Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a set of standard covariance functions. From a weight-space view, this models the objective as a linear function in a feature space implied by the given covariance $K$, with an arbitrary Gaussian weight prior ${\bf w} \sim ormdist ({\bf 0},{\bf I})$. In many practical applications there is data available that has a similar (covariance) structure to the objective, but which, having different form, cannot be used directly in standard transfer learning. In this paper we show how such auxiliary data may be used to construct a GP covariance corresponding to a more appropriate weight prior for the objective function. Building on this, we show that we may accelerate BO by modeling the objective function using this (learned) weight prior, which we demonstrate on both test functions and a practical application to short-polymer fibre manufacture.

In this paper we propose a data-efficient Bayesian active learning framework for factor screening, which is important when dealing with systems which are expensive to evaluate, such as combat simulations. We use Gaussian Process meta-modelling with the Automatic Relevance Determination covariance kernel, which measures the importance of each factor by the inverse of their associated length-scales in the kernel. This importance measures the degree of non-linearity in the simulation response with respect to the corresponding factor. We initially place a prior over the length-scale values, then use the estimated posterior to select the next datum to simulate which maximises the mutual entropy between the length-scales and the unknown simulation response. Our goal-driven Bayesian active learning strategy ensures that we are data-efficient in discovering the correct values of the length-scales compared to either a random-sampling or uncertainty-sampling based approach. We apply our method to an expensive combat simulation and demonstrate the superiority of our approach.

Bayesian optimization (BO) is concerned with efficient optimization using probabilistic methods. Predictive entropy search (PES) is a popular and successful BO strategy to find a point that maximizes the information gained about the optima location of an unknown function. Since the PES analytical form is intractable, it requires approximations and is computationally expensive. These approximations may degrade PES performance in terms of accuracy and efficiency. In this paper, we propose an alternative scheme - predictive variance reduction search (PVRS) - to find a point that maximally reduces the uncertainty at the perceived optima locations. The optimization converges to the true optimum when the uncertainty at all perceived optima locations is vanished. Our novel modification is beneficial in two ways. First, PVRS can be computed in closed-form, unlike the approximations made in PES. Second, PVRS is simple and easy to implement. As a result, the proposed PVRS gains huge speed up for scalable BO whilst showing favorable optimization efficiency. Furthermore, we extend our PVRS framework for batch setting where we select multiple experiments for parallel evaluations at each iteration. Empirically, we demonstrate the effectiveness of the PVRS on both benchmark functions and real-world applications in standard and batch BO settings.

Experimental design is a process of obtaining a product with target property via experimentation. Bayesian optimization offers a sample-efficient tool for experimental design when experiments are expensive. Often, expert experimenters have 'hunches' about the behavior of the experimental system, offering potentials to further improve the efficiency. In this paper, we consider per-variable monotonic trend in the underlying property that results in a unimodal trend in those variables for a target value optimization. For example, sweetness of a candy is monotonic to the sugar content. However, to obtain a target sweetness, the utility of the sugar content becomes a unimodal function, which peaks at the value giving the target sweetness and falls off both ways. In this paper, we propose a novel method to solve such problems that achieves two main objectives: (a) the monotonicity information is used to the fullest extent possible, whilst ensuring that (b) the convergence guarantee remains intact. This is achieved by a two-stage Gaussian process modeling, where the first stage uses the monotonicity trend to model the underlying property, and the second stage uses 'virtual' samples, sampled from the first, to model the target value optimization function. The process is made theoretically consistent by adding appropriate adjustment factor in the posterior computation, necessitated because of using the 'virtual' samples. The proposed method is evaluated through both simulations and real world experimental design problems of (a) new short polymer fiber with the target length, and (b) designing of a new three dimensional porous scaffolding with a target porosity. In all scenarios our method demonstrates faster convergence than the basic Bayesian optimization approach not using such 'hunches'.

Bayesian optimization (BO) is a sample-efficient method for global optimization of expensive, noisy, black-box functions using probabilistic methods. The performance of a BO method depends on its selection strategy through the acquisition function. Expected improvement (EI) is one of the most widely used acquisition functions for BO that finds the expectation of the improvement function over the incumbent. The incumbent is usually selected as the best-observed value so far, termed as $y^\max$ (for the maximizing problem). Recent work has studied the convergence rate for EI under some mild assumptions or zero noise of observations. Especially, the work of Wang and de Freitas (2014) has derived the sublinear regret for EI under a stochastic noise. However, due to the difficulty in stochastic noise setting and to make the convergent proof feasible, they use an alternative choice for the incumbent as the maximum of the Gaussian process predictive mean, $μ^\max$. This modification makes the algorithm computationally inefficient because it requires an additional global optimization step to estimate $μ^\max$ that is costly and may be inaccurate. To address this issue, we derive a sublinear convergence rate for EI using the commonly used $y^\max$. Moreover, our analysis is the first to study a stopping criteria for EI to prevent unnecessary evaluations. Our analysis complements the results of Wang and de Freitas (2014) to theoretically cover two incumbent settings for EI. Finally, we demonstrate empirically that EI using $y^\max$ is both more computationally efficiency and more accurate than EI using $μ^\max$.

