Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate discrete-time Markov process with memory. At any discrete time instant, each observed variable of the multivariate process is a binary string of random length, which is parameterized by an unobservable or hidden [0,1]-valued scalar. The hidden scalars corresponding to the variables evolve according to discrete-time linear stochastic dynamics dictated by the underlying influence graph whose nodes are the variables. We extend an existing algorithm for learning i.i.d. graphical models to this Markovian setting with memory and prove that it can learn the influence graph based on the binary observations using logarithmic (in number of variables or nodes) samples when the degree of the influence graph is bounded. The crucial analytical contribution of this work is the derivation of the sample complexity result by upper and lower bounding the rate of convergence of the observed Markov process with memory to its stationary distribution in terms of the parameters of the influence graph.

In silico methods evaluating the mutation effects of missense mutations are providing an important approach for understanding mutations in personal genomes and identifying disease-relevant biomarkers. However, existing methods, including deep learning methods, heavily rely on sequence-aware information, and do not fully leverage the potential of available 3D structural information. In addition, these methods may exhibit an inability to predict mutations in domains difficult to formulate sequence-based embeddings. In this study, we introduce a novel rationale-guided graph neural network AlphaGMut to evaluate mutation effects and to distinguish pathogenic mutations from neutral mutations. We compute the alpha shapes of protein structures to obtain atomic-resolution edge connectivities and map them to an accurate residue-level graph representation. We then compute structural-, topological-, biophysical-, and sequence properties of the mutation sites, which are assigned as node attributes in the graph. These node attributes could effectively guide the graph neural network to learn the difference between pathogenic and neutral mutations using k-hop message passing with a short training period. We demonstrate that AlphaGMut outperforms state-of-the-art methods, including DeepMind's AlphaMissense, in many performance metrics. In addition, AlphaGMut has the advantage of performing well in alignment-free settings, which provides broader prediction coverage and better generalization compared to current methods requiring deep sequence-aware information.

Offline reinforcement learning (RL) can learn optimal policies from pre-collected offline datasets without interacting with the environment, but the sampled actions of the agent cannot often cover the action distribution under a given state, resulting in the extrapolation error issue. Recent works address this issue by employing generative adversarial networks (GANs). However, these methods often suffer from insufficient constraints on policy exploration and inaccurate representation of behavior policies. Moreover, the generator in GANs fails in fooling the discriminator while maximizing the expected returns of a policy. Inspired by the diffusion, a generative model with powerful feature expressiveness, we propose a new offline RL method named Diffusion Policies with Generative Adversarial Networks (Diff-PoGAN). In this approach, the diffusion serves as the policy generator to generate diverse distributions of actions, and a regularization method based on maximum likelihood estimation (MLE) is developed to generate data that approximate the distribution of behavior policies. Besides, we introduce an additional regularization term based on the discriminator output to effectively constrain policy exploration for policy improvement. Comprehensive experiments are conducted on the datasets for deep data-driven reinforcement learning (D4RL), and experimental results show that DiffPoGAN outperforms state-of-the-art methods in offline RL.

Reinforcement Learning with Human Feedback (RLHF) is at the core of fine-tuning methods for generative AI models for language and images. Such feedback is often sought as rank or preference feedback from human raters, as opposed to eliciting scores since the latter tends to be very noisy. On the other hand, RL theory and algorithms predominantly assume that a reward feedback is available. In particular, approaches for online learning that can be helpful in adaptive data collection via active learning cannot incorporate offline preference data. In this paper, we adopt a finite-armed linear bandit model as a prototypical model of online learning. We consider an offline preference dataset to be available generated by an expert of unknown 'competence'. We propose $\texttt{warmPref-PS}$, a posterior sampling algorithm for online learning that can be warm-started with an offline dataset with noisy preference feedback. We show that by modeling the competence of the expert that generated it, we are able to use such a dataset most effectively. We support our claims with novel theoretical analysis of its Bayesian regret, as well as extensive empirical evaluation of an approximate algorithm which performs substantially better (almost 25 to 50% regret reduction in our studies) as compared to baselines.

State of the art large language models (LLMs) have shown impressive performance on a variety of benchmark tasks and are increasingly used as components in larger applications, where LLM-based predictions serve as proxies for human judgements or decision. This raises questions about the human-likeness of LLM-derived information, alignment with human intuition, and whether LLMs could possibly be considered (parts of) explanatory models of (aspects of) human cognition or language use. To shed more light on these issues, we here investigate the human-likeness of LLMs' predictions for multiple-choice decision tasks from the perspective of Bayesian statistical modeling. Using human data from a forced-choice experiment on pragmatic language use, we find that LLMs do not capture the variance in the human data at the item-level. We suggest different ways of deriving full distributional predictions from LLMs for aggregate, condition-level data, and find that some, but not all ways of obtaining condition-level predictions yield adequate fits to human data. These results suggests that assessment of LLM performance depends strongly on seemingly subtle choices in methodology, and that LLMs are at best predictors of human behavior at the aggregate, condition-level, for which they are, however, not designed to, or usually used to, make predictions in the first place.

