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.

In this paper, we study a joint detection, mapping and navigation problem for a single unmanned aerial vehicle (UAV) equipped with a low complexity radar and flying in an unknown environment. The goal is to optimize its trajectory with the purpose of maximizing the mapping accuracy and, at the same time, to avoid areas where measurements might not be sufficiently informative from the perspective of a target detection. This problem is formulated as a Markov decision process (MDP) where the UAV is an agent that runs either a state estimator for target detection and for environment mapping, and a reinforcement learning (RL) algorithm to infer its own policy of navigation (i.e., the control law). Numerical results show the feasibility of the proposed idea, highlighting the UAV's capability of autonomously exploring areas with high probability of target detection while reconstructing the surrounding environment.

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

We define a message-passing algorithm for computing magnetization s in Restricted Boltzmann machines, which are Ising models on bipartite g raphs introduced as neural network models for probability distributions over spin con figurations. To model nontrivial statistical dependencies between the spins' couplings, we assume that the rectangular coupling matrix is drawn from an arbitrary bi-rotation in variant random matrix ensemble. Using the dynamical functional method of statist ical mechanics we exactly analyze the dynamics of the algorithm in the large system limit. We prove the global convergence of the algorithm under a stability criterion and c ompute asymptotic convergence rates showing excellent agreement with numerical sim ulations.

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.

Continuous time Hamiltonian Monte Carlo is introduced, as a powerful alternative to Markov chain Monte Carlo methods for continuous target distributions. The method is constructed in two steps: First Hamiltonian dynamics are chosen as the deterministic dynamics in a continuous time piecewise deterministic Markov process. Under very mild restrictions, such a process will have the desired target distribution as an invariant distribution. Secondly, the numerical implementation of such processes, based on adaptive numerical integration of second order ordinary differential equations is considered. The numerical implementation yields an approximate, yet highly robust algorithm that, unlike conventional Hamiltonian Monte Carlo, enables the exploitation of the complete Hamiltonian trajectories (and hence the title). The proposed algorithm may yield large speedups and improvements in stability relative to relevant benchmarks, while incurring numerical errors that are negligible relative to the overall Monte Carlo errors.

We extend the framework of Boltzmann machines to a network of complex-valued neurons with variable amplitudes, referred to as Complex Amplitude-Phase Boltzmann machine (CAP-BM). The model is capable of performing unsupervised learning on the amplitude and relative phase distribution in complex data. The sampling rule of the Gibbs distribution and the learning rules of the model are presented. Learning in a Complex Amplitude-Phase restricted Boltzmann machine (CAP-RBM) is demonstrated on synthetic complex-valued images, and handwritten MNIST digits transformed by a complex wavelet transform. Specifically, we show the necessity of a new amplitude-amplitude coupling term in our model. The proposed model is potentially valuable for machine learning tasks involving complex-valued data with amplitude variation, and for developing algorithms for novel computation hardware, such as coupled oscillators and neuromorphic hardware, on which Boltzmann sampling can be executed in the complex domain.