Bayesian optimization (BO) has recently emerged as a powerful and flexible tool for hyper-parameter tuning and more generally for the efficient global optimization of expensive black-box functions. Systems implementing BO has successfully solved difficult problems in automatic design choices and machine learning hyper-parameters tunings. Many recent advances in the methodologies and theories underlying Bayesian optimization have extended the framework to new applications and provided greater insights into the behavior of these algorithms. Still, these established techniques always require a user-defined space to perform optimization. This pre-defined space specifies the ranges of hyper-parameter values. In many situations, however, it can be difficult to prescribe such spaces, as a prior knowledge is often unavailable. Setting these regions arbitrarily can lead to inefficient optimization - if a space is too large, we can miss the optimum with a limited budget, on the other hand, if a space is too small, it may not contain the optimum point that we want to get. The unknown search space problem is intractable to solve in practice. Therefore, in this paper, we narrow down to consider specifically the setting of "weakly specified" search space for Bayesian optimization. By weakly specified space, we mean that the pre-defined space is placed at a sufficiently good region so that the optimization can expand and reach to the optimum. However, this pre-defined space need not include the global optimum. We tackle this problem by proposing the filtering expansion strategy for Bayesian optimization. Our approach starts from the initial region and gradually expands the search space. Wedevelop an efficient algorithm for this strategy and derive its regret bound. These theoretical results are complemented by an extensive set of experiments on benchmark functions and tworeal-world applications which demonstrate the benefits of our proposed approach.

Bayesian optimization is an efficient way to optimize expensive black-box functions such as designing a new product with highest quality or hyperparameter tuning of a machine learning algorithm. However, it has a serious limitation when the parameter space is high-dimensional as Bayesian optimization crucially depends on solving a global optimization of a surrogate utility function in the same sized dimensions. The surrogate utility function, known commonly as acquisition function is a continuous function but can be extremely sharp at high dimension - having only a few peaks marooned in a large terrain of almost flat surface. Global optimization algorithms such as DIRECT are infeasible at higher dimensions and gradient-dependent methods cannot move if initialized in the flat terrain. We propose an algorithm that enables local gradient-dependent algorithms to move through the flat terrain by using a sequence of gross-to-finer Gaussian process priors on the objective function as we leverage two underlying facts - a) there exists a large enough length-scales for which the acquisition function can be made to have a significant gradient at any location in the parameter space, and b) the extrema of the consecutive acquisition functions are close although they are different only due to a small difference in the length-scales. Theoretical guarantees are provided and experiments clearly demonstrate the utility of the proposed method at high dimension using both benchmark test functions and real-world case studies.

Scaling Bayesian optimization to high dimensions is challenging task as the global optimization of high-dimensional acquisition function can be expensive and often infeasible. Existing methods depend either on limited “active” variables or the additive form of the objective function. We propose a new method for high-dimensional Bayesian optimization, that uses a drop-out strategy to optimize only a subset of variables at each iteration. We derive theoretical bounds for the regret and show how it can inform the derivation of our algorithm. We demonstrate the efficacy of our algorithms for optimization on two benchmark functions and two real-world applications - training cascade classifiers and optimizing alloy composition.

Many real-world applications require multi-label classification where multiple target labels are assigned to each instance. In multi-label classification, there exist the intrinsic correlations between the labels and features. These correlations are beneficial for multi-label classification task since they reflect the coexistence of the input and output spaces that can be exploited for prediction. Traditional classification methods have attempted to reveal these correlations in different ways. However, existing methods demand expensive computation complexity for finding such correlation structures. Furthermore, these approaches can not identify the suitable number of label-feature correlation patterns. In this paper, we propose a Bayesian nonparametric (BNP) framework for multi-label classification that can automatically learn and exploit the unknown number of multi-label correlation. We utilize the recent techniques in stochastic inference to derive the cheap (but efficient) posterior inference algorithm for the model. In addition, our model can naturally exploit the useful information from missing label samples. Furthermore, we extend the model to update parameters in an online fashion that highlights the flexibility of our model against the existing approaches. We compare our method with the state-of-the-art multi-label classification algorithms on real-world datasets using both complete and missing label settings. Our model achieves better classification accuracy while our running time is consistently much faster than the baselines in an order of magnitude.

