In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function $f$. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $f$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $f$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibility and to prevent overfitting to data, akin to a Gaussian process state-space model. The priors can alternatively be seen as a regularization, and helps the model in generalizing the data without sacrificing the richness offered by the basis function expansion. To learn the coefficients and other unknown parameters efficiently, we tailor an algorithm using state-of-the-art sequential Monte Carlo methods, which comes with theoretical guarantees on the learning. Our approach indicates promising results when evaluated on a classical benchmark as well as real data.

In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intractable because of two problems: (1) it includes the evaluation of the partition function and (2) it is formulated in the form of functional optimization. We avoid Problem (1) by using Bethe approximation. Bethe approximation is an approximation technique equivalent to the loopy belief propagation. Problem (2) can be solved by using orthonormal function expansion. Orthonormal function expansion can reduce a functional optimization problem to a function optimization problem. Our method can provide an analytic form of the solution of the inverse problem within the framework of Bethe approximation.

In real-time monitoring of hospital patients, high-quality inference of patients' health status using all information available from clinical covariates and lab tests are essential to enable successful medical interventions and improve patient outcomes. In this work, we develop and explore a Bayesian nonparametric model based on Gaussian process (GP) regression for hospital patient monitoring. Our method, MedGP, incorporates 24 clinical and lab covariates and supports a rich reference data set from which the relationships between these observed covariates may be inferred and exploited for high-quality inference of patient state over time. To do this, we develop a highly structured sparse GP kernel to enable tractable computation over tens of thousands of time points while estimating correlations among clinical covariates, patients, and periodicity in high-dimensional time series measurements of physiological signals. We apply MedGP to data from hundreds of thousands of patients treated at the Hospital of the University of Pennsylvania. MedGP has a number of benefits over current methods, including (i) not requiring an alignment of the time series data, (ii) quantifying confidence intervals in the predictions, (iii) exploiting a vast and rich database of patients, and (iv) providing interpretable relationships among clinical covariates. We evaluate and compare results from MedGP on the task of online state prediction for three different patient subgroups. Keywords: Gaussian processes, electronic health records, sparse time series analysis, spectral mixture kernel, kernel density estimation.

Managers of US National Forests must decide what policy to apply for dealing with lightning-caused wildfires. Conflicts among stakeholders (e.g., timber companies, home owners, and wildlife biologists) have often led to spirited political debates and even violent eco-terrorism. One way to transform these conflicts into multi-stakeholder negotiations is to provide a high-fidelity simulation environment in which stakeholders can explore the space of alternative policies and understand the tradeoffs therein. Such an environment needs to support fast optimization of MDP policies so that users can adjust reward functions and analyze the resulting optimal policies. This paper assesses the suitability of SMAC---a black-box empirical function optimization algorithm---for rapid optimization of MDP policies. The paper describes five reward function components and four stakeholder constituencies. It then introduces a parameterized class of policies that can be easily understood by the stakeholders. SMAC is applied to find the optimal policy in this class for the reward functions of each of the stakeholder constituencies. The results confirm that SMAC is able to rapidly find good policies that make sense from the domain perspective. Because the full-fidelity forest fire simulator is far too expensive to support interactive optimization, SMAC is applied to a surrogate model constructed from a modest number of runs of the full-fidelity simulator. To check the quality of the SMAC-optimized policies, the policies are evaluated on the full-fidelity simulator. The results confirm that the surrogate values estimates are valid. This is the first successful optimization of wildfire management policies using a full-fidelity simulation. The same methodology should be applicable to other contentious natural resource management problems where high-fidelity simulation is extremely expensive.

Markov networks are extensively used to model complex sequential, spatial, and relational interactions in a wide range of fields. By learning the structure of independences of a domain, more accurate joint probability distributions can be obtained for inference tasks or, more directly, for interpreting the most significant relations among the variables. Recently, several researchers have investigated techniques for automatically learning the structure from data by obtaining the probabilistic maximum-a-posteriori structure given the available data. However, all the approximations proposed decompose the posterior of the whole structure into local sub-problems, by assuming that the posteriors of the Markov blankets of all the variables are mutually independent. In this work, we propose a scoring function for relaxing such assumption. The Blankets Joint Posterior score computes the joint posterior of structures as a joint distribution of the collection of its Markov blankets. Essentially, the whole posterior is obtained by computing the posterior of the blanket of each variable as a conditional distribution that takes into account information from other blankets in the network. We show in our experimental results that the proposed approximation can improve the sample complexity of state-of-the-art scores when learning complex networks, where the independence assumption between blanket variables is clearly incorrect.

Datasets with hundreds of variables and many missing values are commonplace. In this setting, it is both statistically and computationally challenging to detect true predictive relationships between variables and also to suppress false positives. This paper proposes an approach that combines probabilistic programming, information theory, and non-parametric Bayes. It shows how to use Bayesian non-parametric modeling to (i) build an ensemble of joint probability models for all the variables; (ii) efficiently detect marginal independencies; and (iii) estimate the conditional mutual information between arbitrary subsets of variables, subject to a broad class of constraints. Users can access these capabilities using BayesDB, a probabilistic programming platform for probabilistic data analysis, by writing queries in a simple, SQL-like language. This paper demonstrates empirically that the method can (i) detect context-specific (in)dependencies on challenging synthetic problems and (ii) yield improved sensitivity and specificity over baselines from statistics and machine learning, on a real-world database of over 300 sparsely observed indicators of macroeconomic development and public health.

This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minimizing the misfit with the observations. To obtain a probabilistic estimate of the quantity of interest, a Bayesian approach is employed. The QoI is treated as a random field endowed with a hierarchical prior distribution so that closed-form expressions can be obtained for the posterior distribution. The main contribution of the present work lies in the derivation of \emph{a representation basis consistent with the observation chain} used to infer the associated coefficients. The resulting dictionary is then tailored to be both observable by the sensors and accurate in approximating the posterior mean. An algorithm for deriving such an observable dictionary is presented. The method is illustrated with the estimation of the velocity field of an open cavity flow from a handful of wall-mounted point sensors. Comparison with standard estimation approaches relying on Principal Component Analysis and K-SVD dictionaries is provided and illustrates the superior performance of the present approach.

Machine learning is the art of using computer algorithms to learn from experiences and use those experiences for future predictions. Tom Mitchell gave a really simple definition of machine learning. A computer program is said to learn from experience (E) with respect to some task (T) and some performance measure (P), if its performance on (T), as measured by (P), improves with experience (E). This definition dazzled me a bit, too. In human language, if you want your program to predict, for example, buy patterns at a busy grocery store (task T), you can run it through a Machine Learning algorithm with data about past buying patterns (experience E) and, if it has successfully learned, it will then do better at predicting future buy patterns (performance measure P).

The Fourth Industrial Revolution is upon us, even with the Third is still in progress. Big Data, Machine Learning and Artificial Intelligence are three of the driving forces behind it. While the term'Industrial Revolution' has always applied mainly to manufacturing, it now also involves service industries such as banking and insurance, who are investing heavily in Big Data to help them model credit risk, fraud, marketing success and other key data. Meanwhile manufacturing, retail, telco, pharma and many other sectors constantly need people skilled in building, analysing, monitoring and maintaining data models to gain strategic intelligence that helps them inform and adapt their key business processes. A leader in the world of Data Analytics is the SAS Institute, whose flagship product is SAS (Statistical Analysis System).