Bayes Nets (or Bayesian Networks) give remarkable results in determining the effects of many variables on an outcome. They typically perform strongly even in cases when other methods falter or fail. These networks have had relatively little use with business-related problems, although they have worked successfully for years in fields such as scientific research, public safety, aircraft guidance systems and national defense. Importantly, they often outperform regression, particularly in determining variables' effects. Regression is one of the most august multivariate methods, and among the most studied and applied.

As technology becomes more advanced, those who design, use and are otherwise affected by it want to know that it will perform correctly, and understand why it does what it does, and how to use it appropriately. In essence they want to be able to trust the systems that are being designed. In this survey we present assurances that are the method by which users can understand how to trust autonomous systems. Trust between humans and autonomy is reviewed, and the implications for the design of assurances are highlighted. A survey of existing research related to assurances is presented. Much of the surveyed research originates from fields such as interpretable, comprehensible, transparent, and explainable machine learning, as well as human-computer interaction, human-robot interaction, and e-commerce. Several key ideas are extracted from this work in order to refine the definition of assurances. The design of assurances is found to be highly dependent not only on the capabilities of the autonomous system, but on the characteristics of the human user, and the appropriate trust-related behaviors. Several directions for future research are identified and discussed.

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.

This repository contains the Tensorflow implementation of the Bayesian GAN by Yunus Saatchi and Andrew Gordon Wilson. This paper will be appearing at NIPS 2017. In the Bayesian GAN we propose conditional posteriors for the generator and discriminator weights, and marginalize these posteriors through stochastic gradient Hamiltonian Monte Carlo. Key properties of the Bayesian approach to GANs include (1) accurate predictions on semi-supervised learning problems; (2) minimal intervention for good performance; (3) a probabilistic formulation for inference in response to adversarial feedback; (4) avoidance of mode collapse; and (5) a representation of multiple complementary generative and discriminative models for data, forming a probabilistic ensemble. We illustrate a multimodal posterior over the parameters of the generator.

The extended model(s) can again be subjected to criticism, and the process continues until a satisfactory model is found (O'Hagan, 2003). Model criticism is contrasted with model comparison in that model criticism assesses a single model, while model comparison deals with at least two models to decide which model is a better fit. Model comparison can be applied to compare the original and the extended model after model criticism and extension (O'Hagan, 2003, p. 2). Most work on model criticism makes use of the idea that "if the model fits, then replicated data generated under the model should look similar to observed data" (Gelman et al., 2004, p. 165). In contrast, in this paper we focus on the idea that for latent variable models, we can probabilistically pull back the data into the space of the latent variables, and carry out model criticism in that space.

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power across experiments via hierarchical models. In practice, however, the approximate Bayesian methods necessary for inference have either failed to scale to large data sets or failed to provide theoretical guarantees on the quality of inference. We propose a new approach based on constructing polynomial approximate sufficient statistics for GLMs (PASS-GLM). We demonstrate that our method admits a simple algorithm as well as trivial streaming and distributed extensions that do not compound error across computations. We provide theoretical guarantees on the quality of point (MAP) estimates, the approximate posterior, and posterior mean and uncertainty estimates. We validate our approach empirically in the case of logistic regression using a quadratic approximation and show competitive performance with stochastic gradient descent, MCMC, and the Laplace approximation in terms of speed and multiple measures of accuracy -- including on an advertising data set with 40 million data points and 20,000 covariates.

Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network. Typically these models encode all features of the data into a single variable. Here we are interested in learning disentangled representations that encode distinct aspects of the data into separate variables. We propose to learn such representations using model architectures that generalise from standard VAEs, employing a general graphical model structure in the encoder and decoder. This allows us to train partially-specified models that make relatively strong assumptions about a subset of interpretable variables and rely on the flexibility of neural networks to learn representations for the remaining variables. We further define a general objective for semi-supervised learning in this model class, which can be approximated using an importance sampling procedure. We evaluate our framework's ability to learn disentangled representations, both by qualitative exploration of its generative capacity, and quantitative evaluation of its discriminative ability on a variety of models and datasets.

Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and hyper-parameter tuning. Traditional high-dimensional data reduction techniques, such as principal component analysis (PCA), partial least squares (PLS), reduced rank regression (RRR), projection pursuit regression (PPR) are all shown to be shallow learners. Their deep learning counterparts exploit multiple deep layers of data reduction which provide predictive performance gains. Stochastic gradient descent (SGD) training optimisation and Dropout (DO) regularization provide estimation and variable selection. Bayesian regularization is central to finding weights and connections in networks to optimize the predictive bias-variance trade-off. To illustrate our methodology, we provide an analysis of international bookings on Airbnb. Finally, we conclude with directions for future research.

We investigate the use of alternative divergences to Kullback-Leibler (KL) in variational inference(VI), based on the Variational Dropout \cite{kingma2015}. Stochastic gradient variational Bayes (SGVB) \cite{aevb} is a general framework for estimating the evidence lower bound (ELBO) in Variational Bayes. In this work, we extend the SGVB estimator with using Alpha-Divergences, which are alternative to divergences to VI' KL objective. The Gaussian dropout can be seen as a local reparametrization trick of the SGVB objective. We extend the Variational Dropout to use alpha divergences for variational inference. Our results compare $\alpha$-divergence variational dropout with standard variational dropout with correlated and uncorrelated weight noise. We show that the $\alpha$-divergence with $\alpha \rightarrow 1$ (or KL divergence) is still a good measure for use in variational inference, in spite of the efficient use of Alpha-divergences for Dropout VI \cite{Li17}. $\alpha \rightarrow 1$ can yield the lowest training error, and optimizes a good lower bound for the evidence lower bound (ELBO) among all values of the parameter $\alpha \in [0,\infty)$.

When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.