Study on neural networks' sample complexity with one hidden layer.
problem Understanding how sample complexity is affected by network architecture and norm constraints.
method Norm-based uniform convergence bounds for scalar-valued one-hidden-layer networks, focusing on spectral and Frobenius norms.
result Spectral norm control is insufficient for uniform convergence guarantees, but Frobenius norm control is sufficient, with conditions.
Meta-learning improves support recovery in high-dimensional PCA.
problem Support recovery in high-dimensional Principal Component Analysis.
method Meta-learning approach to reduce sample complexity and support recovery.
result Support recovery can be achieved with significantly fewer samples than traditional methods.
Optimal sample complexity for contrastive learning of distances.
problem Minimum labeled tuples needed for high accuracy in learning distances.
method Analyzes sample complexity in various distance settings, proving tight bounds.
result Almost optimal bound on sample complexity for learning ℓp distances. This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the sample complexity of PAC learning. The technique and analysis build on a recent brea…
Study shows how leveraging hierarchical similarity graphs improves matrix completion in recommender systems.
problem Improving matrix completion in recommender systems using hierarchical similarity graphs.
method Characterizes the optimal sample complexity using hierarchical stochastic block models and low-rank rating matrices.
result Exploiting hierarchical structure of social graphs significantly reduces the number of observed entries needed for accurate matrix completion.
Improved sample complexity for training diffusion models.
problem How many samples are needed to train an accurate diffusion model?
method Analyzing the sample complexity of training diffusion models using neural networks.
result Exponential improvement in the dependence on Wasserstein error and depth, along with improved dependencies on other parameters.
GenSDR tackles SDR by leveraging generative models to fully recover lower-dimensional structures.
problem Challenges in identifying low-dimensional sufficient structures in nonlinear SDR.
method Proposes GenSDR, a method that uses modern generative models to fully recover information in the central σ-field.
result Establishes consistency of GenSDR estimator for sample-level data and extends its applicability to non-Euclidean responses.
Sharp analysis improves RLHF sample complexity with KL-regularization.
problem Improving RLHF sample complexity with KL-regularization.
method Sharp analysis of KL-regularized contextual bandits and RLHF.
result Achieved an O(1/ε) sample complexity when ε is sufficiently small.
New findings show learnable distributions remain learnable even with noisy or adversarial perturbations.
problem Learning from perturbed samples in high-dimensional spaces.
method Developed a perturbation-quantization framework to analyze additive noise and adversarial corruption models.
result Sample compressible families remain learnable even under noisy or adversarial perturbations.
We give new upper and lower bounds on the minimax sample complexity of differentially private mean estimation of distributions with bounded k-th moments. Roughly speaking, in the univariate case, we show that n=Θ(α21+αk−1kε1) samples are necessary and sufficie…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the computational burden of the principal support vector machines method constrains …
Near-optimal sample complexity for phase retrieval with generative priors.
problem Phase retrieval with magnitude-only measurements and sparse signals.
method Near-optimal sample complexity with i.i.d. Gaussian measurements and generative models.
result O(k log L) samples suffice for phase retrieval with generative priors.
Paper develops a theory explaining contrastive pre-training for multimodal AI.
problem Limited theoretical understanding of contrastive pre-training for multi-modal AI.
method Introduces approximate sufficient statistics and Joint Generative Hierarchical Model.
result Near-minimizers of contrastive loss are approximately sufficient, enabling diverse downstream tasks.
Study on LMMSE estimation with model mismatch, quantifying MSE trade-offs.
problem Model mismatch in LMMSE estimation with undermodeling.
method Analyzing the average MSE of LMMSE estimation with random regressors.
result Performance improvement depends on sufficient samples and model complexity.
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.
The study examines property testing and estimation under non-identically distributed samples, finding necessary and sufficient sample complexities.
problem Property testing and estimation under non-identically distributed samples.
method Analysis of distributional property testing and estimation in settings with heterogeneous entities.
result Necessary and sufficient sample complexities for property testing and estimation under non-identically distributed samples.
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.
Improved sample and time complexity for identifying mixtures of product distributions.
problem Identifying a mixture of k product distributions from statistics. method Combining robust tensor decomposition and Hadamard extensions to bound the condition number of key matrices.
result Achieved sample complexity and run-time complexity of (1/ζ)O(k) for n≥2k−1. Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm. This paper studies the sample complexity of identifying the best arm (largest mean) in a m…
Many machine learning problems, especially multi-modal learning problems, have two sets of distinct features (e.g., image and text features in news story classification, or neuroimaging data and neurocognitive data in cognitive science research). This paper addresses the joint dimensionality reduction of two feature ve…
Several approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a supervised learning problem, have been proposed recently. Finding good policies with such methods requires not only an appropriate classifier, but also reliable e…
In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown that this learning procedure is asymptotically successful: with probability one,…
Standard acquisition functions are sufficient for asynchronous Bayesian optimization.
problem Redundant and repeated queries in asynchronous Bayesian optimization.
method Conceptual analysis and theoretical guarantees of standard acquisitions.
result Standard acquisition functions achieve theoretical guarantees equivalent to Thompson sampling in asynchronous settings.
