We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-state pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

Predicting the end-of-life or remaining useful life of batteries in electric vehicles is a critical and challenging problem, predominantly approached in recent years using machine learning to predict the evolution of the state-of-health during repeated cycling. To improve the accuracy of predictive estimates, especially early in the battery lifetime, a number of algorithms have incorporated features that are available from data collected by battery management systems. Unless multiple battery data sets are used for a direct prediction of the end-of-life, which is useful for ball-park estimates, such an approach is infeasible since the features are not known for future cycles. In this paper, we develop a highly-accurate method that can overcome this limitation, by using a modified Gaussian process dynamical model (GPDM). We introduce a kernelised version of GPDM for a more expressive covariance structure between both the observable and latent coordinates. We combine the approach with transfer learning to track the future state-of-health up to end-of-life. The method can incorporate features as different physical observables, without requiring their values beyond the time up to which data is available. Transfer learning is used to improve learning of the hyperparameters using data from similar batteries. The accuracy and superiority of the approach over modern benchmarks algorithms including a Gaussian process model and deep convolutional and recurrent networks are demonstrated on three data sets, particularly at the early stages of the battery lifetime.

How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by additive noise. We go beyond the usual independence assumption on the noise entries, by drawing the noise from a low-order polynomial orthogonal matrix ensemble. The resulting noise correlations make the setting relevant for applications but analytically challenging. We provide the first characterization of the Bayes-optimal limits of inference in this model. If the spike is rotation-invariant, we show that standard spectral PCA is optimal. However, for more general priors, both PCA and the existing approximate message passing algorithm (AMP) fall short of achieving the information-theoretic limits, which we compute using the replica method from statistical mechanics. We thus propose a novel AMP, inspired by the theory of Adaptive Thouless-Anderson-Palmer equations, which saturates the theoretical limit. This AMP comes with a rigorous state evolution analysis tracking its performance. Although we focus on specific noise distributions, our methodology can be generalized to a wide class of trace matrix ensembles at the cost of more involved expressions. Finally, despite the seemingly strong assumption of rotation-invariant noise, our theory empirically predicts algorithmic performance on real data, pointing at remarkable universality properties.

Algorithmic fairness has attracted increasing attention in the machine learning community. Various definitions are proposed in the literature, but the differences and connections among them are not clearly addressed. In this paper, we review and reflect on various fairness notions previously proposed in machine learning literature, and make an attempt to draw connections to arguments in moral and political philosophy, especially theories of justice. We also consider fairness inquiries from a dynamic perspective, and further consider the long-term impact that is induced by current prediction and decision. In light of the differences in the characterized fairness, we present a flowchart that encompasses implicit assumptions and expected outcomes of different types of fairness inquiries on the data generating process, on the predicted outcome, and on the induced impact, respectively. This paper demonstrates the importance of matching the mission (which kind of fairness one would like to enforce) and the means (which spectrum of fairness analysis is of interest, what is the appropriate analyzing scheme) to fulfill the intended purpose.

Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles.

Active learning seeks to reduce the amount of data required to fit the parameters of a model, thus forming an important class of techniques in modern machine learning. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Here we address this gap by proposing a novel framework for maximum-mutual-information input selection for discrete latent variable regression models. We first apply our method to a class of models known as "mixtures of linear regressions" (MLR). While it is well known that active learning confers no advantage for linear-Gaussian regression models, we use Fisher information to show analytically that active learning can nevertheless achieve large gains for mixtures of such models, and we validate this improvement using both simulations and real-world data. We then consider a powerful class of temporally structured latent variable models given by a Hidden Markov Model (HMM) with generalized linear model (GLM) observations, which has recently been used to identify discrete states from animal decision-making data. We show that our method substantially reduces the amount of data needed to fit GLM-HMM, and outperforms a variety of approximate methods based on variational and amortized inference. Infomax learning for latent variable models thus offers a powerful for characterizing temporally structured latent states, with a wide variety of applications in neuroscience and beyond.

To effectively guide the exploration of the code transform space for automated code evolution techniques, we present in this paper the first approach for structurally predicting code transforms at the level of AST nodes using conditional random fields (CRFs). Our approach first learns offline a probabilistic model that captures how certain code transforms are applied to certain AST nodes, and then uses the learned model to predict transforms for arbitrary new, unseen code snippets. {Our approach involves a novel representation of both programs and code transforms. Specifically, we introduce the formal framework for defining the so-called AST-level code transforms and we demonstrate how the CRF model can be accordingly designed, learned, and used for prediction}. We instantiate our approach in the context of repair transform prediction for Java programs. Our instantiation contains a set of carefully designed code features, deals with the training data imbalance issue, and comprises transform constraints that are specific to code. We conduct a large-scale experimental evaluation based on a dataset of bug fixing commits from real-world Java projects. The results show that when the popular evaluation metric \emph{top-3} is used, our approach predicts the code transforms with an accuracy varying from 41\% to 53\% depending on the transforms. Our model outperforms two baselines based on history probability and neural machine translation (NMT), suggesting the importance of considering code structure in achieving good prediction accuracy. In addition, a proof-of-concept synthesizer is implemented to concretize some repair transforms to get the final patches. The evaluation of the synthesizer on the Defects4j benchmark confirms the usefulness of the predicted AST-level repair transforms in producing high-quality patches.

In recent years, particle-based variational inference (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popularity as scalable methods for Bayesian inference. Unfortunately, the properties of such methods invariably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate. In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free. We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demonstrating comparable performance to other ParVI algorithms with no need to tune a learning rate.

Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, and often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.