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.

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.

Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by several experiments with human subjects, yet its theoretical basis remains largely unexplored: why does it work? This paper lays the groundwork for three theoretical conjectures. First, unexpectedness can be seen as a generalization of Bayes' rule. Second, the frequentist core of unexpectedness can be connected to the function of tracking ergodic properties of the world. Third, unexpectedness can be seen as constituent of various measures of divergence between the entropy of the world (environment) and the variety of the observer (system). The resulting framework hints to research directions that go beyond the division between probabilistic and logical approaches, potentially bringing new insights into the extraction of causal relations, and into the role of descriptive mechanisms in learning.

Recovering masked feedback with neural models is a popular paradigm in recommender systems. Seeing the success of diffusion models in solving ill-posed inverse problems, we introduce a conditional diffusion framework for collaborative filtering that iteratively reconstructs a user's hidden preferences guided by its historical interactions. To better align with the intrinsic characteristics of implicit feedback data, we implement forward diffusion by applying synthetic smoothing filters to interaction signals on an item-item graph. The resulting reverse diffusion can be interpreted as a personalized process that gradually refines preference scores. Through graph Fourier transform, we equivalently characterize this model as an anisotropic Gaussian diffusion in the graph spectral domain, establishing both forward and reverse formulations. Our model outperforms state-of-the-art methods by a large margin on one dataset and yields competitive results on the others.

We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE). Motivated by the challenges that arise when trying to learn an (almost arbitrary) latent neural SDE from large-scale data, such as efficient gradient computation, we take a step back and study a specific subclass instead. In our case, the SDE evolves on a homogeneous latent space and is induced by stochastic dynamics of the corresponding (matrix) Lie group. In learning problems, SDEs on the unit $n$-sphere are arguably the most relevant incarnation of this setup. Notably, for variational inference, the sphere not only facilitates using a truly uninformative prior SDE, but we also obtain a particularly simple and intuitive expression for the Kullback-Leibler divergence between the approximate posterior and prior process in the evidence lower bound. Experiments demonstrate that a latent SDE of the proposed type can be learned efficiently by means of an existing one-step geometric Euler-Maruyama scheme. Despite restricting ourselves to a less diverse class of SDEs, we achieve competitive or even state-of-the-art performance on various time series interpolation and classification benchmarks.