Improved learning of multivariate Gaussians with imperfect advice.
problem Learning multivariate Gaussians with inaccurate advice.
method Developed learning algorithms for multivariate Gaussians using imperfect advice.
result Achieved better sample complexity for learning multivariate Gaussians with imperfect advice.
Study on proper learning under relaxed worst-case robust loss for VC classes.
problem Proper adversarially robust PAC learning under relaxed worst-case robust loss.
method Introduced a family of robust loss relaxations and showed their effectiveness for proper learnability.
result VC classes are properly PAC learnable with sample complexity close to standard PAC learning setup.
The paper establishes conditions for optimal sampling configurations on complex manifolds.
problem Finding optimal sampling configurations on complex manifolds.
method Analyzes point configurations on compact complex manifolds using tensor powers of Hermitian ample line bundles.
result Necessary and sufficient conditions for the existence of asymptotically Fekete sequences.
Private estimation with public data reduces sample complexity.
problem Estimating private distributions with limited public data.
method Differentially private estimation with public data under constraints of pure or concentrated DP.
result Public data can significantly reduce private sample complexity for estimation.
Efficiently estimate Boolean product distribution parameters from truncated samples.
problem Estimating parameters of Boolean product distributions from truncated samples.
method Introducing fatness of truncation set, using membership queries, and adapting Stochastic Gradient Descent.
result Efficiently learn Boolean product distributions from truncated samples with small sample complexity.
The paper establishes bounds for score-matching in causal discovery and generative modeling.
problem Estimating causal relationships from data.
method Training a deep neural network to estimate the score function and applying it to causal discovery.
result Bounds on the error rate of causal discovery methods using score-matching.
Introduces t-CCS for flexible tensor sampling.
problem Lack of flexibility in tensor sampling methods.
method Tensor Cross-Concentrated Sampling (t-CCS).
result Effective tensor recovery from t-CCS samples.
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting …
Efficient exploration is one of the key challenges for reinforcement learning (RL) algorithms. Most traditional sample efficiency bounds require strategic exploration. Recently many deep RL algorithms with simple heuristic exploration strategies that have few formal guarantees, achieve surprising success in many domain…
This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing Kth-order tensor data. Tensor observations are assumed to be generated from a Kronecker-structured dictionary multiplied by sparse coefficient tensors that …
Improved sampling strategy reduces Fourier measurements for neural network signals.
problem Efficiently sampling signals from neural networks with random Fourier matrices.
method Model-adapted sampling strategy with improved sample complexity.
result Reduced sample complexity from O(kdnα∞²) to O(kdα²₂) measurements.
A new method reduces complexity of normalizing flows for MCMC preconditioning.
problem Improving sampling efficiency in MCMC algorithms for complex target distributions.
method Factorized preconditioning architecture combining a linear component and a conditional NF.
result Significantly better tail samples and higher effective sample sizes on various distributions.
We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretic…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error rates of sample-consistent classifiers with monotonic error regions, in the real…
LACD uses unlabeled data to improve conditional diffusion models.
problem Costly and time-consuming acquisition of labeled data.
method Label-augmented conditional diffusion (LACD) with joint denoising score matching.
result LACD converges faster in total variation and Wasserstein-1 distances with sufficient unlabeled data.
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, …
New conditions show proxy data can improve policy learning in sparse expert data contexts.
problem Improving sample complexity of policy learning with sparse expert data.
method Sufficient conditions for proxy data to improve sample complexity, adaptable to LLMs.
result Provable improvement in sample complexity for policy learning with proxy data.
New approach for testable learning using moment matching and Rademacher complexity.
problem Replacing hard-to-verify distributional assumptions with testable ones.
method Moment matching and metric distances in probability.
result Improved sample complexity bounds for various concept classes and distributions.
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure, we introduce the notion of spatially stationary distributions over geometric grap…
New algorithm reduces sample complexity for Top Two method.
problem Fixed-confidence best arm identification for Top Two methods.
method UCB-based Top Two algorithm for non-asymptotic analysis.
result First non-asymptotic upper bound on expected sample complexity.
Paper finds sample complexity for learning high-dimensional simplices from noisy data.
problem Learning high-dimensional simplices from noisy samples.
method Combines sample compression, high-dimensional geometry, and Fourier analysis.
result Proves sample complexity bound for achieving a simplex within a certain distance from the true simplex.
In this work, we introduce the concept of bandlimiting into the theory of machine learning because all physical processes are bandlimited by nature, including real-world machine learning tasks. After the bandlimiting constraint is taken into account, our theoretical analysis has shown that all practical machine learnin…
Tensor completion requires fewer samples with weak side information.
problem Tensor completion with limited samples and side information.
method Algorithm utilizing weak side information to reduce sample complexity.
result Consistent estimator with O(n1+κ) samples for any small constant κ>0. SAIL learns from sub-optimal demonstrations to improve sample efficiency in sparse reward tasks.
problem Reducing sample complexity in sparse-rewarded tasks.
method Self-Adaptive Imitation Learning (SAIL) that exploits sub-optimal demonstrations and efficient exploration.
result Significantly improved sample efficiency and better final performance across various tasks.
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and m…