Paper explores low-precision SGLD for neural networks, reducing costs without sacrificing performance.
problem Infeasibility of low-precision sampling in large-scale scenarios.
method Developed low-precision SGLD with quantization function and full-precision gradient accumulators.
result Low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits.
This paper improves low-precision sampling using SGHMC for deep learning models.
problem Enhancing training efficiency of deep neural networks with low-precision training.
method Investigates low-precision sampling via Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) for both log-concave and non-log-concave distributions.
result Low-precision SGHMC achieves quadratic improvement in error compared to SGLD for non-log-concave distributions.
This paper introduces a new method to train normalizing flows using precision-recall divergences.
problem Training generative models with mode dropping and low-quality samples.
method Introduces PR-divergences and proposes a novel generative model to minimize precision-recall trade-offs.
result Normalizing flows can be trained to achieve specific precision-recall trade-offs using PR-divergences.
The paper improves support recovery in high-dimensional precision matrix estimation using meta learning.
problem Support recovery in high-dimensional precision matrix estimation with reduced sample complexity.
method Pooling samples from different tasks and using an improper ℓ1-regularized log-determinant Bregman divergence to estimate a single precision matrix. result The support of the improperly estimated single precision matrix is equal to the true support union with high probability.
GANs improve event generation in physics experiments.
problem Improving statistical precision in event generation.
method Used generative adversarial networks (GANs) to generate events.
result GANs amplify the statistical precision of the training sample.
Improved Thompson Sampling outperforms existing Bayesian optimization methods.
problem Thompson Sampling's performance in Bayesian optimization is suboptimal compared to other methods.
method Developed Stagger Thompson Sampler (STS), which more precisely samples the optimal arm with less computation.
result STS outperforms TS, PSS, and other acquisition methods in various optimization tasks.
Finite-precision learning of anh networks is limited by the Monte Carlo rate.
problem Learning anh neural networks under finite precision method Using iterated anh activations to construct localized bump functions result No adaptive randomized algorithm can achieve higher convergence rate than Monte Carlo rate in finite precision
Differentiable learning via SGD and GD can simulate various learning problems, depending on precision and minibatch size.
problem Understanding the power of differentiable learning via SGD and GD compared to statistical query (SQ) learning.
method Comparing the learning power of SGD and GD on population and empirical losses with statistical query learning.
result The learning power of SGD and GD depends on the precision of gradient calculations relative to the minibatch size or sample size.
This article presents differential equations and solution methods for the functions of the form Q(x)=F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed an…
No GANs can learn disconnected manifolds precisely.
problem Learning disconnected manifolds is challenging due to unimodal latent distributions.
method Formalized a no free lunch theorem and derived a rejection sampling method.
result Upper bound on the precision of the targeted disconnected manifold distribution.
Unified stopping rules ensure accurate policies in contextual learning.
problem Stopping data collection to ensure accurate policies in personalized decision problems.
method Developed unified stopping rules based on GLR statistics for pairwise action comparisons.
result Unified stopping rules achieve target precision with fewer samples than benchmarks.
High-dimensional inference for sparse spectral precision matrices
problem Inference on the spectral precision matrix at a fixed frequency
method Full likelihood-based inference using neighboring discrete Fourier transforms
result Simultaneous control of regularization, finite-sample truncation, and smoothing biases
Study best arm identification with limited precision sampling in bandits.
problem Limited precision sampling in multi-armed bandit problems.
method Proposed a modified tracking-based algorithm to handle non-unique optimal allocations and presented non-asymptotic bounds.
result Asymptotically optimal tracking-based algorithm for best arm identification.
The paper analyzes data augmentation for precision matrix estimation in high dimensions.
problem Precision matrix estimation in high-dimensional settings.
method Linear shrinkage estimators and data augmentation methods.
result Concentration bounds for the quadratic error of estimators.
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gau…
The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy amplification by sampling where the privacy cost of a single evaluation diminishes quadr…
Study precise sample covariance error for Gaussian centered data.
problem Precise characterization of sample covariance error for Gaussian data.
method Developed a Random Duality Theory (RDT) framework to determine upper and lower bounds.
result Upper and lower bounds match in large-dimensional contexts, matching the spectral norm's limiting value.
Protocol learns pure quantum states with minimal disturbance.
problem Efficiently learn quantum states with minimal disturbance.
method Sequential measurements with minimal disturbance.
result Achieves maximal precision with polylogarithmic regret.
Improved DDPMs achieve high log-likelihoods and sample quality with fewer passes.
problem Improving log-likelihoods of DDPMs while maintaining high sample quality.
method Modifying DDPMs with learning variances and using precision-recall metrics.
result DDPMs can achieve competitive log-likelihoods with fewer forward passes.
Paper proposes a method to use in silico experiments with foundation models to reduce sample size.
problem Costly and uncertain randomized experiments.
method Integrates predictions from multiple foundation models with experimental data.
result Estimator offers substantial precision gains, equivalent to a 20% reduction in sample size.
The paper analyzes how combining samples from two tasks can improve performance, especially in high dimensions.
problem Understanding when combining samples from two related tasks outperforms learning with one task alone.
method Applying random matrix theory to high-dimensional linear regression, focusing on proportional sample size increases.
result Precise high-dimensional asymptotics for bias and variance of HPS estimator, showing phase transitions in transfer performance.
Paper proposes efficient algorithms for bandit problems with costly sampling.
problem Maximizing expectation function over a finite set with high sampling cost.
method Proposes naive and adaptive stochastic bandit algorithms for PAC solution.
result Adaptive algorithm outperforms naive in terms of number of samples.