The fairness of AI decision-making has garnered increasing attention, leading to the proposal of numerous fairness algorithms. In this paper, we aim not to address this issue by directly introducing fair learning algorithms, but rather by generating entirely new, fair synthetic data from biased datasets for use in any downstream tasks. Additionally, the distribution of test data may differ from that of the training set, potentially impacting the performance of the generated synthetic data in downstream tasks. To address these two challenges, we propose a diffusion model-based framework, FADM: Fairness-Aware Diffusion with Meta-training. FADM introduces two types of gradient induction during the sampling phase of the diffusion model: one to ensure that the generated samples belong to the desired target categories, and another to make the sensitive attributes of the generated samples difficult to classify into any specific sensitive attribute category. To overcome data distribution shifts in the test environment, we train the diffusion model and the two classifiers used for induction within a meta-learning framework. Compared to other baselines, FADM allows for flexible control over the categories of the generated samples and exhibits superior generalization capability. Experiments on real datasets demonstrate that FADM achieves better accuracy and optimal fairness in downstream tasks.

To mitigate the suboptimal nature of graph structure, Graph Structure Learning (GSL) has emerged as a promising approach to improve graph structure and boost performance in downstream tasks. Despite the proposal of numerous GSL methods, the progresses in this field mostly concentrated on node-level tasks, while graph-level tasks (e.g., graph classification) remain largely unexplored. Notably, applying node-level GSL to graph classification is non-trivial due to the lack of find-grained guidance for intricate structure learning. Inspired by the vital role of subgraph in graph classification, in this paper we explore the potential of subgraph structure learning for graph classification by tackling the challenges of key subgraph selection and structure optimization. We propose a novel Motif-driven Subgraph Structure Learning method for Graph Classification (MOSGSL). Specifically, MOSGSL incorporates a subgraph structure learning module which can adaptively select important subgraphs. A motif-driven structure guidance module is further introduced to capture key subgraph-level structural patterns (motifs) and facilitate personalized structure learning. Extensive experiments demonstrate a significant and consistent improvement over baselines, as well as its flexibility and generalizability for various backbones and learning procedures.

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal Differential Equations (UDEs) are used to combine prior knowledge in the form of mechanistic formulations with universal function approximators, like neural networks. Integral to the efficacy of UDEs is the joint estimation of parameters within mechanistic formulations and the universal function approximators using empirical data. The robustness and applicability of resultant models, however, hinge upon the rigorous quantification of uncertainties associated with these parameters, as well as the predictive capabilities of the overall model or its constituent components. With this work, we provide a formalisation of uncertainty quantification (UQ) for UDEs and investigate important frequentist and Bayesian methods. By analysing three synthetic examples of varying complexity, we evaluate the validity and efficiency of ensembles, variational inference and Markov chain Monte Carlo sampling as epistemic UQ methods for UDEs.

Normalizing Flows (NFs) are powerful and efficient models for density estimation. When modeling densities on manifolds, NFs can be generalized to injective flows but the Jacobian determinant becomes computationally prohibitive. Current approaches either consider bounds on the log-likelihood or rely on some approximations of the Jacobian determinant. In contrast, we propose injective flows for parametric hypersurfaces and show that for such manifolds we can compute the Jacobian determinant exactly and efficiently, with the same cost as NFs. Furthermore, we show that for the subclass of star-like manifolds we can extend the proposed framework to always allow for a Cartesian representation of the density. We showcase the relevance of modeling densities on hypersurfaces in two settings. Firstly, we introduce a novel Objective Bayesian approach to penalized likelihood models by interpreting level-sets of the penalty as star-like manifolds. Secondly, we consider Bayesian mixture models and introduce a general method for variational inference by defining the posterior of mixture weights on the probability simplex.

Learning a parametric model from a given dataset indeed enables to capture intrinsic dependencies between random variables via a parametric conditional probability distribution and in turn predict the value of a label variable given observed variables. In this paper, we undertake a comparative analysis of generative and discriminative approaches which differ in their construction and the structure of the underlying inference problem. Our objective is to compare the ability of both approaches to leverage information from various sources in an epistemic uncertainty aware inference via the posterior predictive distribution. We assess the role of a prior distribution, explicit in the generative case and implicit in the discriminative case, leading to a discussion about discriminative models suffering from imbalanced dataset. We next examine the double role played by the observed variables in the generative case, and discuss the compatibility of both approaches with semi-supervised learning. We also provide with practical insights and we examine how the modeling choice impacts the sampling from the posterior predictive distribution. With regard to this, we propose a general sampling scheme enabling supervised learning for both approaches, as well as semi-supervised learning when compatible with the considered modeling approach. Throughout this paper, we illustrate our arguments and conclusions using the example of affine regression, and validate our comparative analysis through classification simulations using neural network based models.