Medical prediction applications often need to deal with small sample sizes compared to the number of covariates. Such data pose problems for prediction and variable selection, especially when the covariate-response relationship is complicated. To address these challenges, we propose to incorporate co-data, i.e. external information on the covariates, into Bayesian additive regression trees (BART), a sum-of-trees prediction model that utilizes priors on the tree parameters to prevent overfitting. To incorporate co-data, an empirical Bayes (EB) framework is developed that estimates, assisted by a co-data model, prior covariate weights in the BART model. The proposed method can handle multiple types of co-data simultaneously. Furthermore, the proposed EB framework enables the estimation of the other hyperparameters of BART as well, rendering an appealing alternative to cross-validation. We show that the method finds relevant covariates and that it improves prediction compared to default BART in simulations. If the covariate-response relationship is nonlinear, the method benefits from the flexibility of BART to outperform regression-based co-data learners. Finally, the use of co-data enhances prediction in an application to diffuse large B-cell lymphoma prognosis based on clinical covariates, gene mutations, DNA translocations, and DNA copy number data. Keywords: Bayesian additive regression trees; Empirical Bayes; Co-data; High-dimensional data; Omics; Prediction

A Directed Acyclic Graph (DAG) can be partitioned or mapped into clusters to support and make inference more computationally efficient in Bayesian Network (BN), Markov process and other models. However, optimal partitioning with an arbitrary cost function is challenging, especially in statistical inference as the local cluster cost is dependent on both nodes within a cluster, and the mapping of clusters connected via parent and/or child nodes, which we call dependent clusters. We propose a novel algorithm called DCMAP for optimal cluster mapping with dependent clusters. Given an arbitrarily defined, positive cost function based on the DAG, we show that DCMAP converges to find all optimal clusters, and returns near-optimal solutions along the way. Empirically, we find that the algorithm is time-efficient for a Dynamic BN (DBN) model of a seagrass complex system using a computation cost function. For a 25 and 50-node DBN, the search space size was 9.91 10

Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with $q\leq1$. However, most GMMs rely on the $l_1$ norm because the objective is highly non-convex for sub-$l_1$ pseudo-norms. In the frequentist formulation, the $l_1$ norm relaxation provides the solution path as a function of the shrinkage parameter $\lambda$. In the Bayesian formulation, sparsity is instead encouraged through a Laplace prior, but posterior inference for different $\lambda$ requires repeated runs of expensive Gibbs samplers. Here we propose a general framework for variational inference with matrix-variate Normalizing Flow in GGMs, which unifies the benefits of frequentist and Bayesian frameworks. As a key improvement on previous work, we train with one flow a continuum of sparse regression models jointly for all regularization parameters $\lambda$ and all $l_q$ norms, including non-convex sub-$l_1$ pseudo-norms. Within one model we thus have access to (i) the evolution of the posterior for any $\lambda$ and any $l_q$ (pseudo-) norm, (ii) the marginal log-likelihood for model selection, and (iii) the frequentist solution paths through simulated annealing in the MAP limit.

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

Uncertainty Quantification (UQ) has gained traction in an attempt to fix the black-box nature of Deep Learning. Specifically (medical) biosignals such as electroencephalography (EEG), electrocardiography (ECG), electroocculography (EOG) and electromyography (EMG) could benefit from good UQ, since these suffer from a poor signal to noise ratio, and good human interpretability is pivotal for medical applications and Brain Computer Interfaces. In this paper, we review the state of the art at the intersection of Uncertainty Quantification and Biosignal with Machine Learning. We present various methods, shortcomings, uncertainty measures and theoretical frameworks that currently exist in this application domain. Overall it can be concluded that promising UQ methods are available, but that research is needed on how people and systems may interact with an uncertainty model in a (clinical) environment.

In this paper I propose a generative model of supervised learning that unifies two approaches to supervised learning, using a concept of a correct loss function. Addressing two measurability problems, which have been ignored in statistical learning theory, I propose to use convergence in outer probability to characterize the consistency of a learning algorithm. Building upon these results, I extend a result due to Cucker-Smale, which addresses the learnability of a regression model, to the setting of a conditional probability estimation problem. Additionally, I present a variant of Vapnik-Stefanuyk's regularization method for solving stochastic ill-posed problems, and using it to prove the generalizability of overparameterized supervised learning models.

