A common task for recommender systems is to build a pro le of the interests of a user from items in their browsing history and later to recommend items to the user from the same catalog. The users' behavior consists of two parts: the sequence of items that they viewed without intervention (the organic part) and the sequences of items recommended to them and their outcome (the bandit part). In this paper, we propose Bayesian Latent Organic Bandit model (BLOB), a probabilistic approach to combine the 'or-ganic' and 'bandit' signals in order to improve the estimation of recommendation quality. The bandit signal is valuable as it gives direct feedback of recommendation performance, but the signal quality is very uneven, as it is highly concentrated on the recommendations deemed optimal by the past version of the recom-mender system. In contrast, the organic signal is typically strong and covers most items, but is not always relevant to the recommendation task. In order to leverage the organic signal to e ciently learn the bandit signal in a Bayesian model we identify three fundamental types of distances, namely action-history, action-action and history-history distances. We implement a scalable approximation of the full model using variational auto-encoders and the local re-paramerization trick. We show using extensive simulation studies that our method out-performs or matches the value of both state-of-the-art organic-based recommendation algorithms, and of bandit-based methods (both value and policy-based) both in organic and bandit-rich environments.

A KL-divergence objective of the joint distribution of data and labels allows to unify supervised learning, variational autoencoders (VAEs) and semi-supervised learning under one umbrella of variational inference. This viewpoint has several advantages. For VAEs, it clarifies the interpretation of encoder and decoder parts. For supervised learning, it re-iterates that the training procedure approximates the true posterior over labels and can always be viewed as approximate likelihood-free inference. This is typically not discussed, even though the derivation is well-known in the literature. In the context of semi-supervised learning it motivates an extended supervised scheme which allows to calculate a goodness-of-fit p-value using posterior predictive simulations. Flow-based networks with a standard normal base distribution are crucial. We discuss how they allow to rigorously define coverage for arbitrary joint posteriors on $\mathbb{R}^n \times \mathcal{S}^m$, which encompasses posteriors over directions. Finally, systematic uncertainties are naturally included in the variational viewpoint. With the three ingredients of (1) systematics, (2) coverage and (3) goodness-of-fit, flow-based neural networks have the potential to replace a large part of the statistical toolbox of the contemporary high-energy physicist.

Ubiquitous linear Gaussian exploratory tools such as principle component analysis (PCA) and factor analysis (FA) remain widely used as tools for: exploratory analysis, pre-processing, data visualization and related tasks. However, due to their rigid assumptions including crowding of high dimensional data, they have been replaced in many settings by more flexible and still interpretable latent feature models. The Feature allocation is usually modelled using discrete latent variables assumed to follow either parametric Beta-Bernoulli distribution or Bayesian nonparametric prior. In this work we propose a simple and tractable parametric feature allocation model which can address key limitations of current latent feature decomposition techniques. The new framework allows for explicit control over the number of features used to express each point and enables a more flexible set of allocation distributions including feature allocations with different sparsity levels. This approach is used to derive a novel adaptive Factor analysis (aFA), as well as, an adaptive probabilistic principle component analysis (aPPCA) capable of flexible structure discovery and dimensionality reduction in a wide case of scenarios. We derive both standard Gibbs sampler, as well as, an expectation-maximization inference algorithms that converge orders of magnitude faster to a reasonable point estimate solution. The utility of the proposed aPPCA model is demonstrated for standard PCA tasks such as feature learning, data visualization and data whitening. We show that aPPCA and aFA can infer interpretable high level features both when applied on raw MNIST and when applied for interpreting autoencoder features. We also demonstrate an application of the aPPCA to more robust blind source separation for functional magnetic resonance imaging (fMRI).

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known score-and-search approach. However, selecting a single model (i.e., the best scoring BN) can be misleading or may not achieve the best possible accuracy. An alternative to committing to a single model is to perform some form of Bayesian or frequentist model averaging, where the space of possible BNs is sampled or enumerated in some fashion. Unfortunately, existing approaches for model averaging either severely restrict the structure of the Bayesian network or have only been shown to scale to networks with fewer than 30 random variables. In this paper, we propose a novel approach to model averaging inspired by performance guarantees in approximation algorithms. Our approach has two primary advantages. First, our approach only considers credible models in that they are optimal or near-optimal in score. Second, our approach is more efficient and scales to significantly larger Bayesian networks than existing approaches.

