R-NSGP) regression problem we develop a method based on the alternating direction method of multipliers (ADMM) and we also analyze its convergence properties theoretically. We also evaluate the performance of the proposed methods in simulated and real-world datasets.

A key question in causal inference analyses is how to find subgroups with elevated treatment effects. This paper takes a machine learning approach and introduces a generative model, Causal Rule Sets (CRS), for interpretable subgroup discovery. A CRS model uses a small set of short decision rules to capture a subgroup where the average treatment effect is elevated. We present a Bayesian framework for learning a causal rule set. The Bayesian model consists of a prior that favors simple models for better interpretability as well as avoiding overfitting, and a Bayesian logistic regression that captures the likelihood of data, characterizing the relation between outcomes, attributes, and subgroup membership. The Bayesian model has tunable parameters that can characterize subgroups with various sizes, providing users with more flexible choices of models from the \emph{treatment efficient frontier}. We find maximum a posteriori models using iterative discrete Monte Carlo steps in the joint solution space of rules sets and parameters. To improve search efficiency, we provide theoretically grounded heuristics and bounding strategies to prune and confine the search space. Experiments show that the search algorithm can efficiently recover true underlying subgroups. We apply CRS on public and real-world datasets from domains where interpretability is indispensable. We compare CRS with state-of-the-art rule-based subgroup discovery models. Results show that CRS achieved consistently competitive performance on datasets from various domains, represented by high treatment efficient frontiers.

Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes to parameters and/or causal influences. By relying on a tractable representation of Bayesian networks as arithmetic circuits, we provide efficient algorithms for computing guaranteed upper and lower bounds on the interventional robustness probabilities. Experimental results demonstrate that the methods yield useful and interpretable bounds for a range of practical networks, paving the way towards provably causally robust decision-making systems.

Comprehensive synaptic wiring diagrams or "connectomes" provide a detailed map of all the neurons and their interconnections in a brain region or even an entire organism. Since the connectome of the nematode C. elegans was obtained using electron microscopy methods in 1986 [1], methods for data acquisition and analysis have both been scaled up and improved significantly. Today, it has become possible to provide connectomes of much more complex systems such as various Drosophila melanogaster circuits [2, 3], or even a large part of its brain [4, 5]; the olfactory bulb of zebrafish [6]; and various pieces of the rodent retina [7-9], hippocampus [10], and cortex [11-14]. While there still remain a number of formidable challenges on the way to the complete connectome of a mammal or even human brain [15], the data sets available today already give rise to a number of intriguing questions. At the same time, it is becoming increasingly clear that new quantitative methods must be developed to fully exploit the new troves of data that connectomics provides [16]. Here, we focus on local neural networks that store information in their synaptic connectivity. It has been hypothesised that cortical networks with their extensive recurrent synaptic connectivity are optimised for this task [17]. A popular model for these networks are attractor neural networks such as the Hopfield's model [18] and various generalisations [19-22], where memories are stored as

The minimum cost lifted multicut approach has proven practically good performance in a wide range of applications such as image decomposition, mesh segmentation, multiple object tracking, and motion segmentation. It addresses such problems in a graph-based model, where real-valued costs are assigned to the edges between entities such that the minimum cut decomposes the graph into an optimal number of segments. Driven by a probabilistic formulation of minimum cost multicuts, we provide a measure for the uncertainties of the decisions made during the optimization. We argue that access to such uncertainties is crucial for many practical applications and conduct an evaluation by means of sparsifications on three different, widely used datasets in the context of image decomposition (BSDS-500) and motion segmentation (DAVIS2016 and FBMS59) in terms of variation of information (VI) and Rand index (RI).

