相关论文: Generalized Decomposition Priors on R2

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…

We study a new parametric family of distributions on the ordered simplex $\nabla^{d-1} = \{y \in \mathbb{R}^d: y_1 \geq \dots \geq y_d \geq 0, \sum_{k=1}^d y_k = 1\}$, which we call Generalized Rank Dirichlet (GRD) distributions. Their…

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…

Multimodal learning aims to leverage information from diverse data modalities to achieve more comprehensive performance. However, conventional multimodal models often suffer from modality imbalance, where one or a few modalities dominate…

Modern data science applications often involve complex relational data with dynamic structures. An abrupt change in such dynamic relational data is typically observed in systems that undergo regime changes due to interventions. In such a…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these…

The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various…

Group Relative Policy Optimization (GRPO) has emerged as the de facto Reinforcement Learning (RL) objective driving recent advancements in Multimodal Large Language Models. However, extending this success to open-source multimodal…

Machine learning models struggle with generalization when encountering out-of-distribution (OOD) samples with unexpected distribution shifts. For vision tasks, recent studies have shown that test-time adaptation employing diffusion models…

We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…

Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…

Recent work introduced deep kernel processes as an entirely kernel-based alternative to NNs (Aitchison et al. 2020). Deep kernel processes flexibly learn good top-layer representations by alternately sampling the kernel from a distribution…

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…

We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…