Transfer Learning Bayesian Optimization to Design Competitor DNA Molecules for Use in Diagnostic Assays

With the rise in engineered biomolecular devices, there is an increased need for tailor-made biological sequences. Often, many similar biological sequences need to be made for a specific application meaning numerous, sometimes prohibitively expensive, lab experiments are necessary for their optimization. This paper presents a transfer learning design of experiments workflow to make this development feasible. By combining a transfer learning surrogate model with Bayesian optimization, we show how the total number of experiments can be reduced by sharing information between optimization tasks. We demonstrate the reduction in the number of experiments using data from the development of DNA competitors for use in an amplification-based diagnostic assay. We use cross-validation to compare the predictive accuracy of different transfer learning models, and then compare the performance of the models for both single objective and penalized optimization tasks.

Verifying message-passing neural networks via topology-based bounds tightening

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs) using a Rectified Linear Unit (ReLU) activation function. Because our work builds on mixed-integer optimization, it encodes a wide variety of subproblems, for example it admits (i) both adding and removing edges, (ii) both global and local budgets, and (iii) both topological perturbations and feature modifications. Our key technology, topology-based bounds tightening, uses graph structure to tighten bounds. We also experiment with aggressive bounds tightening to dynamically change the optimization constraints by tightening variable bounds. To demonstrate the effectiveness of these strategies, we implement an extension to the open-source branch-and-cut solver SCIP. We test on both node and graph classification problems and consider topological attacks that both add and remove edges.

Mixed-Output Gaussian Process Latent Variable Models

This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) to incorporate the case where each data point comprises the weighted sum of a known number of pure component signals, observed across several input locations. Our framework allows the use of a range of priors for the weights of each observation. This flexibility enables us to represent use cases including sum-to-one constraints for estimating fractional makeup, and binary weights for classification. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample. To demonstrate the applicability to both spectroscopy and other domains, we consider several applications: a near-infrared spectroscopy data set with varying temperatures, a simulated data set for identifying flow configuration through a pipe, and a data set for determining the type of rock from its reflectance.

Transition Constrained Bayesian Optimization via Markov Decision Processes

Bayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in particular, the search space of the next query may depend on previous ones. Example challenges arise in the physical sciences in the form of local movement constraints, required monotonicity in certain variables, and transitions influencing the accuracy of measurements. Altogether, such transition constraints necessitate a form of planning. This work extends Bayesian optimization via the framework of Markov Decision Processes, iteratively solving a tractable linearization of our objective using reinforcement learning to obtain a policy that plans ahead over long horizons. The resulting policy is potentially history-dependent and non-Markovian. We showcase applications in chemical reactor optimization, informative path planning, machine calibration, and other synthetic examples.

Practical Path-based Bayesian Optimization

There has been a surge in interest in data-driven experimental design with applications to chemical engineering and drug manufacturing. Bayesian optimization (BO) has proven to be adaptable to such cases, since we can model the reactions of interest as expensive black-box functions. Sometimes, the cost of this black-box functions can be separated into two parts: (a) the cost of the experiment itself, and (b) the cost of changing the input parameters. In this short paper, we extend the SnAKe algorithm to deal with both types of costs simultaneously. We further propose extensions to the case of a maximum allowable input change, as well as to the multi-objective setting.

Gaussian Processes for Monitoring Air-Quality in Kampala

Monitoring air pollution is of vital importance to the overall health of the population. Unfortunately, devices that can measure air quality can be expensive, and many cities in low and middle-income countries have to rely on a sparse allocation of them. In this paper, we investigate the use of Gaussian Processes for both nowcasting the current air-pollution in places where there are no sensors and forecasting the air-pollution in the future at the sensor locations. In particular, we focus on the city of Kampala in Uganda, using data from AirQo's network of sensors. We demonstrate the advantage of removing outliers, compare different kernel functions and additional inputs. We also compare two sparse approximations to allow for the large amounts of temporal data in the dataset.

Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimization

Bayesian Optimization is a useful tool for experiment design. Unfortunately, the classical, sequential setting of Bayesian Optimization does not translate well into laboratory experiments, for instance battery design, where measurements may come from different sources and their evaluations may require significant waiting times. Multi-fidelity Bayesian Optimization addresses the setting with measurements from different sources. Asynchronous batch Bayesian Optimization provides a framework to select new experiments before the results of the prior experiments are revealed. This paper proposes an algorithm combining multi-fidelity and asynchronous batch methods. We empirically study the algorithm behavior, and show it can outperform single-fidelity batch methods and multi-fidelity sequential methods. As an application, we consider designing electrode materials for optimal performance in pouch cells using experiments with coin cells to approximate battery performance.

Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces

Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little to no manual tuning, naturally handle discrete feature spaces, and are relatively insensitive to outliers in the training data. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. To address both points simultaneously, we propose using the kernel interpretation of tree ensembles as a Gaussian Process prior to obtain model variance estimates, and we develop a compatible optimization formulation for the acquisition function. The latter further allows us to seamlessly integrate known constraints to improve sampling efficiency by considering domain-knowledge in engineering settings and modeling search space symmetries, e.g., hierarchical relationships in neural architecture search. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.

SnAKe: Bayesian Optimization with Pathwise Exploration

Bayesian Optimization is a very effective tool for optimizing expensive black-box functions. Inspired by applications developing and characterizing reaction chemistry using droplet microfluidic reactors, we consider a novel setting where the expense of evaluating the function can increase significantly when making large input changes between iterations. We further assume we are working asynchronously, meaning we have to decide on new queries before we finish evaluating previous experiments. This paper investigates the problem and introduces 'Sequential Bayesian Optimization via Adaptive Connecting Samples' (SnAKe), which provides a solution by considering future queries and preemptively building optimization paths that minimize input costs. We investigate some convergence properties and empirically show that the algorithm is able to achieve regret similar to classical Bayesian Optimization algorithms in both the synchronous and asynchronous settings, while reducing the input costs significantly.

P-split formulations: A class of intermediate formulations between big-M and convex hull for disjunctive constraints

We develop a class of mixed-integer formulations for disjunctive constraints intermediate to the big-M and convex hull formulations in terms of relaxation strength. The main idea is to capture the best of both the big-M and convex hull formulations: a computationally light formulation with a tight relaxation. The "$P$-split" formulations are based on a lifted transformation that splits convex additively separable constraints into $P$ partitions and forms the convex hull of the linearized and partitioned disjunction. We analyze the continuous relaxation of the $P$-split formulations and show that, under certain assumptions, the formulations form a hierarchy starting from a big-M equivalent and converging to the convex hull. The goal of the $P$-split formulations is to form a strong approximation of the convex hull through a computationally simpler formulation. We computationally compare the $P$-split formulations against big-M and convex hull formulations on 320 test instances. The test problems include K-means clustering, P_ball problems, and optimization over trained ReLU neural networks. The computational results show promising potential of the $P$-split formulations. For many of the test problems, $P$-split formulations are solved with a similar number of explored nodes as the convex hull formulation, while reducing the solution time by an order of magnitude and outperforming big-M both in time and number of explored nodes.