Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their excessive computational cost and by the difficulty in adapting them for analyzing sequences (e.g. amino acid and nucleotide sequences) and graphs (e.g. ones representing small molecules). In this study, we develop efficient and scalable approaches for fitting GP models as well as fast convolution kernels which scale linearly with graph or sequence size. We implement these improvements by building an open-source Python library called xGPR. We compare the performance of xGPR with the reported performance of various deep learning models on 20 benchmarks, including small molecule, protein sequence and tabular data. We show that xGRP achieves highly competitive performance with much shorter training time. Furthermore, we also develop new kernels for sequence and graph data and show that xGPR generally outperforms convolutional neural networks on predicting key properties of proteins and small molecules. Importantly, xGPR provides uncertainty information not available from typical deep learning models. Additionally, xGPR provides a representation of the input data that can be used for clustering and data visualization. These results demonstrate that xGPR provides a powerful and generic tool that can be broadly useful in protein engineering and drug discovery.

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is challenging and requires restrictive approximations. Monte Carlo Dropout has been widely used as a relatively cheap way for approximate Inference and to estimate uncertainty with deep neural networks. Traditionally, the dropout mask is sampled independently from a fixed distribution. Recent works show that the dropout mask can be viewed as a latent variable, which can be inferred with variational inference. These methods face two important challenges: (a) the posterior distribution over masks can be highly multi-modal which can be difficult to approximate with standard variational inference and (b) it is not trivial to fully utilize sample-dependent information and correlation among dropout masks to improve posterior estimation. In this work, we propose GFlowOut to address these issues. GFlowOut leverages the recently proposed probabilistic framework of Generative Flow Networks (GFlowNets) to learn the posterior distribution over dropout masks. We empirically demonstrate that GFlowOut results in predictive distributions that generalize better to out-of-distribution data, and provide uncertainty estimates which lead to better performance in downstream tasks.

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that ensuring \emph{marginal fairness} for every dimension independently is not sufficient in general. Due to the exponential number of subgroups, however, directly measuring intersectional fairness from data is impossible. In this paper, our primary goal is to understand in detail the relationship between marginal and intersectional fairness through statistical analysis. We first identify a set of sufficient conditions under which an exact relationship can be obtained. Then, we prove bounds (easily computable through marginal fairness and other meaningful statistical quantities) in high-probability on intersectional fairness in the general case. Beyond their descriptive value, we show that these theoretical bounds can be leveraged to derive a heuristic improving the approximation and bounds of intersectional fairness by choosing, in a relevant manner, protected attributes for which we describe intersectional subgroups. Finally, we test the performance of our approximations and bounds on real and synthetic data-sets.

To date, various neural methods have been proposed for causal effect estimation based on observational data, where a default assumption is the same distribution and availability of variables at both training and inference (i.e., runtime) stages. However, distribution shift (i.e., domain shift) could happen during runtime, and bigger challenges arise from the impaired accessibility of variables. This is commonly caused by increasing privacy and ethical concerns, which can make arbitrary variables unavailable in the entire runtime data and imputation impractical. We term the co-occurrence of domain shift and inaccessible variables runtime domain corruption, which seriously impairs the generalizability of a trained counterfactual predictor. To counter runtime domain corruption, we subsume counterfactual prediction under the notion of domain adaptation. Specifically, we upper-bound the error w.r.t. the target domain (i.e., runtime covariates) by the sum of source domain error and inter-domain distribution distance. In addition, we build an adversarially unified variational causal effect model, named VEGAN, with a novel two-stage adversarial domain adaptation scheme to reduce the latent distribution disparity between treated and control groups first, and between training and runtime variables afterwards. We demonstrate that VEGAN outperforms other state-of-the-art baselines on individual-level treatment effect estimation in the presence of runtime domain corruption on benchmark datasets.

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.

