Related papers: Manifold Sampling via Entropy Maximization
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-$s$ principle submatrix of a given order $n$ covariance matrix $C$. Exact algorithms are based on a branch-and-bound framework. The…
Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Here we present an investigation into using nested sampling algorithms in cosmological likelihood analysis. We present a new nested sampling algorithm, ESNested, that uses Evolution Strategies for sample proposals. This quickly finds the…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…
This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in…
Token sampling strategies critically influence text generation quality in large language models (LLMs). However, existing methods introduce additional hyperparameters, requiring extensive tuning and complicating deployment. We present…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental constraints project onto a subspace of viable…
Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…
Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing…
Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…