Fast machine learning-based surrogate models are trained to emulate slow, high-fidelity engineering simulation models to accelerate engineering design tasks. This introduces uncertainty as the surrogate is only an approximation of the original model. Bayesian methods can quantify that uncertainty, and deep learning models exist that follow the Bayesian paradigm. These models, namely Bayesian neural networks and Gaussian process models, enable us to give predictions together with an estimate of the model's uncertainty. As a result we can derive uncertainty-aware surrogate models that can automatically suspect unseen design samples that cause large emulation errors. For these samples, the high-fidelity model can be queried instead. This outlines how the Bayesian paradigm allows us to hybridize fast, but approximate, and slow, but accurate models. In this paper, we train two types of Bayesian models, dropout neural networks and stochastic variational Gaussian Process models, to emulate a complex high dimensional building energy performance simulation problem. The surrogate model processes 35 building design parameters (inputs) to estimate 12 different performance metrics (outputs). We benchmark both approaches, prove their accuracy to be competitive, and show that errors can be reduced by up to 30% when the 10% of samples with the highest uncertainty are transferred to the high-fidelity model.

Contrastive approaches to representation learning have recently shown great promise. In contrast to generative approaches, these contrastive models learn a deterministic encoder with no notion of uncertainty or confidence. In this paper, we introduce a simple approach based on "contrasting distributions" that learns to assign uncertainty for pretrained contrastive representations. In particular, we train a deep network from a representation to a distribution in representation space, whose variance can be used as a measure of confidence. In our experiments, we show that this deep uncertainty model can be used (1) to visually interpret model behavior, (2) to detect new noise in the input to deployed models, (3) to detect anomalies, where we outperform 10 baseline methods across 11 tasks with improvements of up to 14% absolute, and (4) to classify out-of-distribution examples where our fully unsupervised model is competitive with supervised methods. The success of supervised learning relies heavily on large datasets with semantic annotations. But as the prediction tasks we are interested in become increasingly complex -- such as applications in radiology (Irvin et al., 2019), law (Wang et al., 2013), and autonomous driving (Maurer et al., 2016) -- the expense and difficulty of annotation quickly grows to be unmanageable. As such, learning useful representations without human annotation is an important, longstanding problem. These "unsupervised" approaches largely span two categories: generative and discriminative. Generative models seek to capture the data density using ideas from approximate Bayesian inference (Hinton et al., 2006; Kingma & Welling, 2013; Rezende et al., 2014) and game theory (Goodfellow et al., 2014; Dumoulin et al., 2016).

Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual information. Although showing promise for this difficult problem, the variational methods have been theoretically and empirically proven to have serious statistical limitations: 1) many methods struggle to produce accurate estimates when the underlying mutual information is either low or high; 2) the resulting estimators may suffer from high variance. Our approach is based on training a classifier that provides the probability that a data sample pair is drawn from the joint distribution rather than from the product of its marginal distributions. Moreover, we establish a direct connection between mutual information and the average log odds estimate produced by the classifier on a test set, leading to a simple and accurate estimator of mutual information. We show theoretically that our method and other variational approaches are equivalent when they achieve their optimum, while our method sidesteps the variational bound. Empirical results demonstrate high accuracy of our approach and the advantages of our estimator in the context of representation learning. Mutual information (MI) measures the information that two random variables share.

Learning data representations that capture task-related features, but are invariant to nuisance variations remains a key challenge in machine learning. We introduce an automated Bayesian inference framework, called AutoBayes, that explores different graphical models linking classifier, encoder, decoder, estimator and adversary network blocks to optimize nuisance-invariant machine learning pipelines. AutoBayes also enables learning disentangled representations, where the latent variable is split into multiple pieces to impose different relation with nuisance variation and task labels. We benchmark the framework on several public datasets, where we have access to subject and class labels during training, and provide analysis of its capability for subject-transfer learning with/without variational modeling and adversarial training. We demonstrate a significant performance improvement by ensemble stacking across explored graphical models.

