Related papers: Fast Gumbel-Max Sketch and its Applications
Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…
We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…
We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three…
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…
We revise the problem of extracting one independent component from an instantaneous linear mixture of signals. The mixing matrix is parameterized by two vectors, one column of the mixing matrix and one row of the de-mixing matrix. The…
Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and…
Probabilistic graphical models (PGMs) serve as a powerful framework for modeling complex systems with uncertainty and extracting valuable insights from data. However, users face challenges when applying PGMs to their problems in terms of…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
In this paper, we investigate combining blocking and collapsing -- two widely used strategies for improving the accuracy of Gibbs sampling -- in the context of probabilistic graphical models (PGMs). We show that combining them is not…
Learning a Gaussian mixture model (GMM) is a fundamental problem in machine learning, learning theory, and statistics. One notion of learning a GMM is proper learning: here, the goal is to find a mixture of $k$ Gaussians $\mathcal{M}$ that…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
Consistency in the output of language models is critical for their reliability and practical utility. Due to their training objective, language models learn to model the full space of possible continuations, leading to outputs that can vary…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
Graph Neural Networks (GNNs) have shown great superiority on non-Euclidean graph data, achieving ground-breaking performance on various graph-related tasks. As a practical solution to train GNN on large graphs with billions of nodes and…
While deep generative models have succeeded in image processing, natural language processing, and reinforcement learning, training that involves discrete random variables remains challenging due to the high variance of its gradient…
Superpixel segmentation algorithms are to partition an image into perceptually coherence atomic regions by assigning every pixel a superpixel label. Those algorithms have been wildly used as a preprocessing step in computer vision works, as…
Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…
Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…