Bayesian optimization (BO) is a powerful black-box optimization framework that looks to efficiently learn the global optimum of an unknown system by systematically trading-off between exploration and exploitation. However, the use of BO as a tool for coordinated decision-making in multi-agent systems with unknown structure has not been widely studied. This paper investigates a black-box optimization problem over a multi-agent network coupled via shared variables or constraints, where each subproblem is formulated as a BO that uses only its local data. The proposed multi-agent BO (MABO) framework adds a penalty term to traditional BO acquisition functions to account for coupling between the subsystems without data sharing. We derive a suitable form for this penalty term using alternating directions method of multipliers (ADMM), which enables the local decision-making problems to be solved in parallel (and potentially asynchronously). The effectiveness of the proposed MABO method is demonstrated on an intelligent transport system for fuel efficient vehicle platooning.

Conditional neural processes (CNPs; Garnelo et al., 2018a) are attractive meta-learning models which produce well-calibrated predictions and are trainable via a simple maximum likelihood procedure. Although CNPs have many advantages, they are unable to model dependencies in their predictions. Various works propose solutions to this, but these come at the cost of either requiring approximate inference or being limited to Gaussian predictions. In this work, we instead propose to change how CNPs are deployed at test time, without any modifications to the model or training procedure. Instead of making predictions independently for every target point, we autoregressively define a joint predictive distribution using the chain rule of probability, taking inspiration from the neural autoregressive density estimator (NADE) literature. We show that this simple procedure allows factorised Gaussian CNPs to model highly dependent, non-Gaussian predictive distributions. Perhaps surprisingly, in an extensive range of tasks with synthetic and real data, we show that CNPs in autoregressive (AR) mode not only significantly outperform non-AR CNPs, but are also competitive with more sophisticated models that are significantly more computationally expensive and challenging to train. This performance is remarkable given that AR CNPs are not trained to model joint dependencies. Our work provides an example of how ideas from neural distribution estimation can benefit neural processes, and motivates research into the AR deployment of other neural process models.

Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one `best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a consensus matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name.

In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in synthetic chemistry and materials science is time and cost-intensive to collect. On the other hand, knowledge about the data-generation mechanism is often available in the sciences, such as the measurement error of a piece of laboratory apparatus. Both characteristics, small data and knowledge of the underlying physics, make Gaussian processes (GPs) ideal candidates for fitting such datasets. GPs can make predictions with consideration of uncertainty, for example in the virtual screening of molecules and materials, and can also make inferences about incomplete data such as the latent emission signature from a black hole accretion disc. Furthermore, GPs are currently the workhorse model for Bayesian optimisation, a methodology foreseen to be a guide for laboratory experiments in scientific discovery campaigns. The first contribution of this thesis is to use GP modelling to reason about the latent emission signature from the Seyfert galaxy Markarian 335, and by extension, to reason about the applicability of various theoretical models of black hole accretion discs. The second contribution is to extend the GP framework to molecular and chemical reaction representations and to provide an open-source software library to enable the framework to be used by scientists. The third contribution is to leverage GPs to discover novel and performant photoswitch molecules. The fourth contribution is to introduce a Bayesian optimisation scheme capable of modelling aleatoric uncertainty to facilitate the identification of material compositions that possess intrinsic robustness to large scale fabrication processes.

An abundance of information about cancer exists online, but categorizing and extracting useful information from it is difficult. Almost all research within healthcare data processing is concerned with formal clinical data, but there is valuable information in non-clinical data too. The present study combines methods within distributed computing, text retrieval, clustering, and classification into a coherent and computationally efficient system, that can clarify cancer patient trajectories based on non-clinical and freely available information. We produce a fully-functional prototype that can retrieve, cluster and present information about cancer trajectories from non-clinical forum posts. We evaluate three clustering algorithms (MR-DBSCAN, DBSCAN, and HDBSCAN) and compare them in terms of Adjusted Rand Index and total run time as a function of the number of posts retrieved and the neighborhood radius. Clustering results show that neighborhood radius has the most significant impact on clustering performance. For small values, the data set is split accordingly, but high values produce a large number of possible partitions and searching for the best partition is hereby time-consuming. With a proper estimated radius, MR-DBSCAN can cluster 50000 forum posts in 46.1 seconds, compared to DBSCAN (143.4) and HDBSCAN (282.3). We conduct an interview with the Danish Cancer Society and present our software prototype. The organization sees a potential in software that can democratize online information about cancer and foresee that such systems will be required in the future.

Open-domain dialogue systems aim to interact with humans through natural language texts in an open-ended fashion. Despite the recent success of super large dialogue systems such as ChatGPT, using medium-to-small-sized dialogue systems remains the common practice as they are more lightweight and accessible; however, generating diverse dialogue responses is challenging, especially with smaller models. In this work, we propose an Equal-size Hard Expectation--Maximization (EqHard-EM) algorithm to train a multi-decoder model for diverse dialogue generation. Our algorithm assigns a sample to a decoder in a hard manner and additionally imposes an equal-assignment constraint to ensure that all decoders are well-trained. We provide detailed theoretical analysis to justify our approach. Further, experiments on two large-scale open-domain dialogue datasets verify that our EqHard-EM algorithm generates high-quality diverse responses.

Each year, deep learning demonstrates new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to counting parameters or encountering sample complexity bounds that are exponential in depth. Perhaps it may be fruitful to try to analyze modern machine learning under a different lens. In this paper, we propose a novel information-theoretic framework with its own notions of regret and sample complexity for analyzing the data requirements of machine learning. With our framework, we first work through some classical examples such as scalar estimation and linear regression to build intuition and introduce general techniques. Then, we use the framework to study the sample complexity of learning from data generated by deep neural networks with ReLU activation units. For a particular prior distribution on weights, we establish sample complexity bounds that are simultaneously width independent and linear in depth. This prior distribution gives rise to high-dimensional latent representations that, with high probability, admit reasonably accurate low-dimensional approximations. We conclude by corroborating our theoretical results with experimental analysis of random single-hidden-layer neural networks.

We consider the problem of controlling an unknown stochastic linear system with quadratic costs - called the adaptive LQ control problem. We re-examine an approach called ''Reward Biased Maximum Likelihood Estimate'' (RBMLE) that was proposed more than forty years ago, and which predates the ''Upper Confidence Bound'' (UCB) method as well as the definition of ''regret'' for bandit problems. It simply added a term favoring parameters with larger rewards to the criterion for parameter estimation. We show how the RBMLE and UCB methods can be reconciled, and thereby propose an Augmented RBMLE-UCB algorithm that combines the penalty of the RBMLE method with the constraints of the UCB method, uniting the two approaches to optimism in the face of uncertainty. We establish that theoretically, this method retains $\Tilde{\mathcal{O}}(\sqrt{T})$ regret, the best-known so far. We further compare the empirical performance of the proposed Augmented RBMLE-UCB and the standard RBMLE (without the augmentation) with UCB, Thompson Sampling, Input Perturbation, Randomized Certainty Equivalence and StabL on many real-world examples including flight control of Boeing 747 and Unmanned Aerial Vehicle. We perform extensive simulation studies showing that the Augmented RBMLE consistently outperforms UCB, Thompson Sampling and StabL by a huge margin, while it is marginally better than Input Perturbation and moderately better than Randomized Certainty Equivalence.

Today, deep learning is increasingly applied in security-critical situations such as autonomous driving and medical diagnosis. Despite its success, the behavior and robustness of deep networks are not fully understood yet, posing a significant risk. In particular, researchers recently found that neural networks are overly confident in their predictions, even on data they have never seen before. To tackle this issue, one can differentiate two approaches in the literature. One accounts for uncertainty in the predictions, while the second estimates the underlying density of the training data to decide whether a given input is close to the training data, and thus the network is able to perform as expected.In this thesis, we investigate the capabilities of EBMs at the task of fitting the training data distribution to perform detection of out-of-distribution (OOD) inputs. We find that on most datasets, EBMs do not inherently outperform other density estimators at detecting OOD data despite their flexibility. Thus, we additionally investigate the effects of supervision, dimensionality reduction, and architectural modifications on the performance of EBMs. Further, we propose Energy-Prior Network (EPN) which enables estimation of various uncertainties within an EBM for classification, bridging the gap between two approaches for tackling the OOD detection problem. We identify a connection between the concentration parameters of the Dirichlet distribution and the joint energy in an EBM. Additionally, this allows optimization without a held-out OOD dataset, which might not be available or costly to collect in some applications. Finally, we empirically demonstrate that Energy-Prior Network (EPN) is able to detect OOD inputs, datasets shifts, and adversarial examples. Theoretically, EPN offers favorable properties for the asymptotic case when inputs are far from the training data.

The spread of an undesirable contact process, such as an infectious disease (e.g. COVID-19), is contained through testing and isolation of infected nodes. The temporal and spatial evolution of the process (along with containment through isolation) render such detection as fundamentally different from active search detection strategies. In this work, through an active learning approach, we design testing and isolation strategies to contain the spread and minimize the cumulative infections under a given test budget. We prove that the objective can be optimized, with performance guarantees, by greedily selecting the nodes to test. We further design reward-based methodologies that effectively minimize an upper bound on the cumulative infections and are computationally more tractable in large networks. These policies, however, need knowledge about the nodes' infection probabilities which are dynamically changing and have to be learned by sequential testing. We develop a message-passing framework for this purpose and, building on that, show novel tradeoffs between exploitation of knowledge through reward-based heuristics and exploration of the unknown through a carefully designed probabilistic testing. The tradeoffs are fundamentally distinct from the classical counterparts under active search or multi-armed bandit problems (MABs). We provably show the necessity of exploration in a stylized network and show through simulations that exploration can outperform exploitation in various synthetic and real-data networks depending on the parameters of the network and the spread.