Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search the space stochastically (typically using genetic programming) and hence do not necessarily find the best function. Second, the criteria used to select the equation optimally balancing accuracy with simplicity have been variable and subjective. To address these issues we introduce Exhaustive Symbolic Regression (ESR), which systematically and efficiently considers all possible equations -- made with a given basis set of operators and up to a specified maximum complexity -- and is therefore guaranteed to find the true optimum (if parameters are perfectly optimised) and a complete function ranking subject to these constraints. We implement the minimum description length principle as a rigorous method for combining these preferences into a single objective. To illustrate the power of ESR we apply it to a catalogue of cosmic chronometers and the Pantheon+ sample of supernovae to learn the Hubble rate as a function of redshift, finding $\sim$40 functions (out of 5.2 million trial functions) that fit the data more economically than the Friedmann equation. These low-redshift data therefore do not uniquely prefer the expansion history of the standard model of cosmology. We make our code and full equation sets publicly available.

We study the task of spatio-temporal extrapolation that generates data at target locations from surrounding contexts in a graph. This task is crucial as sensors that collect data are sparsely deployed, resulting in a lack of fine-grained information due to high deployment and maintenance costs. Existing methods either use learning-based models like Neural Networks or statistical approaches like Gaussian Processes for this task. However, the former lacks uncertainty estimates and the latter fails to capture complex spatial and temporal correlations effectively. To address these issues, we propose Spatio-Temporal Graph Neural Processes (STGNP), a neural latent variable model which commands these capabilities simultaneously. Specifically, we first learn deterministic spatio-temporal representations by stacking layers of causal convolutions and cross-set graph neural networks. Then, we learn latent variables for target locations through vertical latent state transitions along layers and obtain extrapolations. Importantly during the transitions, we propose Graph Bayesian Aggregation (GBA), a Bayesian graph aggregator that aggregates contexts considering uncertainties in context data and graph structure. Extensive experiments show that STGNP has desirable properties such as uncertainty estimates and strong learning capabilities, and achieves state-of-the-art results by a clear margin.

Neural HMMs are a type of neural transducer recently proposed for sequence-to-sequence modelling in text-to-speech. They combine the best features of classic statistical speech synthesis and modern neural TTS, requiring less data and fewer training updates, and are less prone to gibberish output caused by neural attention failures. In this paper, we combine neural HMM TTS with normalising flows for describing the highly non-Gaussian distribution of speech acoustics. The result is a powerful, fully probabilistic model of durations and acoustics that can be trained using exact maximum likelihood. Experiments show that a system based on our proposal needs fewer updates than comparable methods to produce accurate pronunciations and a subjective speech quality close to natural speech. Please see https://shivammehta25.github.io/OverFlow/ for audio examples and code.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Maximum Likelihood and the method of Least Squares are fundamental procedures in statistics. The study of asymptotic consistency of Maximum Likelihood has been central to the field for almost a century (Wald, 1949). Along with consistency, failures of Maximum Likelihood have been thoroughly investigated for nearly as long (Neyman and Scott, 1948; Bahadur, 1958; Ferguson, 1982). In the context of estimation of nonparametric models, the seminal work of (Birgé and Massart, 1993) provided sufficient conditions for minimax optimality (in a non-asymptotic sense) of Least Squares while also presenting an example of a model class where this basic procedure is sub-optimal. Three decades later, we still do not have necessary and sufficient conditions for minimax optimality of Least Squares when the model class is large. While the present paper does not resolve this question, it makes several steps towards understanding the behavior of Least Squares -- equivalently, Empirical Risk Minimization (ERM) with square loss -- in large models. Beyond intellectual curiosity, the question of minimax optimality of Least Squares is driven by the desire to understand the current practice of fitting large or overparametrized models, such as neural networks, to data (cf.

Digital technologies have dramatically accelerated the digital transformation in process industries, boosted new industrial applications, upgraded the production system, and enhanced operational efficiency. In contrast, the challenges and gaps between human and artificial intelligence (AI) have become more and more prominent, whereas the digital divide in process safety is aggregating. The study attempts to address the following questions: (i)What is AI in the process safety context? (ii)What is the difference between AI and humans in process safety? (iii)How do AI and humans collaborate in process safety? (iv)What are the challenges and gaps in human-AI collaboration? (v)How to quantify the risk of human-AI collaboration in process safety? Qualitative risk analysis based on brainstorming and literature review, and quantitative risk analysis based on layer of protection analysis (LOPA) and Bayesian network (BN), were applied to explore and model. The importance of human reliability should be stressed in the digital age, not usually to increase the reliability of AI, and human-centered AI design in process safety needs to be propagated.

The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in artificial intelligence research have recently boosted the application of machine learning (ML) algorithms to obtain data-driven surrogate models for the HTC. For most supervised learning algorithms, the task is that of a nonlinear regression problem. Despite the fact that these models have been proven capable of outperforming traditional empirical correlations, they have key limitations such as overfitting the data, the lack of uncertainty estimation, and interpretability of the results. To address these limitations, in this paper, we use a multi-output Gaussian process regression (GPR) to estimate the HTC in microchannels as a function of the mass flow rate, heat flux, system pressure and channel diameter and length. The model is trained using the Brunel Two-Phase Flow database of high-fidelity experimental data. The advantages of GPR are data efficiency, the small number of hyperparameters to be trained (typically of the same order of the number of input dimensions), and the automatic trade-off between data fit and model complexity guaranteed by the maximization of the marginal likelihood (Bayesian approach). Our paper proposes research directions to improve the performance of the GPR-based model in extrapolation.

Reinforcement learning can effectively learn amortised design policies for designing sequences of experiments. However, current methods rely on contrastive estimators of expected information gain, which require an exponential number of contrastive samples to achieve an unbiased estimation. We propose an alternative lower bound estimator, based on the cross-entropy of the joint model distribution and a flexible proposal distribution. This proposal distribution approximates the true posterior of the model parameters given the experimental history and the design policy. Our estimator requires no contrastive samples, can achieve more accurate estimates of high information gains, allows learning of superior design policies, and is compatible with implicit probabilistic models. We assess our algorithm's performance in various tasks, including continuous and discrete designs and explicit and implicit likelihoods.

Offline inverse reinforcement learning (Offline IRL) aims to recover the structure of rewards and environment dynamics that underlie observed actions in a fixed, finite set of demonstrations from an expert agent. Accurate models of expertise in executing a task has applications in safety-sensitive applications such as clinical decision making and autonomous driving. However, the structure of an expert's preferences implicit in observed actions is closely linked to the expert's model of the environment dynamics (i.e. the ``world''). Thus, inaccurate models of the world obtained from finite data with limited coverage could compound inaccuracy in estimated rewards. To address this issue, we propose a bi-level optimization formulation of the estimation task wherein the upper level is likelihood maximization based upon a conservative model of the expert's policy (lower level). The policy model is conservative in that it maximizes reward subject to a penalty that is increasing in the uncertainty of the estimated model of the world. We propose a new algorithmic framework to solve the bi-level optimization problem formulation and provide statistical and computational guarantees of performance for the associated reward estimator. Finally, we demonstrate that the proposed algorithm outperforms the state-of-the-art offline IRL and imitation learning benchmarks by a large margin, over the continuous control tasks in MuJoCo and different datasets in the D4RL benchmark.