Linear mixed modelling is a popular approach for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known, estimating simultaneously the contribution of known and latent variance components in linear mixed models is a challenge that has so far relied on numerical gradient-based optimizers to maximize the likelihood function. This is unsatisfactory because the resulting solution is poorly characterized and the efficiency of the method may be suboptimal. Here we prove analytically that maximum-likelihood latent variables can always be chosen orthogonal to the known confounding factors, in other words, that maximum-likelihood latent variables explain sample covariances not already explained by known factors. Based on this result we propose a restricted maximum-likelihood method which estimates the latent variables by maximizing the likelihood on the restricted subspace orthogonal to the known confounding factors, and show that this reduces to probabilistic PCA on that subspace. The method then estimates the variance-covariance parameters by maximizing the remaining terms in the likelihood function given the latent variables, using a newly derived analytic solution for this problem. Compared to gradient-based optimizers, our method attains equal or higher likelihood values, can be computed using standard matrix operations, results in latent factors that don't overlap with any known factors, and has a runtime reduced by several orders of magnitude. We anticipate that the restricted maximum-likelihood method will facilitate the application of linear mixed modelling strategies for learning latent variance components to much larger gene expression datasets than currently possible.

Recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic, as the laws of thought, is a product and practice of the human brain, it leads to another hypothesis that there is a Bayesian algorithm and data-structure for logical reasoning. In this paper, we give a Bayesian account of entailment and characterize its abstract inferential properties. The Bayesian entailment is shown to be a monotonic consequence relation in an extreme case. In general, it is a sort of non-monotonic consequence relation without Cautious monotony or Cut. The preferential entailment, which is a representative non-monotonic consequence relation, is shown to be maximum a posteriori entailment, which is an approximation of the Bayesian entailment. We finally discuss merits of our proposals in terms of encoding preferences on defaults, handling change and contradiction, and modeling human entailment.

In this paper, we study the problem of fair classification in the presence of prior probability shifts, where the training set distribution differs from the test set. This phenomenon can be observed in the yearly records of several real-world datasets, such as recidivism records and medical expenditure surveys. If unaccounted for, such shifts can cause the predictions of a classifier to become unfair towards specific population subgroups. While the fairness notion called Proportional Equality (PE) accounts for such shifts, a procedure to ensure PE-fairness was unknown. In this work, we propose a method, called CAPE, which provides a comprehensive solution to the aforementioned problem. CAPE makes novel use of prevalence estimation techniques, sampling and an ensemble of classifiers to ensure fair predictions under prior probability shifts. We introduce a metric, called prevalence difference (PD), which CAPE attempts to minimize in order to ensure PE-fairness. We theoretically establish that this metric exhibits several desirable properties. We evaluate the efficacy of CAPE via a thorough empirical evaluation on synthetic datasets. We also compare the performance of CAPE with several popular fair classifiers on real-world datasets like COMPAS (criminal risk assessment) and MEPS (medical expenditure panel survey). The results indicate that CAPE ensures PE-fair predictions, while performing well on other performance metrics.

Driver models are invaluable for planning in autonomous vehicles as well as validating their safety in simulation. Highly parameterized black-box driver models are very expressive, and can capture nuanced behavior. However, they usually lack interpretability and sometimes exhibit unrealistic-even dangerous-behavior. Rule-based models are interpretable, and can be designed to guarantee "safe" behavior, but are less expressive due to their low number of parameters. In this article, we show that online parameter estimation applied to the Intelligent Driver Model captures nuanced individual driving behavior while providing collision free trajectories. We solve the online parameter estimation problem using particle filtering, and benchmark performance against rule-based and black-box driver models on two real world driving data sets. We evaluate the closeness of our driver model to ground truth data demonstration and also assess the safety of the resulting emergent driving behavior.

Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models to ground-truth models available for benchmark datasets, which in turn requires a notion of distance between causal models. While such distances have been proposed previously, they are limited by focusing on graphical properties of the causal models being compared. Here, we overcome this limitation by defining distances derived from the causal distributions induced by the models, rather than exclusively from their graphical structure. Pearl and Mackenzie (2018) have arranged the properties of causal models in a hierarchy called the "ladder of causation" spanning three rungs: observational, interventional, and counterfactual. Following this organization, we introduce a hierarchy of three distances, one for each rung of the ladder. Our definitions are intuitively appealing as well as efficient to compute approximately. We put our causal distances to use by benchmarking standard causal discovery systems on both synthetic and real-world datasets for which ground-truth causal models are available. Finally, we highlight the usefulness of our causal distances by briefly discussing further applications beyond the evaluation of causal discovery techniques.

