Bayesian structure learning allows one to capture uncertainty over the causal directed acyclic graph (DAG) responsible for generating given data. In this work, we present Tractable Uncertainty for STructure learning (TRUST), a framework for approximate posterior inference that relies on probabilistic circuits as the representation of our posterior belief. In contrast to sample-based posterior approximations, our representation can capture a much richer space of DAGs, while also being able to tractably reason about the uncertainty through a range of useful inference queries. We empirically show how probabilistic circuits can be used as an augmented representation for structure learning methods, leading to improvement in both the quality of inferred structures and posterior uncertainty. Experimental results on conditional query answering further demonstrate the practical utility of the representational capacity of TRUST.

Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g., balancing the Kullback Leibler (KL) and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolution during training. Because of the inefficiency of exhaustive search in a high-dimensional hyperparameter space for the expensive to train models, here we explored a latent Bayesian optimization (zBO) approach for the hyperparameter trajectory optimization for the unsupervised and semi-supervised ML and demonstrate for joint-VAE with rotational invariances. We demonstrate an application of this method for finding joint discrete and continuous rotationally invariant representations for MNIST and experimental data of a plasmonic nanoparticles material system. The performance of the proposed approach has been discussed extensively, where it allows for any high dimensional hyperparameter tuning or trajectory optimization of other ML models.

Automated decision support systems that are able to infer second opinions from experts can potentially facilitate a more efficient allocation of resources; they can help decide when and from whom to seek a second opinion. In this paper, we look at the design of this type of support systems from the perspective of counterfactual inference. We focus on a multiclass classification setting and first show that, if experts make predictions on their own, the underlying causal mechanism generating their predictions needs to satisfy a desirable set invariant property. Further, we show that, for any causal mechanism satisfying this property, there exists an equivalent mechanism where the predictions by each expert are generated by independent sub-mechanisms governed by a common noise. This motivates the design of a set invariant Gumbel-Max structural causal model where the structure of the noise governing the sub-mechanisms underpinning the model depends on an intuitive notion of similarity between experts which can be estimated from data. Experiments on both synthetic and real data show that our model can be used to infer second opinions more accurately than its non-causal counterpart.

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between generalisation bounds based on the regularity of the loss function, and their chained counterparts, which can be obtained by lifting the regularity assumption from the loss onto its gradient. This allows us to re-derive the chaining mutual information bound from the literature, and to obtain novel chained information-theoretic generalisation bounds, based on the Wasserstein distance and other probability metrics. We show on some toy examples that the chained generalisation bound can be significantly tighter than its standard counterpart, particularly when the distribution of the hypotheses selected by the algorithm is very concentrated.

We propose a message passing algorithm, based on variational Bayesian inference, for low-rank tensor completion with automatic rank determination in the canonical polyadic format when additional side information (SI) is given. The SI comes in the form of low-dimensional subspaces the contain the fiber spans of the tensor (columns, rows, tubes, etc.). We validate the regularization properties induced by SI with extensive numerical experiments on synthetic and real-world data and present the results about tensor recovery and rank determination. The results show that the number of samples required for successful completion is significantly reduced in the presence of SI. We also discuss the origin of a bump in the phase transition curves that exists when the dimensionality of SI is comparable with that of the tensor.

In plant breeding the presence of a genotype by environment (GxE) interaction has a strong impact on cultivation decision making and the introduction of new crop cultivars. The combination of linear and bilinear terms has been shown to be very useful in modelling this type of data. A widely-used approach to identify GxE is the Additive Main Effects and Multiplicative Interaction Effects (AMMI) model. However, as data frequently can be high-dimensional, Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible. In this article, we consider a variational inference approach for such a model. We derive variational approximations for estimating the parameters and we compare the approximations to MCMC using both simulated and real data. The new inferential framework we propose is on average two times faster whilst maintaining the same predictive performance as MCMC.

When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods deal with truncated density estimation problems by turning to score matching, where the access to the intractable normalising constant is not required. We present a novel extension to truncated score matching for a Riemannian manifold. Applications are presented for the von Mises-Fisher and Kent distributions on a two dimensional sphere in $\R^3$, as well as a real-world application of extreme storm observations in the USA. In simulated data experiments, our score matching estimator is able to approximate the true parameter values with a low estimation error and shows improvements over a maximum likelihood estimator.

More robust approaches are studied to this effect Data smoothing is heavily utilized in many learning [41]-[43], where a prominent example is the moving median problems to detect certain patters in the data or mitigate filter. Although the moving median is a nonlinear smoother noisy/anomalous values [1]. The notion of smoothing stems and the smoothed signal is acquired by the weighted median from the inference that the data points close to each other in of close groups of samples, it is efficiently computable by their features should have close mappings (functional evaluations), use of indexable skiplist [44]. We point out that specifically i.e., behave similarly. The most prominent example is for the moving median, the smoothed signal is statistically a time-series dataset where data points closer in time should optimal in the maximum likelihood sense, when the signal have similar values, e.g, unnaturally high or low values should contamination results from a Laplace distribution [45]. The be suppressed to match the nominal data pattern. Smoothing moving median filter has many applications including mass is mainly done on the datasets for easier extraction of their spectrometry [46], edge detection [47]. The application is information and consequently ease their analyses [2]. This especially rich in the field of image processing because of approach is applied in many fields including signal processing the edge-preserving capabilities [48].

In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian networks, from data. Defining such a distribution is very challenging, due to the combinatorially large sample space, and approximations based on MCMC are often required. Recently, a novel class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling of discrete and composite objects, such as graphs. In this work, we propose to use a GFlowNet as an alternative to MCMC for approximating the posterior distribution over the structure of Bayesian networks, given a dataset of observations. Generating a sample DAG from this approximate distribution is viewed as a sequential decision problem, where the graph is constructed one edge at a time, based on learned transition probabilities. Through evaluation on both simulated and real data, we show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs, and it compares favorably against other methods based on MCMC or variational inference.

Real-world applications of reinforcement learning for recommendation and experimentation faces a practical challenge: the relative reward of different bandit arms can evolve over the lifetime of the learning agent. To deal with these non-stationary cases, the agent must forget some historical knowledge, as it may no longer be relevant to minimise regret. We present a solution to handling non-stationarity that is suitable for deployment at scale, to provide business operators with automated adaptive optimisation. Our solution aims to provide interpretable learning that can be trusted by humans, whilst responding to non-stationarity to minimise regret. To this end, we develop an adaptive Bayesian learning agent that employs a novel form of dynamic memory. It enables interpretability through statistical hypothesis testing, by targeting a set point of statistical power when comparing rewards and adjusting its memory dynamically to achieve this power. By design, the agent is agnostic to different kinds of non-stationarity. Using numerical simulations, we compare its performance against an existing proposal and show that, under multiple non-stationary scenarios, our agent correctly adapts to real changes in the true rewards. In all bandit solutions, there is an explicit trade-off between learning and achieving maximal performance. Our solution sits on a different point on this trade-off when compared to another similarly robust approach: we prioritise interpretability, which relies on more learning, at the cost of some regret. We describe the architecture of a large-scale deployment of automatic optimisation-as-a-service where our agent achieves interpretability whilst adapting to changing circumstances.