Enhances Bayesian model selection for high-dimensional problems.
problem Bayesian model selection for high-dimensional problems.
method Proximal nested sampling with data-driven priors.
result Improves model selection for log-convex likelihood models.
We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an ε stationary point where the expected norm of the subgradient of corresponding augmented Lag…
We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained v…
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
Gradient-guided nested sampling improves posterior inference efficiency.
problem Efficiently sampling from complex posterior distributions.
method Gradient-guided nested sampling combining differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization.
result Significantly faster mode discovery and more accurate partition function estimates.
Nested Slice Sampling accelerates Nested Sampling for GPU acceleration.
problem Challenging inference for complex, multimodal targets.
method Vectorized Nested Slice Sampling using Hit-and-Run Slice Sampling.
result NSS maintains accurate evidence estimates and high-quality posterior samples, robust on multimodal problems.
Nested sampling improved for arbitrary priors.
problem Technical obstacle to using nested sampling with arbitrary priors.
method Parametric bijectors trained on samples from a desired prior density.
result Nested sampling can be used with arbitrary priors.
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual ℓ1 and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to nonsmooth problems that are difficult to optimize, and we propose in this paper a suit…
Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary invariant norm and the indicator function of an upper bounding rank constraint. The most well-known member of this family is the so-called nuclear norm. To …
Paper proposes a new estimator for nested expectations with faster convergence.
problem Estimating nested expectations is computationally challenging.
method Nested kernel quadrature estimators with proof of faster convergence rate.
result The proposed method requires fewer samples for accurate estimation.
New model approximates sparse mean-CVaR portfolio optimization efficiently.
problem NP-hard ℓ0-constrained mean-CVaR optimization. method Proximal alternating linearized minimization algorithm with nested fixed-point proximity.
result The model offers a guaranteed approximation of the ℓ0-constrained mean-CVaR model. Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
Unified SGD method improves convergence for nested optimization problems.
problem Stochastic nested optimization problems.
method ALTERNATE dESCEN (ALSET) method leveraging hidden smoothness.
result Requires O(ε−2) samples to achieve an ε-stationary point. This paper uses Nested Sampling to improve Gaussian Process uncertainty quantification.
problem Underestimating predictive uncertainty and overfitting in Gaussian Process models.
method Marginalises hyperparameters using Nested Sampling for spectral mixture kernels.
result Improves predictive performance and uncertainty quantification across various data sets.
The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing with variable errors, and deriving parameter uncertainties is often an after-th…
New method uses zeroth-order queries to approximate proximal sampling efficiently.
problem Approximating proximal sampling with zeroth-order information.
method Direct simulation of heat flow dynamics, treating intermediate distribution as Gaussian mixture.
result Inherits exponential convergence under isoperimetric conditions, avoids rejection sampling.
Riemannian Proximal Sampler improves sampling on manifold data.
problem Sampling from densities on Riemannian manifolds.
method Uses MBI and RHK oracles for high-accuracy sampling.
result Sampling with ε-accuracy requires O(log(1/ε)) iterations in KL divergence.
Nested learning improves model performance on multi-granular tasks.
problem Overconfident models and lack of fine-grained confidence in predictions.
method Introducing nested learning with a sequence of nested feature embeddings and explicit combination of outputs.
result Nested learning outperforms standard end-to-end training on various datasets.
Nested sampling is a powerful technique for exploring high-likelihood regions, but its theoretical derivation is complex and involves approximations.
problem Sampling from likelihood-constrained priors in nested sampling
method Providing a comprehensive and detailed exposition of nested sampling derivation and practical challenges
result Deepening understanding of nested sampling and fostering future enhancements
Paper tackles robust model training with a new stochastic algorithm.
problem Training robust models against data distribution shift.
method Derives a novel dual formulation and proposes a nested stochastic gradient descent algorithm.
result Establishes polynomial iteration and sample complexities for large-scale DRO problems.
New sampling algorithm for non-smooth potentials.
problem Sampling from non-smooth potentials.
method Proximal algorithm based on rejection sampling.
result Achieves better complexity than existing methods.
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulti…
DE-PSGLD samples from constrained distributions in a decentralized manner.
problem Sampling from log-concave distributions with constraints.
method Decentralized Proximal Stochastic Gradient Langevin Dynamics with proximal regularization.
result DE-PSGLD converges to a regularized Gibbs distribution and maintains posterior concentration.
PDNS tackles multimodal sampling challenges using proximal point method.
problem Multimodal distributions with significant barriers between modes.
method Proximal point method on path measures, decomposing into simpler subproblems.
result PDNS effectively promotes thorough exploration across modes.
New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.
problem The difficulty of sampling from heavy-tailed distributions using Gaussian versus stable oracles.
method Comparison of Gaussian and stable oracles for proximal samplers.
result Gaussian samplers have a fundamental barrier for high-accuracy guarantees in heavy-tailed sampling, while stable samplers excel.