Low bit-width integer weights and activations are very important for efficient inference, especially with respect to lower power consumption. We propose Monte Carlo methods to quantize the weights and activations of pre-trained neural networks without any re-training. By performing importance sampling we obtain quantiz…
Trans-Glasso uses transfer learning to estimate precision matrices from related studies.
problem Challenges in precision matrix estimation with limited target samples.
method Two-step transfer learning: multi-task learning followed by differential network estimation.
result Trans-Glasso achieves minimax optimality under certain conditions and outperforms baseline methods in simulations and real-world applications.
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables p→∞ and the sample size n→∞ so that p/n→c∈(0,+∞). The precision matrix is estimated directly, wit…
BOSH optimizes functions with stochastic evaluations more efficiently and precisely.
problem Optimizing functions with noisy evaluations can lead to suboptimal solutions.
method BOSH uses a hierarchical Gaussian process to generate a growing pool of realizations.
result BOSH provides more efficient and higher-precision optimization than standard BO.
Study precise estimators for correlated data using RDT.
problem Analyzing estimators in correlated linear regression models.
method Utilized Random Duality Theory to characterize prediction risk.
result Precise closed form characterizations of estimators' risk.
Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train …
This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approac…
The study examines how the number of noise samples affects diffusion models' performance.
problem Understanding the balance between generalization and memorization in diffusion models.
method Theoretical analysis and empirical experiments with Denoising Score Matching (DSM) using random features.
result Precise expressions for test and train errors under specific conditions reveal the mechanisms of generalization and memorization.
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
problem Selecting an appropriate regularization parameter for sparse precision matrix estimation.
method Developed a closed-form matrix-valued regularization parameter based on the sampling distribution of optimality conditions.
result The proposed method achieves comparable estimation accuracy and superior support recovery to cross-validation, with significant runtime improvements.
Structure discovery in graphical models is the determination of the topology of a graph that encodes conditional independence properties of the joint distribution of all variables in the model. For some class of probability distributions, an edge between two variables is present if and only if the corresponding entry i…
Noise-cleaning fMRI brain activity matrices for better precision estimation.
problem Denoise precision matrices of fMRI time series to estimate true matrices.
method Comparison of various noise-cleaning algorithms on synthetic and real fMRI data.
result Optimal Rotationally Invariant Estimator outperforms others in fMRI data.
The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
problem Estimating sparse precision matrices in high-dimensional settings.
method Tempered posterior with fully specified horseshoe prior.
result Concentration results and theoretical oracle inequality for posterior.
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are considered. Focusing on the fundamental problem of separating a two-class Gauss…
In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by…
Boosts A/B test precision using auxiliary data from historical users.
problem Small sample sizes and imprecise estimates in A/B tests.
method Coupling design-based causal estimation with machine-learning models of historical user data.
result Effect estimates using auxiliary data are roughly equivalent to increasing sample size by 20%, or up to 50-80% in some cases.
The paper tackles efficient change point detection with limited samples.
problem Identifying multiple change points with minimal queries in noisy environments.
method Adaptive algorithm that first detects likely change points and refines their locations.
result The sample complexity is jointly governed by jump magnitudes and change point positions.
A neural framework corrects bias in estimating individual treatment effects.
problem Estimating individual treatment effects from observational data.
method An anchored neural architecture and precision-corrected intersection-bound inference.
result Corrected bias and maintained nominal coverage in high-dimensional settings.
Machine learning accurately diagnoses cancer from whole genome sequencing data.
problem Accurate cancer diagnosis at all stages.
method Novel MLAC (Machine Learning Against Cancer) method using next-gen RNA sequencing.
result Perfect precision, sensitivity, and specificity achieved for most tumor types.
The paper analyzes learning curves for kernel ridge regression with dot-product kernels.
problem Understanding the learning curves for different scaling regimes of data and model.
method Precise formulas for mean test error, bias, and variance in the mo∞ with m/dr constant regime. result A peak in the learning curve at m≈dr/r! for any integer r. Efficient event generation for collider phenomenology using parallel Langevin sampling and learned Stein diagnostics.
problem Event generation for precision collider phenomenology.
method Parallel Langevin sampling with learned Stein diagnostics.
result Relaxation time is estimated using a data-driven approach.
Suppose that one particular block in a stochastic block model is of interest, but block labels are only observed for a few of the vertices in the network. Utilizing a graph realized from the model and the observed block labels, the vertex nomination task is to order the vertices with unobserved block labels into a rank…
In this article we revisit the definition of Precision-Recall (PR) curves for generative models proposed by Sajjadi et al. (arXiv:1806.00035). Rather than providing a scalar for generative quality, PR curves distinguish mode-collapse (poor recall) and bad quality (poor precision). We first generalize their formulation …
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an n×n SDDM matrix M, and a constant −1≤p≤1, our algorithm gives efficient access to a…
In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classi…
In this paper we propose strategies for estimating performance of a classifier when labels cannot be obtained for the whole test set. The number of test instances which can be labeled is very small compared to the whole test data size. The goal then is to obtain a precise estimate of classifier performance using as lit…
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
problem Challenges in inferring conditional dependence relationships in high-dimensional compositional data.
method Composition adaptive regularized estimation (CARE) method for sparse basis precision matrix.
result CARE estimator achieves minimax optimality in high dimensions, performing as well as if the basis were observed.