New method compresses large sample data for faster discriminant analysis.
problem Large sample sizes in discriminant analysis increase computational burden.
method Proposes a new compression approach for reducing training samples.
result Significant computational gains and superior predictive ability compared to random sub-sampling.
The paper shows how to efficiently generate large Gaussian process samples with reliability guarantees.
problem Generating large-scale Gaussian process samples efficiently and with reliability.
method Demonstrates scaling data generation to large \(n\) while providing high probability guarantees.
result Efficiently generates large Gaussian process samples with reliability guarantees.
We introduce a new sampling method for large language models that balances diversity and parallelism.
problem Balancing diversity and parallelism in decoding for large language models.
method Arithmetic sampling framework compatible with various sampling variations.
result Improves estimation of expected BLEU score reward and reduces the gap with beam search.
Algorithm recovers large causal tree from small samples.
problem Determining causal structure in large gene networks.
method Algorithm that recovers tree with high accuracy under mild conditions.
result High accuracy in recovering causal tree from small samples.
Paper connects sampling and labeling biases in large-output spaces.
problem Efficient training in large-output spaces with label imbalance.
method Unified approach to address sampling and labeling biases.
result Different negative sampling schemes trade-off performance on dominant and rare labels.
Study laws of large numbers in online classification, determining optimal regret bounds.
problem Understanding how sequential sampling affects online learning and classification.
method Characterized online learnable classes and determined optimal regret bounds using Littlestone's dimension.
result Optimal regret bounds in online learning are determined, resolving open questions.
The paper introduces a sampling theory for graphons with a Poincaré inequality and proves consistency.
problem Sampling on large graphs is challenging due to their non-Euclidean nature.
method The paper introduces a signal sampling theory for graphons, proving a Poincaré inequality and showing consistency.
result Unique sampling sets for graphon signals are consistent across graph sequences.
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L_2 regularization: We introduce the γ-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the s…
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We study the problem of sampling a discrete random variable with a high degree of depen…
In importance sampling (IS)-based reinforcement learning algorithms such as Proximal Policy Optimization (PPO), IS weights are typically clipped to avoid large variance in learning. However, policy update from clipped statistics induces large bias in tasks with high action dimensions, and bias from clipping makes it di…
PCA-Guided Quantile Sampling preserves data structure in large datasets.
problem Preserving data structure in large-scale subsampling.
method PCA QS uses leading principal components to guide stratified sampling.
result PCA QS maintains statistical and geometric structure without distorting semantics.
An algorithm solves optimization problems with large sample sets, improving worst-case complexity.
problem Continuous nonlinear-equality-constrained optimization problems with large numbers of terms.
method Progressively sampled finite sets to solve related problems with growing sample sizes.
result Better worst-case sample complexity compared to solving with full sets of samples.
Infinitesimal boosting converges to a deterministic process in large sample limit.
problem Characterizing the asymptotic behavior of infinitesimal gradient boosting in large sample sizes.
method Proving convergence to a deterministic process using large sample theory and differential equations.
result The test error decreases over time in the population limit.
New RL method reduces sample complexity for large state-action spaces.
problem Handling large state-action spaces in RL with general Q-functions.
method Nonparametric Q-learning using kernel ridge regression.
result Sample complexity is order optimal with respect to ε and kernel complexity.
Paper analyzes and accelerates Langevin Monte Carlo methods using large deviations theory.
problem High-dimensional sampling problems in machine learning.
method Unified approach using large deviations theory to study and accelerate Langevin dynamics variants.
result Efficiency of Langevin dynamics variants demonstrated through numerical experiments.
Develops large-sample theory for non-stationary source separation.
problem Lack of large-sample results for non-stationary source separation methods.
method Large-sample theory for NSS-JD method under specific assumptions.
result Consistency of unmixing estimator and its convergence to Gaussian distribution.
Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also inefficient for large count values and requires averaging over many samples to reduce …
LIIT uses large deviations to train neural networks faster.
problem Training neural networks requires large amounts of data, leading to inefficiencies.
method LIIT uses large deviations principle to generate and update training samples.
result LIIT achieves similar classification performance with smaller, more representative samples.
This paper shows using sub-sample estimates can improve optimization results in large-scale problems.
problem Large-scale optimization problems with uncertain parameters often lead to suboptimal solutions due to mis-specifications or extreme sample characteristics.
method The paper introduces the use of sub-sample estimates to reduce errors in stochastic optimization models, providing theoretical analysis and numerical examples.
result Sub-sample optimization can achieve improved results over full-sample solution estimates in large-scale problems.
Online method learns sparse models efficiently in large scale settings.
problem Sparse model learning in large scale settings with high computational and memory costs.
method Online learning approach, mini-batch methods, hard thresholding based stochastic gradient algorithm.
result Sparsity promoted by batch methods is not preserved in online fashion.
Cross-validation under sample selection bias can, in principle, be done by importance-weighting the empirical risk. However, the importance-weighted risk estimator produces sub-optimal hyperparameter estimates in problem settings where large weights arise with high probability. We study its sampling variance as a funct…
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.
problem Estimating causal effects with limited overlap in multivalued treatments.
method Stable Probability Weighting (SPW) and Finite-Sample Stable Probability Weighting (FPW) methods.
result SPW and FPW provide practical solutions for estimating and inferring causal effects with limited overlap.
