The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.
problem Sampling from strongly Rayleigh distributions efficiently.
method Optimal sublinear sampling algorithms for random spanning trees and determinantal point processes.
result Achieves optimal sublinear sampling for strongly Rayleigh distributions.
Estimator calculates surface curvature from point cloud samples.
problem Accurately estimating curvature from limited point cloud data.
method Algorithm using probability distribution and nearby points control.
result Controlled number of points ensures accurate curvature estimation.
New sampling method reduces variance in correlated high-dimensional distributions.
problem Reducing variance in Monte Carlo estimators for correlated high-dimensional distributions.
method DPPMC (Determinantal Point Processes Monte Carlo) method for structured sampling.
result DPPMCs improve state-of-the-art in various optimization and machine learning problems.
Reweighted ALPS improves sampling from multimodal distributions using warm start points.
problem Sampling from multimodal distributions is hard due to exponential mixing times.
method Introduces Reweighted ALPS, a modified Annealed Leap-Point Sampler that uses warm start points.
result First polynomial-time bound for Re-ALPS in a general setting, under a natural assumption.
Paper proposes a new numerical scheme for solving BSDEs.
problem Solving backward stochastic differential equations (BSDEs).
method Uses Lagrange interpolation to approximate derivatives and changes sample point distributions for different stability and convergence.
result Guarantees convergence of the scheme under certain conditions on sample point distributions.
New MCMC method samples from lattice distributions efficiently.
problem Sampling from probability distributions on lattice structures.
method Metropolis-Hastings algorithm with a pull-back measure.
result The method is uniformly ergodic under certain conditions.
Correcting bias in least squares regression with volume-rescaled sampling.
problem Bias in linear least squares solutions without distributional assumptions.
method Volume-rescaled sampling to correct bias in i.i.d. samples.
result Combined sample becomes unbiased with rescaled volume additional sample.
The paper presents unbiased estimators for random design regression.
problem Bias in least squares solutions for random design regression.
method Volume-rescaled sampling of input points to produce unbiased estimators.
result An unbiased estimator can be constructed with a sample size of O(dlogd + d/ε).
New algorithm speeds up determinantal point process sampling.
problem Efficiently sampling from determinantal point processes with minimal preprocessing and sampling costs.
method Introducing a Poisson random variable to control subset probabilities, reducing the number of rows to poly(d) for sampling.
result The new algorithm achieves poly(d) sampling time, independent of n, without distorting probabilities.
New statistical test for change-point detection using relative entropy.
problem Offline change-point detection using divergence metrics.
method Study of empirical relative entropy distributions, derivation of approximations, introduction of new Berry-Esseen bounds.
result Theoretical and practical validation of relative entropy for change-point detection.
Improved reasoning model by sampling from power distribution without additional training.
problem Efficiently sampling from a sharpened distribution to improve reasoning models.
method Entropy-Cut Metropolis-Hastings algorithm that identifies key decision points for resampling.
result The method consistently improves reasoning models across various datasets.
Paper tests DPPs for diversity models, distinguishing them from other distributions.
problem Testing whether a given distribution is a Determinantal Point Process (DPP) or far from any DPP.
method Proposes the first algorithm for DPP testing and establishes a lower bound on sample complexity.
result Establishes a matching lower bound on the sample complexity of DPP testing.
A method for estimating parameters from entangled single-sample distributions, robust to high-noise data.
problem Estimating common parameters from entangled single-sample distributions.
method Iterative trimming of samples to estimate the parameter.
result The method can tolerate a constant fraction of high-noise data points.
The study examines conditions for achieving a simple lower bound in estimating mean from samples.
problem Achieving a simple lower bound for estimating the mean of a distribution.
method Analyzes conditions for nearly attaining Le Cam's two-point testing lower bound for mean estimation.
result An algorithm nearly attains the two-point testing rate for mixtures of symmetric, log-concave distributions with a common mean.
Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K K K that can be seen as a matrix storing the similarity between points. The diversity comes from the fact that the inclusion probability of a subset is equal to the determinan…
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We are motivated to study the optimal distribution of finite sampling points. Formul…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest treating a group of data points as an i.i.d. sample set from an underlying feature dis…
ASK-NN detects distribution drifts in LLM-generated text.
problem Hallucinations and artificial text in LLM-generated outputs.
method Asymmetric two-sample test based on directed k-nearest-neighbor graph.
result ASK-NN is competitive with baselines on various benchmarks.
Accelerates TPP sampling with speculative decoding for faster sequence generation.
problem Efficiently sampling from complex temporal point processes.
method Adapting speculative decoding techniques from language models to TPPs.
result Achieves significant speedup (2-6x) while maintaining distributional accuracy.
This paper improves signal reconstruction using determinantal sampling from random nodes.
problem Approximating square-integrable functions from random node evaluations.
method Combines determinantal point processes and mixtures thereof for RKHS-adapted approximations.
result Proves mean-square guarantees in L 2 L^2 L 2 norm and shows faster convergence rates. ManiFlow models manifold data by optimizing NFs on perturbed data.
problem Capturing manifold data with NFs' invertibility constraint.
method Train NFs on perturbed data to implicitly represent manifold.
result NFs implicitly model manifold in regions of maximum likelihood.
The paper proves consistency of archetypal analysis for multivariate data.
problem Finding optimal archetype points for multivariate data.
method Uses convex polytope to summarize data, proving consistency under specific distribution assumptions.
result Archetype points converge to optimal solution under certain conditions.
Energy-efficient sampling for machine learning using magnetic tunnel junctions.
problem Costly and inefficient random sampling in machine learning.
method Energy-efficient algorithm using stochastic magnetic tunnel junctions for uniform Float16 sampling.
result Higher energy efficiency than state-of-the-art algorithms, with a minimum factor of 9721.
