Bayesian optimization has emerged as a strong candidate tool for global optimization of functions with expensive evaluation costs. However, due to the dynamic nature of research in Bayesian approaches, and the evolution of computing technology, using Bayesian optimization in a parallel computing environment remains a challenge for the non-expert. In this report, I review the state-of-the-art in parallel and scalable Bayesian optimization methods. In addition, I propose practical ways to avoid a few of the pitfalls of Bayesian optimization, such as oversampling of edge parameters and over-exploitation of high performance parameters. Finally, I provide relatively simple, heuristic algorithms, along with their open source software implementations, that can be immediately and easily deployed in any computing environment.

This paper is based on a previous publication [29]. Our work extends exception mining and outlier detection to the case of object-relational data. Object-relational data represent a complex heterogeneous network [12], which comprises objects of different types, links among these objects, also of different types, and attributes of these links. This special structure prohibits a direct vectorial data representation. We follow the well-established Exceptional Model Mining framework, which leverages machine learning models for exception mining: A object is exceptional to the extent that a model learned for the object data differs from a model learned for the general population. Exceptional objects can be viewed as outliers. We apply state of-the-art probabilistic modelling techniques for object-relational data that construct a graphical model (Bayesian network), which compactly represents probabilistic associations in the data. A new metric, derived from the learned object-relational model, quantifies the extent to which the individual association pattern of a potential outlier deviates from that of the whole population. The metric is based on the likelihood ratio of two parameter vectors: One that represents the population associations, and another that represents the individual associations. Our method is validated on synthetic datasets and on real-world data sets about soccer matches and movies. Compared to baseline methods, our novel transformed likelihood ratio achieved the best detection accuracy on all datasets.

New technologies have enabled the investigation of biology and human health at an unprecedented scale and in multiple dimensions. These dimensions include myriad properties describing genome, epigenome, transcriptome, microbiome, phenotype, and lifestyle. No single data type, however, can capture the complexity of all the factors relevant to understanding a phenomenon such as a disease. Integrative methods that combine data from multiple technologies have thus emerged as critical statistical and computational approaches. The key challenge in developing such approaches is the identification of effective models to provide a comprehensive and relevant systems view. An ideal method can answer a biological or medical question, identifying important features and predicting outcomes, by harnessing heterogeneous data across several dimensions of biological variation. In this Review, we describe the principles of data integration and discuss current methods and available implementations. We provide examples of successful data integration in biology and medicine. Finally, we discuss current challenges in biomedical integrative methods and our perspective on the future development of the field.

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use of approximate inference, Bayesian uncertainty estimates are often inaccurate -- for example, a 90% credible interval may not contain the true outcome 90% of the time. Here, we propose a simple procedure for calibrating any regression algorithm; when applied to Bayesian and probabilistic models, it is guaranteed to produce calibrated uncertainty estimates given enough data. Our procedure is inspired by Platt scaling and extends previous work on classification. We evaluate this approach on Bayesian linear regression, feedforward, and recurrent neural networks, and find that it consistently outputs well-calibrated credible intervals while improving performance on time series forecasting and model-based reinforcement learning tasks.

We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data of input and ouput. A compositional variable satisfies the constraints that the elements of the variable are all non-negative and sum to unity. We quantified the uncertainty in the trained operator and present the convergence rates of training in explicit forms for several interesting cases under stochastic compositional models. The trained linear operator with the covariance matrix, estimated from the training set of pairs of ground-truth input and noisy output data, is further used in evaluation of posterior uncertainty of the solution. This posterior uncertainty clearly demonstrates uncertainty propagation from noisy training data and addresses possible mismatch between the true operator and the estimated one in the final solution.

Exploiting the appropriate inductive bias based on the knowledge of data is essential for achieving good performance in statistical machine learning. In practice, however, the domain knowledge of interest often provides information on the relationship of data attributes only distantly, which hinders direct utilization of such domain knowledge in popular regularization methods. In this paper, we propose the knowledge-based distant regularization framework, in which we utilize the distant information encoded in a knowledge graph for regularization of probabilistic model estimation. In particular, we propose to impose prior distributions on model parameters specified by knowledge graph embeddings. As an instance of the proposed framework, we present the factor analysis model with the knowledge-based distant regularization. We show the results of preliminary experiments on the improvement of the generalization capability of such model.

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian nonparametric approach to learning that makes use of statistical models, but does not assume that the model is true. Our approach has provably better properties than using a parametric model and admits a trivially parallelizable Monte Carlo sampling scheme that affords massive scalability on modern computer architectures. The model-based aspect of learning is particularly attractive for regularizing nonparametric inference when the sample size is small, and also for correcting approximate approaches such as variational Bayes (VB). We demonstrate the approach on a number of examples including VB classifiers and Bayesian random forests.

Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed simultaneously. To this end, we propose to leverage the spatial structure of a typical oracle by constructing a statistical surrogate for the underlying logistic regression step. We investigate several non-parametric surrogates, including Binomial Gaussian Processes (B-GP), Polynomial, Kernel, and Spline Logistic Regression. In parallel, we develop sampling policies that adaptively balance learning the oracle distribution and learning the root. One of our proposals mimics active learning with B-GPs and provides a novel look-ahead predictive variance formula. The resulting gains of our Spatial PBA algorithm relative to earlier G-PBA models are illustrated with synthetic examples and a challenging stochastic root finding problem from Bermudan option pricing.

We present a Bayesian view of counterfactual risk minimization (CRM), also known as offline policy optimization from logged bandit feedback. Using PAC-Bayesian analysis, we derive a new generalization bound for the truncated IPS estimator. We apply the bound to a class of Bayesian policies, which motivates a novel, potentially data-dependent, regularization technique for CRM.

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results.