Parameter settings profoundly impact the performance of machine learning algorithms and laboratory experiments. The classical trial-error methods are exponentially expensive in large parameter spaces, and Bayesian optimization (BO) offers an elegant alternative for global optimization of black box functions. In situations where the functions can be evaluated at multiple points simultaneously, batch Bayesian optimization is used. Current batch BO approaches are restrictive in fixing the number of evaluations per batch, and this can be wasteful when the number of specified evaluations is larger than the number of real maxima in the underlying acquisition function. We present the budgeted batch Bayesian optimization (B3O) for hyper-parameter tuning and experimental design - we identify the appropriate batch size for each iteration in an elegant way. In particular, we use the infinite Gaussian mixture model (IGMM) for automatically identifying the number of peaks in the underlying acquisition functions. We solve the intractability of estimating the IGMM directly from the acquisition function by formulating the batch generalized slice sampling to efficiently draw samples from the acquisition function. We perform extensive experiments for benchmark functions and two real world applications - machine learning hyper-parameter tuning and experimental design for alloy hardening. We show empirically that the proposed B3O outperforms the existing fixed batch BO approaches in finding the optimum whilst requiring a fewer number of evaluations, thus saving cost and time.

The stability matters in clinical prediction models because it makes the model to be interpretable and generalizable. It is paramount for high dimensional data, which employ sparse models with feature selection ability. We propose a new method to stabilize sparse support vector machines using intrinsic graph structure of the electronic medical records. The graph structure is exploited using the Jaccard similarity among features. Our method employs a convex function to penalize the pairwise l∞-norm of connected feature coefficients in the graph. We apply the alternating direction method of multipliers to solve the proposed formulation. Our experiments are conducted on a synthetic and three real-world hospital datasets. We show that our proposed method is more stable than the state-of-the-art feature selection and classification techniques in terms of three stability measures namely, Jaccard similarity measure, Spearman's rank correlation coefficient and Kuncheva index. We further show that our method has resulted in better classification performance compared to the baselines.

Adverse effects, such as voice change and fatigue, are prevalent in cancer treatment duration. These adverse effects have been significant burden for patients physically and emotionally. Predicting multiple adverse effects becomes important for patients and oncologists. In this paper, we formulate the prediction of multiple adverse effects in cancer treatment as a longitudinal multiple-output regression problem. The correlated multiple outputs are first decoupled to uncorrelated ones in a new output space. We then propose a comprehensive framework to capture the empirical loss between the predicted value and the ground truth in the transformed space and the temporal smoothness at neighboring prediction points. Experiments were performed on one synthetic data and two real-world datasets including radiotherapy and chemotherapy treatments. Results in terms of root mean square errors (RMSE) and R-value show that our proposed approach is promising for the longitudinal multiple-output regression problem.

We propose a novel hierarchical Bayesian framework, word-distance-dependent Chinese restaurant franchise (wd-dCRF) for topic discovery from a document corpus regularized by side information in the form of word-to-word relations, with an application on Electronic Medical Records (EMRs). Typically, a EMRs dataset consists of several patients (documents) and each patient contains many diagnosis codes (words). We exploit the side information available in the form of a semantic tree structure among the diagnosis codes for semantically-coherent disease topic discovery. We introduce novel functions to compute word-to-word distances when side information is available in the form of tree structures. We derive an efficient inference method for the wddCRF using MCMC technique. We evaluate on a real world medical dataset consisting of about 1000 patients with PolyVascular disease. Compared with the popular topic analysis tool, hierarchical Dirichlet process (HDP), our model discovers topics which are superior in terms of both qualitative and quantitative measures.

Multimedia contents often possess weakly annotated data such as tags, links and interactions. The weakly annotated data is called side information. It is the auxiliary information of data and provides hints for exploring the link structure of data. Most clustering algorithms utilize pure data for clustering. A model that combines pure data and side information, such as images and tags, documents and keywords, can perform better at understanding the underlying structure of data. We demonstrate how to incorporate different types of side information into a recently proposed Bayesian nonparametric model, the distance dependent Chinese restaurant process (DD-CRP). Our algorithm embeds the affinity of this information into the decay function of the DD-CRP when side information is in the form of subsets of discrete labels. It is flexible to measure distance based on arbitrary side information instead of only the spatial layout or time stamp of observations. At the same time, for noisy and incomplete side information, we set the decay function so that the DD-CRP reduces to the traditional Chinese restaurant process, thus not inducing side effects of noisy and incomplete side information. Experimental evaluations on two real-world datasets NUS WIDE and 20 Newsgroups show exploiting side information in DD-CRP significantly improves the clustering performance.