Related papers: Snowballing Nested Sampling
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics:…
New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…
Synaptic Sampling Machine (SSM) is a type of neural network model that considers biological unreliability of the synapses. We propose the circuit design of the SSM neural network which is realized through the memristive-CMOS crossbar…
Nested stochastic modeling has been on the rise in many fields of the financial industry. Such modeling arises whenever certain components of a stochastic model are stochastically determined by other models. There are at least two main…
Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble of districting plans which are drawn from a prescribed probability distribution that adheres to a realistic and…
Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…
Multi-hypothesis tracking is a flexible and intuitive approach to tracking multiple nearby objects. However, the original formulation of its data association step is widely thought to scale poorly with the number of tracked objects. We…
The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a…
Sequential Monte Carlo (SMC) is a class of algorithms that approximate high-dimensional expectations of a Markov chain. SMC algorithms typically include a resampling step. There are many possible ways to resample, but the relative…
Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…
Augmenting the multi-step reasoning abilities of Large Language Models (LLMs) has been a persistent challenge. Recently, verification has shown promise in improving solution consistency by evaluating generated outputs. However, current…
Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a…
Active Learning aims to optimize performance while minimizing annotation costs by selecting the most informative samples from an unlabelled pool. Traditional uncertainty sampling often leads to sampling bias by choosing similar uncertain…
A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation),…