Despite the success of autoregressive large language models in text generation, it remains a major challenge to generate text that satisfies complex constraints: sampling from the conditional distribution ${\Pr}(\text{text} | \alpha)$ is intractable for even the simplest lexical constraints $\alpha$. To overcome this challenge, we propose to use tractable probabilistic models (TPMs) to impose lexical constraints in autoregressive text generation models, which we refer to as GeLaTo (Generating Language with Tractable Constraints). To demonstrate the effectiveness of this framework, we use distilled hidden Markov models, where we can efficiently compute ${\Pr}(\text{text} | \alpha)$, to guide autoregressive generation from GPT2. GeLaTo achieves state-of-the-art performance on challenging benchmarks for constrained text generation (e.g., CommonGen), beating various strong baselines by a large margin. Our work not only opens up new avenues for controlling large language models but also motivates the development of more expressive TPMs.

Self-supervised representation learning often uses data augmentations to induce some invariance to "style" attributes of the data. However, with downstream tasks generally unknown at training time, it is difficult to deduce a priori which attributes of the data are indeed "style" and can be safely discarded. To address this, we introduce a more principled approach that seeks to disentangle style features rather than discard them. The key idea is to add multiple style embedding spaces where: (i) each is invariant to all-but-one augmentation; and (ii) joint entropy is maximized. We formalize our structured data-augmentation procedure from a causal latent-variable-model perspective, and prove identifiability of both content and (multiple blocks of) style variables. We empirically demonstrate the benefits of our approach on synthetic datasets and then present promising but limited results on ImageNet.

Relying on crowdsourced workers, data crowdsourcing platforms are able to efficiently provide vast amounts of labeled data. Due to the variability in the annotation quality of crowd workers, modern techniques resort to redundant annotations and subsequent label aggregation to infer true labels. However, these methods require model updating during the inference, posing challenges in real-world implementation. Meanwhile, in recent years, many data labeling tasks have begun to require skilled and experienced annotators, leading to an increasing demand for long-term annotators. These annotators could leave substantial historical annotation records on the crowdsourcing platforms, which can benefit label aggregation, but are ignored by previous works. Hereby, in this paper, we propose a novel label aggregation technique, which does not need any model updating during inference and can extensively explore the historical annotation records. We call it SuperLA, a Supervised Label Aggregation method. Inside this model, we design three types of input features and a straightforward neural network structure to merge all the information together and subsequently produce aggregated labels. Based on comparison experiments conducted on 22 public datasets and 11 baseline methods, we find that SuperLA not only outperforms all those baselines in inference performance but also offers significant advantages in terms of efficiency.

There has been a resurgence of applications focused on Human Activity Recognition (HAR) in smart homes, especially in the field of ambient intelligence and assisted living technologies. However, such applications present numerous significant challenges to any automated analysis system operating in the real world, such as variability, sparsity, and noise in sensor measurements. Although state-of-the-art HAR systems have made considerable strides in addressing some of these challenges, they especially suffer from a practical limitation: they require successful pre-segmentation of continuous sensor data streams before automated recognition, i.e., they assume that an oracle is present during deployment, which is capable of identifying time windows of interest across discrete sensor events. To overcome this limitation, we propose a novel graph-guided neural network approach that performs activity recognition by learning explicit co-firing relationships between sensors. We accomplish this by learning a more expressive graph structure representing the sensor network in a smart home, in a data-driven manner. Our approach maps discrete input sensor measurements to a feature space through the application of attention mechanisms and hierarchical pooling of node embeddings. We demonstrate the effectiveness of our proposed approach by conducting several experiments on CASAS datasets, showing that the resulting graph-guided neural network outperforms the state-of-the-art method for HAR in smart homes across multiple datasets and by large margins. These results are promising because they push HAR for smart homes closer to real-world applications.