In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.

In recent years, AI-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are atomlevel-based methods, which consider atoms as basic components and generate atom positions and types. In this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, we propose D3FG, a functional-groupbased diffusion model for pocket-specific molecule generation and elaboration. D3FG decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds of components can together form complicated fragments that enhance ligand-protein interactions. To be specific, in the diffusion process, D3FG diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks. In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, D3FG as a solution to a new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins.

A central problem in unsupervised domain adaptation is determining what to transfer from labeled source domains to an unlabeled target domain. To handle high-dimensional observations (e.g., images), a line of approaches use deep learning to learn latent representations of the observations, which facilitate knowledge transfer in the latent space. However, existing approaches often rely on restrictive assumptions to establish identifiability of the joint distribution in the target domain, such as independent latent variables or invariant label distributions, limiting their real-world applicability. In this work, we propose a general domain adaptation framework that learns compact latent representations to capture distribution shifts relative to the prediction task and address the fundamental question of what representations should be learned and transferred. Notably, we first demonstrate that learning representations based on all the predictive information, i.e., the label's Markov blanket in terms of the learned representations, is often underspecified in general settings. Instead, we show that, interestingly, general domain adaptation can be achieved by partitioning the representations of Markov blanket into those of the label's parents, children, and spouses. Moreover, its identifiability guarantee can be established. Building on these theoretical insights, we develop a practical, nonparametric approach for domain adaptation in a general setting, which can handle different types of distribution shifts.

Figure 5: CPA-VAE represented as an generative process (left) and as a graphical model (right). A.1 Mini-batch optimization In this section, we provide a detailed description of how the ELBO is computed from mini-batches for optimization. During training, we iterate through shuffled versions of the training dataset and receive batches of indices B = {i1,...,i |B|}. Di,t be the total number of samples in the batch that have received perturbation t. Let P be a hyperparameter number of particles.

We present AutoStan, a framework in which a command-line interface (CLI) coding agent autonomously builds and iteratively improves Bayesian models written in Stan. The agent operates in a loop, writing a Stan model file, executing MCMC sampling, then deciding whether to keep or revert each change based on two complementary feedback signals: the negative log predictive density (NLPD) on held-out data and the sampler's own diagnostics (divergences, R-hat, effective sample size). We evaluate AutoStan on five datasets with diverse modeling structures. On a synthetic regression dataset with outliers, the agent progresses from naive linear regression to a model with Student-t robustness, nonlinear heteroscedastic structure, and an explicit contamination mixture, matching or outperforming TabPFN, a state-of-the-art black-box method, while remaining fully interpretable. Across four additional experiments, the same mechanism discovers hierarchical partial pooling, varying-slope models with correlated random effects, and a Poisson attack/defense model for soccer. No search algorithm, critic module, or domain-specific instructions are needed. This is, to our knowledge, the first demonstration that a CLI coding agent can autonomously write and iteratively improve Stan code for diverse Bayesian modeling problems.

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