Generative neural networks enable quasi-random sampling for diverse multivariate distributions.
problem Generating quasi-random samples for complex multivariate distributions is challenging and restricted.
method Generative moment matching networks (GMMNs) for quasi-random sampling.
result GMMNs allow quasi-random sampling for a broader range of multivariate distributions.
We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from and the target distribution is log-concave, this can be tractably solved with c…
Improved uncertainty estimation through diverse sampling in neural networks.
problem Enhancing uncertainty estimation for machine learning models.
method Data-driven correlations and determinantal point processes-based sampling for dropout layers.
result State-of-the-art results in uncertainty estimation for regression and classification tasks.
DPPy offers Python tools for sampling DPPs.
problem Sampling from DPPs is challenging.
method Gathers exact and approximate sampling algorithms for finite and continuous DPPs.
result DPPy provides Python tools for DPP sampling.
New algorithm samples determinantal point processes with sublinear preprocessing time.
problem Sampling from determinantal point processes efficiently with small expected subset size.
method Proposes an algorithm with sublinear preprocessing and independent sampling cost.
result Achieves sublinear preprocessing time and independent sampling cost.
Compress++ speeds up distribution compression to near-linear time.
problem Accurately summarize a probability distribution using a small number of points efficiently.
method Introduces Compress++, a meta-procedure to speed up any thinning algorithm.
result Achieves n \sqrt{n} n points with O ( log n / n ) \mathcal{O}(\sqrt{\log n/n}) O ( log n / n ) integration error in O ( n log 3 n ) \mathcal{O}(n \log^3 n) O ( n log 3 n ) time and O ( n log 2 n ) \mathcal{O}( \sqrt{n} \log^2 n ) O ( n log 2 n ) space. In this paper we propose a multi-armed bandit inspired, pool based active learning algorithm for the problem of binary classification. By carefully constructing an analogy between active learning and multi-armed bandits, we utilize ideas such as lower confidence bounds, and self-concordant regularization from the multi…
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.
Method identifies change points in high-dimensional models using sample weights.
problem Identifying change points in high-dimensional generalized linear models.
method Sample-weighted empirical risk minimization (Weighted ERM).
result Weighted ERM yields precise asymptotic performance characterization for Gaussian designs.
CTT compresses samples to test distributions near-linearly, outperforming existing methods.
problem Efficiently testing distributions with high power and near-linear runtime.
method Sample compression followed by permutation testing.
result CTT achieves near-linear runtime while maintaining high statistical power.
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio s / d s/d s / d , where s s s and d d d encode the smoothness and dimension of the integrand. However, an empirical investigation re…
NSFs learn SDE transition laws for efficient sampling.
problem Efficiently sampling between arbitrary time points in SDEs.
method Conditional normalising flows with architectural constraints.
result Up to two orders of magnitude speed-ups at large time gaps.
Framework improves gradient estimation for faster training convergence.
problem Efficiently estimating noisy gradients in stochastic optimization.
method Dynamic adaptive importance sampling combining multiple distributions.
result Adaptively weighted multiple importance sampling yields superior gradient estimates.
Detects change points in time series focusing on specific components.
problem Identifying moments when specific components of multivariate time series change distributions.
method Two-stage non-parametric algorithm: causal structure learning followed by change point detection.
result Validated the approach on synthetic and real-world datasets.
Paper reproduces a kernel-based scan B-statistic for online change-point detection.
problem Continuous detection of distribution changes in online data streams.
method Efficient kernel-based scan B-statistic for online change-point detection.
result Scan B-statistic outperforms parametric methods in challenging scenarios.
New method infers and samples point processes from latent diffusion.
problem Modeling point processes with latent diffusion.
method Itô's excursion theory for inference and sampling.
result Proposes a new method to infer and sample point processes.
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown stationary ergodic distributions. No modelling, independence or mixing assumptions…
Improves GANs by sampling meaningful points from latent manifold.
problem Lack of semantic information in GANs' prior distribution.
method Local Coordinate Coding (LCC) for sampling and improved generator approximation.
result Improves GANs' performance in generating realistic data.
A new point process for clustering distributions with repulsion.
problem Clustering distributions with repulsion.
method Distributional Determinantal Point Process (dDPP) with sliced Wasserstein kernel.
result Validated dDPP as a well-defined point process and applied to gene expression and epilepsy data.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
problem Improving numerical integration accuracy in high dimensions.
method Median-of-means sampling compared to mean-of-means using RQMC methods.
result Median-of-means sampling is superior for large sample sizes, while mean-of-means is better for smaller sample sizes.
New KL-divergence for Gaussian distributions based on Wasserstein geometry.
problem Computing KL-divergence for Gaussian distributions efficiently.
method Introducing WKL-divergence based on Wasserstein geometry.
result WKL-divergence evaluates to squared distance between points for Dirac measures.
VRM uses mixtures to adaptively reduce variance in stochastic optimization.
problem Improving convergence in stochastic optimization through variance reduction.
method Proposes VRM, an adaptive scheme using mixtures of predefined sampling distributions.
result VRM asymptotically recovers the best mixture weights in hindsight.
Neural networks compress and sample WDN contamination dynamics efficiently.
problem Infrastructure monitoring of complex, networked systems like water distribution networks is expensive and challenging.
method Developed Graph Fourier Transform (GFT) operators and neural networks (NN) for efficient data collection and inference.
result High accuracy reconstruction of contamination dynamics using only 5-10% of the sample set.
Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point to try out. This recommendation is usually selected by optimizing a given acquis…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorpora…