Choosing the values of hyper-parameters in sparse Bayesian learning (SBL) can significantly impact performance. However, the hyper-parameters are normally tuned manually, which is often a difficult task. Most recently, effective automatic hyper-parameter tuning was achieved by using an empirical auto-tuner. In this work, we address the issue of hyper-parameter auto-tuning using neural network (NN)-based learning. Inspired by the empirical auto-tuner, we design and learn a NN-based auto-tuner, and show that considerable improvement in convergence rate and recovery performance can be achieved.

Agent-based modeling (ABM) is a well-established paradigm for simulating complex systems via interactions between constituent entities. Machine learning (ML) refers to approaches whereby statistical algorithms 'learn' from data on their own, without imposing a priori theories of system behavior. Biological systems -- from molecules, to cells, to entire organisms -- consist of vast numbers of entities, governed by complex webs of interactions that span many spatiotemporal scales and exhibit nonlinearity, stochasticity and intricate coupling between entities. The macroscopic properties and collective dynamics of such systems are difficult to capture via continuum modelling and mean-field formalisms. ABM takes a 'bottom-up' approach that obviates these difficulties by enabling one to easily propose and test a set of well-defined 'rules' to be applied to the individual entities (agents) in a system. Evaluating a system and propagating its state over discrete time-steps effectively simulates the system, allowing observables to be computed and system properties to be analyzed. Because the rules that govern an ABM can be difficult to abstract and formulate from experimental data, there is an opportunity to use ML to help infer optimal, system-specific ABM rules. Once such rule-sets are devised, ABM calculations can generate a wealth of data, and ML can be applied there too -- e.g., to probe statistical measures that meaningfully describe a system's stochastic properties. As an example of synergy in the other direction (from ABM to ML), ABM simulations can generate realistic datasets for training ML algorithms (e.g., for regularization, to mitigate overfitting). In these ways, one can envision various synergistic ABM$\rightleftharpoons$ML loops. This review summarizes how ABM and ML have been integrated in contexts that span spatiotemporal scales, from cellular to population-level epidemiology.

Prediction failures of machine learning models often arise from deficiencies in training data, such as incorrect labels, outliers, and selection biases. However, such data points that are responsible for a given failure mode are generally not known a priori, let alone a mechanism for repairing the failure. This work draws on the Bayesian view of continual learning, and develops a generic framework for both, identifying training examples which have given rise to the target failure, and fixing the model through erasing information about them. This framework naturally allows leveraging recent advances in continual learning to this new problem of model repairment, while subsuming the existing works on influence functions and data deletion as specific instances. Experimentally, the proposed approach outperforms the baselines for both identification of detrimental training data and fixing model failures in a generalisable manner.

This paper revisits the work of Rauch et al. (1965) and develops a novel method for recursive maximum likelihood particle filtering for general state-space models. The new method is based on statistical analysis of incomplete observations of the systems. Score function and conditional observed information of the incomplete observations/data are introduced and their distributional properties are discussed. Some identities concerning the score function and information matrices of the incomplete data are derived. Maximum likelihood estimation of state-vector is presented in terms of the score function and observed information matrices. In particular, to deal with nonlinear state-space, a sequential Monte Carlo method is developed. It is given recursively by an EM-gradient-particle filtering which extends the work of Lange (1995) for state estimation. To derive covariance matrix of state-estimation errors, an explicit form of observed information matrix is proposed. It extends Louis (1982) general formula for the same matrix to state-vector estimation. Under (Neumann) boundary conditions of state transition probability distribution, the inverse of this matrix coincides with the Cramer-Rao lower bound on the covariance matrix of estimation errors of unbiased state-estimator. In the case of linear models, the method shows that the Kalman filter is a fully efficient state estimator whose covariance matrix of estimation error coincides with the Cramer-Rao lower bound. Some numerical examples are discussed to exemplify the main results.

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods. In this paper we describe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approach in so-called simulation-based inference) naturally evades these issues, improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthiness of the inferred posteriors. Using measurements of the Cosmic Microwave Background (CMB), we show that TMNRE can achieve converged posteriors using orders of magnitude fewer simulator calls than conventional Markov Chain Monte Carlo (MCMC) methods. Remarkably, the required number of samples is effectively independent of the number of nuisance parameters. In addition, a property called \emph{local amortization} allows the performance of rigorous statistical consistency checks that are not accessible to sampling-based methods. TMNRE promises to become a powerful tool for cosmological data analysis, particularly in the context of extended cosmologies, where the timescale required for conventional sampling-based inference methods to converge can greatly exceed that of simple cosmological models such as $\Lambda$CDM. To perform these computations, we use an implementation of TMNRE via the open-source code \texttt{swyft}.

Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer from high computational complexity due to the combinatorial nature of estimating the directed acyclic graph (DAG). Motivated by the `Cause-Effect Pair' NIPS 2013 Workshop on Causality Challenge, in this paper, we take a different approach and generate a probability distribution over all possible graphs informed by the cause-effect pair features proposed in response to the workshop challenge. The goal of the paper is to propose new methods based on this probabilistic information and compare their performance with traditional and state-of-the-art approaches. Our experiments, on both synthetic and real datasets, show that our proposed methods not only have statistically similar or better performances than some traditional approaches but also are computationally faster.

Mission teams are exposed to the emotional toll of life and death decisions. These are small groups of specially trained people supported by intelligent machines for dealing with stressful environments and scenarios. We developed a composite model for stress monitoring in such teams of human and autonomous machines. This modelling aims to identify the conditions that may contribute to mission failure. The proposed model is composed of three parts: 1) a computational logic part that statically describes the stress states of teammates; 2) a decision part that manifests the mission status at any time; 3) a stress propagation part based on standard Susceptible-Infected-Susceptible (SIS) paradigm. In contrast to the approaches such as agent-based, random-walk and game models, the proposed model combines various mechanisms to satisfy the conditions of stress propagation in small groups. Our core approach involves data structures such as decision tables and decision diagrams. These tools are adaptable to human-machine teaming as well.

Data-driven interatomic potentials have emerged as a powerful class of surrogate models for {\it ab initio} potential energy surfaces that are able to reliably predict macroscopic properties with experimental accuracy. In generating accurate and transferable potentials the most time-consuming and arguably most important task is generating the training set, which still requires significant expert user input. To accelerate this process, this work presents \text{\it hyperactive learning} (HAL), a framework for formulating an accelerated sampling algorithm specifically for the task of training database generation. The key idea is to start from a physically motivated sampler (e.g., molecular dynamics) and add a biasing term that drives the system towards high uncertainty and thus to unseen training configurations. Building on this framework, general protocols for building training databases for alloys and polymers leveraging the HAL framework will be presented. For alloys, ACE potentials for AlSi10 are created by fitting to a minimal HAL-generated database containing 88 configurations (32 atoms each) with fast evaluation times of <100 microsecond/atom/cpu-core. These potentials are demonstrated to predict the melting temperature with excellent accuracy. For polymers, a HAL database is built using ACE, able to determine the density of a long polyethylene glycol (PEG) polymer formed of 200 monomer units with experimental accuracy by only fitting to small isolated PEG polymers with sizes ranging from 2 to 32.

Chain event graphs (CEGs) are a family of probabilistic graphical models that were first proposed in Smith and Anderson (2008) as an alternative to the family of Bayesian networks (BNs). In particular, CEGs were developed to explicitly accommodate processes exhibiting asymmetries of two types: (1) asymmetric independence structures or context-specific conditional independences where some statistical independences hold for certain values of the conditioning variables but not the others; and (2) asymmetric event spaces which are precisely event spaces that do not admit a product space structure. The latter asymmetry arises due to the presence of structural zeros and structural missing values, often-times by design (Shenvi & Smith, 2020). For example, consider modelling hospitalisations arising from infection caused by a circulating virus, and suppose that one of the two strains (call it strain A) of the virus has no treatment currently available while the other has a choice of two possible treatments. On the one hand, a variable of "Treatment" with state space {Treatment 1, Treatment 2} would be structurally missing and have no sensible value for those infected by strain A of the virus. Whereas on the other hand, if its state space is redefined to be {Treatment 1, Treatment 2, No treatment} then Treatment 1 and Treatment 2 would have structurally zero counts for those infected by strain A, i.e. irrespective of the sample size, there would always be zero individuals who are treated with either Treatment 1 or Treatment 2 among those infected by strain A. Such a process is inherently asymmetric. BNs, being variable-based - i.e. they use variables as the building blocks of their models - are unable to fully describe such asymmetries within their underlying statistical model and graphical structure.

Transfer Learning is an area of statistics and machine learning research that seeks answers to the following question: how do we build successful learning algorithms when the data available for training our model is qualitatively different from the data we hope the model will perform well on? In this thesis, we focus on a specific area of Transfer Learning called label shift, also known as quantification. In quantification, the aforementioned discrepancy is isolated to a shift in the distribution of the response variable. In such a setting, accurately inferring the response variable's new distribution is both an important estimation task in its own right and a crucial step for ensuring that the learning algorithm can adapt to the new data. We make two contributions to this field. First, we present a new procedure called SELSE which estimates the shift in the response variable's distribution. Second, we prove that SELSE is semiparametric efficient among a large family of quantification algorithms, i.e., SELSE's normalized error has the smallest possible asymptotic variance matrix compared to any other algorithm in that family. This family includes nearly all existing algorithms, including ACC/PACC quantifiers and maximum likelihood based quantifiers such as EMQ and MLLS. Empirical experiments reveal that SELSE is competitive with, and in many cases outperforms, existing state-of-the-art quantification methods, and that this improvement is especially large when the number of test samples is far greater than the number of train samples.