Order effects occur when judgments about a hypothesis's probability given a sequence of information do not equal the probability of the same hypothesis when the information is reversed. Different experiments have been performed in the literature that supports evidence of order effects. We proposed a Bayesian update model for order effects where each question can be thought of as a mini-experiment where the respondents reflect on their beliefs. We showed that order effects appear, and they have a simple cognitive explanation: the respondent's prior belief that two questions are correlated. The proposed Bayesian model allows us to make several predictions: (1) we found certain conditions on the priors that limit the existence of order effects; (2) we show that, for our model, the QQ equality is not necessarily satisfied (due to symmetry assumptions); and (3) the proposed Bayesian model has the advantage of possessing fewer parameters than its quantum counterpart.

Class-conditional noise commonly exists in machine learning tasks, where the class label is corrupted with a probability depending on its ground-truth. Many research efforts have been made to improve the model robustness against the class-conditional noise. However, they typically focus on the single label case by assuming that only one label is corrupted. In real applications, an instance is usually associated with multiple labels, which could be corrupted simultaneously with their respective conditional probabilities. In this paper, we formalize this problem as a general framework of learning with Class-Conditional Multi-label Noise (CCMN for short). We establish two unbiased estimators with error bounds for solving the CCMN problems, and further prove that they are consistent with commonly used multi-label loss functions. Finally, a new method for partial multi-label learning is implemented with unbiased estimator under the CCMN framework. Empirical studies on multiple datasets and various evaluation metrics validate the effectiveness of the proposed method.

We present a workflow for clinical data analysis that relies on Bayesian Structure Learning (BSL), an unsupervised learning approach, robust to noise and biases, that allows to incorporate prior medical knowledge into the learning process and that provides explainable results in the form of a graph showing the causal connections among the analyzed features. The workflow consists in a multi-step approach that goes from identifying the main causes of patient's outcome through BSL, to the realization of a tool suitable for clinical practice, based on a Binary Decision Tree (BDT), to recognize patients at high-risk with information available already at hospital admission time. We evaluate our approach on a feature-rich COVID-19 dataset, showing that the proposed framework provides a schematic overview of the multi-factorial processes that jointly contribute to the outcome. We discuss how these computational findings are confirmed by current understanding of the COVID-19 pathogenesis. Further, our approach yields to a highly interpretable tool correctly predicting the outcome of 85% of subjects based exclusively on 3 features: age, a previous history of chronic obstructive pulmonary disease and the PaO2/FiO2 ratio at the time of arrival to the hospital.

Bayesian neural networks have shown great promise in many applications where calibrated uncertainty estimates are crucial and can often also lead to a higher predictive performance. However, it remains challenging to choose a good prior distribution over their weights. While isotropic Gaussian priors are often chosen in practice due to their simplicity, they do not reflect our true prior beliefs well and can lead to suboptimal performance. Our new library, BNNpriors, enables state-of-the-art Markov Chain Monte Carlo inference on Bayesian neural networks with a wide range of predefined priors, including heavy-tailed ones, hierarchical ones, and mixture priors. Moreover, it follows a modular approach that eases the design and implementation of new custom priors. It has facilitated foundational discoveries on the nature of the cold posterior effect in Bayesian neural networks and will hopefully catalyze future research as well as practical applications in this area.

Synthetic data generation is of great interest in diverse applications, such as for privacy protection. Deep generative models, such as variational autoencoders (VAEs), are a popular approach for creating such synthetic datasets from original data. Despite the success of VAEs, there are limitations when it comes to the bimodal and skewed marginal distributions. These deviate from the unimodal symmetric distributions that are encouraged by the normality assumption typically used for the latent representations in VAEs. While there are extensions that assume other distributions for the latent space, this does not generally increase flexibility for data with many different distributions. Therefore, we propose a novel method, pre-transformation variational autoencoders (PTVAEs), to specifically address bimodal and skewed data, by employing pre-transformations at the level of original variables. Two types of transformations are used to bring the data close to a normal distribution by a separate parameter optimization for each variable in a dataset. We compare the performance of our method with other state-of-the-art methods for synthetic data generation. In addition to the visual comparison, we use a utility measurement for a quantitative evaluation. The results show that the PTVAE approach can outperform others in both bimodal and skewed data generation. Furthermore, the simplicity of the approach makes it usable in combination with other extensions of VAE.