New method estimates nested expectations with biased and antithetic sampling.
problem Estimating nested expectations with biased and antithetic sampling.
method Nested multilevel Monte Carlo with biased and antithetic sampling.
result Estimator achieves order ε^(-2) asymptotic cost.
Study compares MCMC and nested sampling for high-dimensional physics problems.
problem Efficiently sampling high-dimensional Bayesian posterior distributions in particle physics and cosmology.
method Review and comparison of MCMC and nested sampling techniques on high-dimensional test functions and real physics examples.
result Modern MCMC algorithms can outperform nested sampling in certain cases, highlighting implementation details.
New sampling method using regularized Wasserstein proximal for Gibbs distributions.
problem Sampling from Gibbs distributions with numerical stability and efficiency.
method Preconditioned regularized Wasserstein proximal operator.
result Discrete-time convergence analysis and explicit bias characterization.
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
Deriving and applying Proximal Policy Optimization to GFlowNets for efficient training of discrete sampling policies
problem Training stochastic policies to sample from structured discrete probability distributions
method Deriving policy gradient algorithms for GFlowNets and applying Proximal Policy Optimization
result Improved convergence speed and data efficiency compared to standard GFlowNet training objectives
Improved sampling algorithm with state-of-the-art complexity bounds.
problem Efficient sampling from various probability distributions.
method Proximal sampler with inexact restricted Gaussian oracle.
result State-of-the-art complexity bounds in almost all settings.
A new method for efficient nested Monte Carlo simulations in financial modeling.
problem Computational challenges in nested stochastic modeling for financial risk assessment.
method Sample recycling approach to speed up inner loop estimations.
result Significantly more efficient than traditional techniques.
We investigate the problem of computing a nested expectation of the form P[E[X∣Y]≥0]=E[H(E[X∣Y])] where H is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial portfo…
Method estimates Bayesian evidence from posterior samples using normalizing flows.
problem Estimating Bayesian evidence from posterior samples.
method Normalizing flows for evidence estimation.
result Method is more robust to sharp features in posterior distributions, especially in higher dimensions.
Paper tackles robust optimization under uncertainty using nested distance.
problem Optimizing under distributionally robust uncertainty with nested distance.
method Equivalent recursive and dynamic programming reformulations for tractable optimization.
result Optimal robust policies can be found efficiently using convex optimization.
New sampling methods for constrained and composite distributions.
problem Sampling from log-concave distributions with constraints and composite structures.
method Proximal sampler applied to lifted convex sets with separation and subgradient oracles.
result Practical and unbiased samplers for constrained and composite distributions.
Simple algorithms identify best items or full rankings from choice-based feedback.
problem Learning to identify the best item or full ranking from choice-based feedback.
method Nested Elimination (NE) and Nested Partition (NP) algorithms.
result NE is worst-case asymptotically optimal, NP is optimal up to a constant factor.
Accelerates sampling from Gibbs distributions using ARWP method.
problem Sampling from Gibbs distributions efficiently.
method ARWP method, combining Nesterov acceleration and regularized Wasserstein proximal.
result ARWP exhibits higher contraction rate and faster tail exploration.
Deep learning and genetic algorithms speed up cosmological Bayesian inference.
problem Substantial computational demands in Bayesian inference for cosmological parameter estimation.
method Deep learning using feedforward neural networks to approximate likelihood functions dynamically, optimized with genetic algorithms.
result Significant speed-up in Bayesian inference process for cosmological models and datasets.
New metrics using Laplace approximation improve Gaussian process model selection.
problem Finding a balance between model accuracy, interpretability, and simplicity.
method Introducing multiple metrics based on the Laplace approximation to evaluate Gaussian process models.
result Our metrics provide comparable performance to dynamic nested sampling but are significantly faster.
We accelerate Bayesian inference for neutrino physics experiments by 100-60x.
problem Complex posterior geometries in multi-dimensional parameter spaces.
method GPU acceleration, automatic differentiation, neural-network-guided reparameterization.
result Significant performance improvements in Bayesian inference for direct detection experiments.
RFX accelerates and compresses Random Forests for large datasets.
problem Memory bottleneck in proximity matrices limits Random Forest analysis.
method QLORA compression, CPU TriBlock storage, GPU batch sizing, 3D MDS visualization.
result Proximity-based Random Forest analysis on larger datasets is feasible.
Improved MLMC method boosts risk estimation efficiency.
problem Estimating risk measures like Value-at-Risk in financial risk management.
method Novel MLMC parametrization and antithetic sampling.
result Significantly improved performance in practical settings.
Proximal Diffusion Models improve generative model efficiency.
problem Improving generative model efficiency and accuracy.
method Developed Proximal Diffusion Models using proximal maps instead of scores.
result Proximal Diffusion Models achieve faster convergence and higher accuracy.
New method estimates Bayesian evidence more accurately and faster.
problem Estimating normalizing constants in Bayesian inference.
method Gaussianized Bridge Sampling (GBS) using posterior samples and Normalizing Flows.
result GBS is significantly faster and more accurate than existing methods.
Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an "exact" description of reality. This le…