Neural autoregressive sequence models are used to generate sequences in a variety of natural language processing (NLP) tasks, where they are evaluated according to sequence-level task losses. These models are typically trained with maximum likelihood estimation, which ignores the task loss, yet empirically performs well as a surrogate objective. Typical approaches to directly optimizing the task loss such as policy gradient and minimum risk training are based around sampling in the sequence space to obtain candidate update directions that are scored based on the loss of a single sequence. In this paper, we develop an alternative method based on random search in the parameter space that leverages access to the maximum likelihood gradient. We propose maximum likelihood guided parameter search (MGS), which samples from a distribution over update directions that is a mixture of random search around the current parameters and around the maximum likelihood gradient, with each direction weighted by its improvement in the task loss. MGS shifts sampling to the parameter space, and scores candidates using losses that are pooled from multiple sequences. Our experiments show that MGS is capable of optimizing sequence-level losses, with substantial reductions in repetition and non-termination in sequence completion, and similar improvements to those of minimum risk training in machine translation.

This paper shows a novel fuzzy approximate reasoning method based on the least common multiple (LCM). I ts fundamental idea is to obtain a new fuzzy reasoning result by the extended distance measure based on LCM between the antecedent fuzzy set and the consequent one in discrete SISO fuzzy system. T he proposed metho d is called LCM one. And then this paper analyzes its some properties, i.e., the reductive property, information loss occurred in reasoning process, and the convergence of fuzzy control. Theoretical and experimental research results highlight that proposed method meaningfully improve the reductive property and information loss and controllability than the previous fuzzy reasoning methods.

As Machine Learning technologies become increasingly used in contexts that affect citizens, companies as well as researchers need to be confident that their application of these methods will not have unexpected social implications, such as bias towards gender, ethnicity, and/or people with disabilities. There is significant literature on approaches to mitigate bias and promote fairness, yet the area is complex and hard to penetrate for newcomers to the domain. This article seeks to provide an overview of the different schools of thought and approaches to mitigating (social) biases and increase fairness in the Machine Learning literature. It organises approaches into the widely accepted framework of pre-processing, in-processing, and post-processing methods, subcategorizing into a further 11 method areas. Although much of the literature emphasizes binary classification, a discussion of fairness in regression, recommender systems, unsupervised learning, and natural language processing is also provided along with a selection of currently available open source libraries. The article concludes by summarising open challenges articulated as four dilemmas for fairness research.

In this paper, we propose the multivariate quantile Bayesian structural time series (MQB-STS) model for the joint quantile time series forecast, which is the first such model for correlated multivariate time series to the author's best knowledge. The MQBSTS model also enables quantile based feature selection in its regression component where each time series has its own pool of contemporaneous external time series predictors, which is the first time that a fully data-driven quantile feature selection technique applicable to time series data to the author's best knowledge. Different from most machine learning algorithms, the MQBSTS model has very few hyper-parameters to tune, requires small datasets to train, converges fast, and is executable on ordinary personal computers. Extensive examinations on simulated data and empirical data confirmed that the MQBSTS model has superior performance in feature selection, parameter estimation, and forecast.

We define deep kernel processes in which positive definite Gram matrices are progressively transformed by nonlinear kernel functions and by sampling from (inverse) Wishart distributions. Remarkably, we find that deep Gaussian processes (DGPs), Bayesian neural networks (BNNs), infinite BNNs, and infinite BNNs with bottlenecks can all be written as deep kernel processes. For DGPs the equivalence arises because the Gram matrix formed by the inner product of features is Wishart distributed, and as we show, standard isotropic kernels can be written entirely in terms of this Gram matrix -- we do not need knowledge of the underlying features. We define a tractable deep kernel process, the deep inverse Wishart process, and give a doubly-stochastic inducing-point variational inference scheme that operates on the Gram matrices, not on the features, as in DGPs. We show that the deep inverse Wishart process gives superior performance to DGPs and infinite BNNs on standard fully-connected baselines.

This paper introduces Distributed Stein Variational Gradient Descent (DSVGD), a non-parametric generalized Bayesian inference framework for federated learning. DSVGD maintains a number of non-random and interacting particles at a central server to represent the current iterate of the model global posterior. The particles are iteratively downloaded and updated by one of the agents with the end goal of minimizing the global free energy. By varying the number of particles, DSVGD enables a flexible trade-off between per-iteration communication load and number of communication rounds. DSVGD is shown to compare favorably to benchmark frequentist and Bayesian federated learning strategies, also scheduling a single device per iteration, in terms of accuracy and scalability with respect to the number of agents, while also providing well-calibrated, and hence trustworthy, predictions.