Synthetic Aperture Radar (SAR) image understanding is crucial in remote sensing applications, but it is hindered by its intrinsic noise contamination, called speckle. Sophisticated statistical models, such as the $\mathcal{G}^0$ family of distributions, have been employed to SAR data and many of the current advancements in processing this imagery have been accomplished through extracting information from these models. In this paper, we propose improvements to parameter estimation in $\mathcal{G}^0$ distributions using the Method of Log-Cumulants. First, using Bayesian modeling, we construct that regularly produce reliable roughness estimates under both $\mathcal{G}^0_A$ and $\mathcal{G}^0_I$ models. Second, we make use of an approximation of the Trigamma function to compute the estimated roughness in constant time, making it considerably faster than the existing method for this task. Finally, we show how we can use this method to achieve fast and reliable SAR image understanding based on roughness information.

Predicting the presence of major depressive disorder (MDD) using behavioural and cognitive signals is a highly non-trivial task. The heterogeneous clinical profile of MDD means that any given speech, facial expression and/or observed cognitive pattern may be associated with a unique combination of depressive symptoms. Conventional discriminative machine learning models potentially lack the complexity to robustly model this heterogeneity. Bayesian networks, however, may instead be well-suited to such a scenario. These networks are probabilistic graphical models that efficiently describe the joint probability distribution over a set of random variables by explicitly capturing their conditional dependencies. This framework provides further advantages over standard discriminative modelling by offering the possibility to incorporate expert opinion in the graphical structure of the models, generating explainable model predictions, informing about the uncertainty of predictions, and naturally handling missing data. In this study, we apply a Bayesian framework to capture the relationships between depression, depression symptoms, and features derived from speech, facial expression and cognitive game data collected at thymia.

Modelling and forecasting real-life human behaviour using online social media is an active endeavour of interest in politics, government, academia, and industry. Since its creation in 2006, Twitter has been proposed as a potential laboratory that could be used to gauge and predict social behaviour. During the last decade, the user base of Twitter has been growing and becoming more representative of the general population. Here we analyse this user base in the context of the 2021 Mexican Legislative Election. To do so, we use a dataset of 15 million election-related tweets in the six months preceding election day. We explore different election models that assign political preference to either the ruling parties or the opposition. We find that models using data with geographical attributes determine the results of the election with better precision and accuracy than conventional polling methods. These results demonstrate that analysis of public online data can outperform conventional polling methods, and that political analysis and general forecasting would likely benefit from incorporating such data in the immediate future. Moreover, the same Twitter dataset with geographical attributes is positively correlated with results from official census data on population and internet usage in Mexico. These findings suggest that we have reached a period in time when online activity, appropriately curated, can provide an accurate representation of offline behaviour.

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure, where "local" parameters impact individual events and "global" parameters influence the entire dataset. We introduce practical approaches for optimal dataset-wide probabilistic inference in cases where the likelihood is intractable, but simulations can be realized via forward modeling. We construct neural estimators for the likelihood(-ratio) or posterior and show that explicitly accounting for the model's hierarchical structure can lead to tighter parameter constraints. We ground our discussion using case studies from the physical sciences, focusing on examples from particle physics (particle collider data) and astrophysics (strong gravitational lensing observations).

Assessing the predictive uncertainty of deep neural networks is crucial for safety-related applications of deep learning. Although Bayesian deep learning offers a principled framework for estimating model uncertainty, the approaches that are commonly used to approximate the posterior often fail to deliver reliable estimates of predictive uncertainty. In this paper we propose a novel criterion for predictive uncertainty, that a model's predictive variance should be grounded in the empirical density of the input. It should produce higher uncertainty for inputs that are improbable in the training data and lower uncertainty for those inputs that are more probable. To operationalize this criterion, we develop the density uncertainty layer, an architectural element for a stochastic neural network that guarantees that the density uncertain criterion is satisfied. We study neural networks with density uncertainty layers on the CIFAR-10 and CIFAR-100 uncertainty benchmarks. Compared to existing approaches, we find that density uncertainty layers provide reliable uncertainty estimates and robust out-of-distribution detection performance.