The overarching goal of Explainable AI is to develop systems that not only exhibit intelligent behaviours, but also are able to explain their rationale and reveal insights. In explainable machine learning, methods that produce a high level of prediction accuracy as well as transparent explanations are valuable. In this work, we present an explainable classification method. Our method works by first constructing a symbolic Knowledge Base from the training data, and then performing probabilistic inferences on such Knowledge Base with linear programming. Our approach achieves a level of learning performance comparable to that of traditional classifiers such as random forests, support vector machines and neural networks. It identifies decisive features that are responsible for a classification as explanations and produces results similar to the ones found by SHAP, a state of the art Shapley Value based method. Our algorithms perform well on a range of synthetic and non-synthetic data sets.

Many applications of Bayesian data analysis involve sensitive information such as personal documents or medical records, motivating methods which ensure that privacy is protected. We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method. Our framework respects differential privacy, the gold-standard privacy criterion, and encompasses a large class of probabilistic models, called the Conjugate Exponential (CE) family. We observe that we can straightforwardly privatise VB's approximate posterior distributions for models in the CE family, by perturbing the expected sufficient statistics of the complete-data likelihood. For a broadly-used class of non-CE models, those with binomial likelihoods, we show how to bring such models into the CE family, such that inferences in the modified model resemble the private variational Bayes algorithm as closely as possible, using the Pólya-Gamma data augmentation scheme. The iterative nature of variational Bayes presents a further challenge since iterations increase the amount of noise needed. We overcome this by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple VB iterations and thus significantly decreases the amount of additive noise; and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning. We empirically demonstrate the effectiveness of our method in CE and non-CE models including latent Dirichlet allocation, Bayesian logistic regression, and sigmoid belief networks, evaluated on real-world datasets.

Using the ML approach, we can now assess diabetes in the patient. Learn more about how the algorithms used are dramatically changing health care. Diabetes is one of the deadliest diseases in the world. It is not only a disease, but also a creator of a variety of diseases such as heart attacks, blindness, and kidney diseases. The usual detection process is that patients visit the diagnostic center, consult their physician, and sit tight for a day or more to get their reports.

Algorithmic approaches to interpreting machine learning models have proliferated in recent years. We carry out human subject tests that are the first of their kind to isolate the effect of algorithmic explanations on a key aspect of model interpretability, simulatability, while avoiding important confounding experimental factors. A model is simulatable when a person can predict its behavior on new inputs. Through two kinds of simulation tests involving text and tabular data, we evaluate five explanations methods: (1) LIME, (2) Anchor, (3) Decision Boundary, (4) a Prototype model, and (5) a Composite approach that combines explanations from each method. Clear evidence of method effectiveness is found in very few cases: LIME improves simulatability in tabular classification, and our Prototype method is effective in counterfactual simulation tests. We also collect subjective ratings of explanations, but we do not find that ratings are predictive of how helpful explanations are. Our results provide the first reliable and comprehensive estimates of how explanations influence simulatability across a variety of explanation methods and data domains. We show that (1) we need to be careful about the metrics we use to evaluate explanation methods, and (2) there is significant room for improvement in current methods. All our supporting code, data, and models are publicly available at: https://github.com/peterbhase/InterpretableNLP-ACL2020

Deep neural networks ("deep learning") have emerged as a technology of choice to tackle problems in natural language processing, computer vision, speech recognition and gameplay, and in just a few years has led to superhuman level performance and ushered in a new wave of "AI." Buoyed by these successes, researchers in the physical sciences have made steady progress in incorporating deep learning into their respective domains. However, such adoption brings substantial challenges that need to be recognized and confronted. Here, we discuss both opportunities and roadblocks to implementation of deep learning within materials science, focusing on the relationship between correlative nature of machine learning and causal hypothesis driven nature of physical sciences. We argue that deep learning and AI are now well positioned to revolutionize fields where causal links are known, as is the case for applications in theory. When confounding factors are frozen or change only weakly, this leaves open the pathway for effective deep learning solutions in experimental domains. Similarly, these methods offer a pathway towards understanding the physics of real-world systems, either via deriving reduced representations, deducing algorithmic complexity, or recovering generative physical models. However, extending deep learning and "AI" for models with unclear causal relationship can produce misleading and potentially incorrect results. Here, we argue the broad adoption of Bayesian methods incorporating prior knowledge, development of DL solutions with incorporated physical constraints, and ultimately adoption of causal models, offers a path forward for fundamental and applied research. Most notably, while these advances can change the way science is carried out in ways we cannot imagine, machine learning is not going to substitute science any time soon.