Discovering high-level causal relations from low-level data is an important and challenging problem that comes up frequently in the natural and social sciences. In a series of papers, Chalupka et al. (2015, 2016a, 2016b, 2017) develop a procedure for causal feature learning (CFL) in an effort to automate this task. We argue that CFL does not recommend coarsening in cases where pragmatic considerations rule in favor of it, and recommends coarsening in cases where pragmatic considerations rule against it. We propose a new technique, pragmatic causal feature learning (PCFL), which extends the original CFL algorithm in useful and intuitive ways. We show that PCFL has the same attractive measure-theoretic properties as the original CFL algorithm. We compare the performance of both methods through theoretical analysis and experiments.

Predicting a customer's propensity-to-pay at an early point in the revenue cycle can provide organisations many opportunities to improve the customer experience, reduce hardship and reduce the risk of impaired cash flow and occurrence of bad debt. With the advancements in data science; machine learning techniques can be used to build models to accurately predict a customer's propensity-to-pay. Creating effective machine learning models without access to large and detailed datasets presents some significant challenges. This paper presents a case-study, conducted on a dataset from an energy organisation, to explore the uncertainty around the creation of machine learning models that are able to predict residential customers entering financial hardship which then reduces their ability to pay energy bills. Incorrect predictions can result in inefficient resource allocation and vulnerable customers not being proactively identified. This study investigates machine learning models' ability to consider different contexts and estimate the uncertainty in the prediction. Seven models from four families of machine learning algorithms are investigated for their novel utilisation. A novel concept of utilising a Baysian Neural Network to the binary classification problem of propensity-to-pay energy bills is proposed and explored for deployment.

We propose a novel amortized variational inference scheme for an empirical Bayes meta-learning model, where model parameters are treated as latent variables. We learn the prior distribution over model parameters conditioned on limited training data using a variational autoencoder approach. Our framework proposes sharing the same amortized inference network between the conditional prior and variational posterior distributions over the model parameters. While the posterior leverages both the labeled support and query data, the conditional prior is based only on the labeled support data. We show that in earlier work, relying on Monte-Carlo approximation, the conditional prior collapses to a Dirac delta function. In contrast, our variational approach prevents this collapse and preserves uncertainty over the model parameters. We evaluate our approach on the miniImageNet, CIFAR-FS and FC100 datasets, and present results demonstrating its advantages over previous work.

The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach. This article establishes the analytical properties of the LCE in an infinite-dimensional Hilbert space context. In addition, working in the space of affine Hilbert--Schmidt operators, we establish a regularisation procedure for this LCE. As an important application, we obtain a simple alternative derivation and intuitive justification of the conditional mean embedding formula, a concept widely used in machine learning to perform the conditioning of random variables by embedding them into reproducing kernel Hilbert spaces.

We consider the multiple-source adaptation (MSA) problem and improve a previously proposed MSA solution, where accurate density estimation per domain is required to obtain favorable learning guarantees. In this work, we replace the difficult task of density estimation per domain with a much easier task of domain classification, and show that the two solutions are equivalent given the true densities and domain classifier, yet the newer approach benefits from more favorable guarantees when densities and domain classifier are estimated from finite samples. Our experiments with real-world applications demonstrate that the new discriminative MSA solution outperforms the previous solution with density estimation, as well as other domain adaptation baselines.

Incorporating a human-in-the-loop system when deploying automated decision support is critical in healthcare contexts to create trust, as well as provide reliable performance on a patient-to-patient basis. Deep learning methods while having high performance, do not allow for this patient-centered approach due to the lack of uncertainty representation. Thus, we present a framework of uncertainty representation evaluated for medical image segmentation, using MCU-Net which combines a U-Net with Monte Carlo Dropout, evaluated with four different uncertainty metrics. The framework augments this by adding a human-in-the-loop aspect based on an uncertainty threshold for automated referral of uncertain cases to a medical professional. We demonstrate that MCU-Net combined with epistemic uncertainty and an uncertainty threshold tuned for this application maximizes automated performance on an individual patient level, yet refers truly uncertain cases. This is a step towards uncertainty representations when deploying machine learning based decision support in healthcare settings.