Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's vari-ational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation.

Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's vari-ational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation.

Nonlinear data visualization using t-distributed stochastic neighbor embedding (t-SNE) enables the representation of complex single-cell transcriptomic landscapes in two or three dimensions to depict biological populations accurately. However, t-SNE often fails to account for uncertainties in the original dataset, leading to misleading visualizations where cell subsets with noise appear indistinguishable. To address these challenges, we introduce uncertainty-aware t-SNE (Ut-SNE), a noise-defending visualization tool tailored for uncertain single-cell RNA-seq data. By creating a probabilistic representation for each sample, Our Ut-SNE accurately incorporates noise about transcriptomic variability into the visual interpretation of single-cell RNA sequencing data, revealing significant uncertainties in transcriptomic variability. Through various examples, we showcase the practical value of Ut-SNE and underscore the significance of incorporating uncertainty awareness into data visualization practices. This versatile uncertainty-aware visualization tool can be easily adapted to other scientific domains beyond single-cell RNA sequencing, making them valuable resources for high-dimensional data analysis.

Despite the recent success of machine learning (ML) in materials science, its success heavily relies on the structural description of crystal, which is itself computationally demanding and occasionally unattainable. Stoichiometry descriptors can be an alternative approach, which reveals the ratio between elements involved to form a certain compound without any structural information. However, it is not trivial to learn the representations of stoichiometry due to the nature of materials science called polymorphism, i.e., a single stoichiometry can exist in multiple structural forms due to the flexibility of atomic arrangements, inducing uncertainties in representation. To this end, we propose PolySRL, which learns the probabilistic representation of stoichiometry by utilizing the readily available structural information, whose uncertainty reveals the polymorphic structures of stoichiometry. Extensive experiments on sixteen datasets demonstrate the superiority of PolySRL, and analysis of uncertainties shed light on the applicability of PolySRL in real-world material discovery.

Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's variational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation. Experiments in several real-world datasets show that our VIR can outperform state-of-the-art imbalanced regression models in terms of both accuracy and uncertainty estimation.

In this paper, we propose an end-to-end lifelong learning mixture of experts. Each expert is implemented by a Variational Autoencoder (VAE). The experts in the mixture system are jointly trained by maximizing a mixture of individual component evidence lower bounds (MELBO) on the log-likelihood of the given training samples. The mixing coefficients in the mixture, control the contributions of each expert in the goal representation. These are sampled from a Dirichlet distribution whose parameters are determined through non-parametric estimation during lifelong learning. The model can learn new tasks fast when these are similar to those previously learnt. The proposed Lifelong mixture of VAE (L-MVAE) expands its architecture with new components when learning a completely new task. After the training, our model can automatically determine the relevant expert to be used when fed with new data samples. This mechanism benefits both the memory efficiency and the required computational cost as only one expert is used during the inference. The L-MVAE inference model is able to perform interpolation in the joint latent space across the data domains associated with different tasks and is shown to be efficient for disentangled learning representation.

Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid under conditional independence assumptions on the inducing random variables. We discuss five inequalities of this particular type, four of which has appeared earlier in the literature. Besides the proof of the new fifth inequality, simpler proofs of (some of) former inequalities are presented. These five information inequalities are used to characterize all conditional independence structures induced by four discrete random variables.