We study the problem of learning similarity functions over very large corpora using neural network embedding models. These models are typically trained using SGD with sampling of random observed and unobserved pairs, with a number of samples that grows quadratically with the corpus size, making it expensive to scale to…
Knowledge distillation is an effective technique that transfers knowledge from a large teacher model to a shallow student. However, just like massive classification, large scale knowledge distillation also imposes heavy computational costs on training models of deep neural networks, as the softmax activations at the la…
The study proves sampling-based GNNs can approximate training on full graphs with small subgraphs.
problem Training Graph Neural Networks (GNNs) on large graphs is computationally expensive.
method Theoretical framework using graph local limits to prove approximation of GNN training on small samples.
result Parameters learned from sampling-based GNNs on small subgraphs are close to those on full graphs.
Predictive models ground many state-of-the-art developments in statistical brain image analysis: decoding, MVPA, searchlight, or extraction of biomarkers. The principled approach to establish their validity and usefulness is cross-validation, testing prediction on unseen data. Here, I would like to raise awareness on e…
Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and ℓ2-norm-based representation, and have achieved state-of-the-art performance. Howeve…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on…
Changes (returns) in stock index prices and exchange rates for currencies are argued, based on empirical data, to obey a stable distribution with characteristic exponent α<2 for short sampling intervals and a Gaussian distribution for long sampling intervals. In order to explain this phenomenon, an Ehrenfest model…
Estimates covariance matrices with correlations between samples.
problem Estimating large-dimensional covariance matrices with correlated samples.
method Generalized Marcenko-Pastur equation and Ledoit-Peche shrinkage estimator using random matrix theory and free probability. Developed an efficient algorithm based on Ledoit-Wolf kernel estimation.
result Efficient algorithm for estimating large covariance matrices with correlations.
Efficient algorithms improve learning of large-margin halfspaces.
problem Learning large-margin halfspaces efficiently and reproducibly.
method Design of efficient, dimension-independent, polynomial-time algorithms; SGD-based approach; DP-to-Replicability reduction.
result Improved sample complexity compared to previous algorithms, with optimal sample complexity for one algorithm.
LoCoV reduces portfolio optimization errors from sample covariance matrices.
problem Large errors in sample covariance matrix for optimal portfolio weights.
method LoCoV (low dimension covariance voting) algorithm to reduce these errors.
result LoCoV outperforms classical methods in portfolio optimization experiments.
YOASOVI improves stochastic VI for large models with fast, self-correcting sampling.
problem Efficiently performing stochastic Variational Inference on large Bayesian models.
method YOASOVI uses acceptance sampling to draw only one sample per iteration, improving convergence speed and accuracy.
result YOASOVI converges faster and more accurately than regular Monte Carlo and Quasi-Monte Carlo methods.
A new, fast kernel test for large data.
problem Efficient kernel two-sample tests for high-dimensional, large-scale data.
method A new kernel-based test that is computationally efficient and robust to high dimensions.
result The new test performs well across various alternatives and dimensions.
New RL method reduces sample complexity for large policy spaces.
problem Large-scale RL with unknown optimal policies and state/action spaces.
method Introduces eluder dimension for policy space, proving near-optimal sample complexity.
result Near-optimal sample complexity upper bound that depends linearly on eluder dimension.
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of…
The covariance matrix of a p-dimensional random variable is a fundamental quantity in data analysis. Given n i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of O(np2) operations. When n,p are large, this computation may be prohibitively slow. Moreover, …
A new LLM-based method enhances diversity in oversampling for imbalanced classification.
problem Limited diversity in synthetic minority samples generated by current LLM-based approaches reduces robustness and generalizability.
method Condition synthetic sample generation on minority labels and features, use permutation strategy for fine-tuning, fine-tune on minority and interpolated samples.
result Significantly outperforms eight SOTA baselines in diverse synthetic sample generation and downstream classification tasks.
This work accelerates constrained sampling using large deviation principles.
problem Sampling constrained probability distributions efficiently.
method Large deviation principles applied to skew-reflected non-reversible Langevin dynamics.
result The skew-symmetric matrix accelerates convergence and reduces asymptotic variance.
We introduce a simple framework for designing private boosting algorithms. We give natural conditions under which these algorithms are differentially private, efficient, and noise-tolerant PAC learners. To demonstrate our framework, we use it to construct noise-tolerant and private PAC learners for large-margin halfspa…
This paper improves reinforcement learning efficiency for large-scale MDPs.
problem High sample complexity in tabular RL settings with large state and action spaces.
method Model-based approach and Q-learning with linearly parameterized features.
result Provably efficient learning with sample complexity bounds.
Paper proposes an attention sampler for reducing attention mechanism computation.
problem Computational challenges in large-scale attention-based models.
method Importance sampling in streaming setting, attention sampler.
result Significantly reduces the computational burden of attention mechanisms.
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
ConMeZO speeds up zeroth-order optimization for large language models.
problem Slow convergence in high-dimensional parameter spaces of large language models.
method Adaptive directional sampling in a cone centered around a momentum estimate.
result Achieves the same convergence rate as MeZO but up to 2X faster.
New Q-learning algorithm reduces sample complexity for large discount factors.
problem Large discount factors make Q-learning algorithms inefficient.
method Introduces a new Q-learning algorithm with uniformly bounded sample complexity.
result The new algorithm achieves asymptotic covariance that is a quadratic in 1/(1−ρ∗γ). We consider large scale empirical risk minimization (ERM) problems, where both the problem dimension and variable size is large. In these cases, most second order methods are infeasible due to the high cost in both computing the Hessian over all samples and computing its inverse in high dimensions. In this paper, we pr…