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
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.
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 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…
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.
The paper analyzes the excess risk of PCA and provides a precise characterization.
problem Understanding the excess risk of principal component analysis (PCA).
method Established a central limit theorem for PCA error and derived the excess risk distribution.
result Obtained a non-asymptotic upper bound on the excess risk of PCA.
Generative diffusion models improve channel sampling from limited data.
problem Challenges in channel modelling and data collection for wireless systems.
method Diffusion model with U-Net architecture for frequency domain synthesis.
result Stable training and diverse high-fidelity samples generated from true channel distribution.
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.
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood. In this paper, we provide precise information theoretic …
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.
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.
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.
Study examines influence diagnostics in high-dimensional M-estimation.
problem Understanding influence diagnostics in high-dimensional settings.
method Characterized the distribution of leave-one-out influences in high-dimensional Gaussian M-estimation.
result The distribution of influences converges to a limiting measure in high-dimensional settings.
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.
AI-enabled precision medicine promises a transformational improvement in healthcare outcomes by enabling data-driven personalized diagnosis, prognosis, and treatment. However, the well-known "curse of dimensionality" and the clustered structure of biomedical data together interact to present a joint challenge in the hi…
Paper approximates solutions for complex decision processes with limited precision.
problem Approximating the set of all solutions for Multi-objective Markov Decision Processes.
method Limited precision approach based on White's multi-objective value-iteration dynamic programming algorithm.
result The number of calculated solutions is tractable and approximates the true Pareto front.
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…
Study identifies three quantization regimes for ReLU networks.
problem Approximation of Lipschitz functions by ReLU networks with finite-precision weights.
method Established through nonasymptotic tight lower and upper bounds on minimax approximation error.
result Memory-optimality achieved in proper quantization regime for deep networks.
Proposes a new method for subgroup analysis using optimal trees with parameter fusion.
problem Challenges of greedy heuristics and overfitting in tree-based recursive partitioning methods.
method Fused optimal causal tree method leveraging mixed integer optimization (MIO) for globally optimal partitions and parameter fusion.
result Substantial improvement in subgroup discovery accuracy and statistical efficiency.
Restricted Boltzmann machines (RBMs) are powerful machine learning models, but learning and some kinds of inference in the model require sampling-based approximations, which, in classical digital computers, are implemented using expensive MCMC. Physical computation offers the opportunity to reduce the cost of sampling …
This study improves uncertainty quantification in seismic inversion.
problem Uncertainty in seismic inversion due to limited data and model diversity.
method Integrates ensemble methods with importance sampling.
result More accurate uncertainty quantification in velocity models.
Novel AMP framework for multi-environment transfer learning.
problem Characterizing risk of Lasso-based transfer learning estimators.
method Multi-Environment Generalized Long AMP (multi-environment GLAMP) framework.
result Precise characterization of the risk of three Lasso-based transfer learning estimators.
Neural causal discovery methods fail to accurately uncover causal structures due to the faithfulness property.
problem Accuracy in neural causal discovery is limited, especially when distinguishing between existing and non-existing causal relationships.
method Systematic evaluation of neural causal discovery methods, focusing on their performance in finite sample regimes and their ability to recover ground-truth graphs.
result Neural networks lack the precision to reliably recover ground-truth causal graphs, even for small graphs and large sample sizes.
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. This paper tackles label-efficient evaluation in extreme class imbalance.
problem Challenges in obtaining a sufficient sample for accurate evaluation in tasks with extreme class imbalance.
method Develops a framework for online evaluation based on adaptive importance sampling.
result Establishes strong consistency and a central limit theorem for performance estimates.
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…
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.
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…
Extended study improves covariance matrix estimation for portfolio managers.
problem Limited sample sizes and poor performance of PCA estimator in high-dimensional returns.
method Developed a more general shrinkage framework targeting further information.
result Improves the PCA estimator of beta by shrinking it toward a target.
Low-precision streaming PCA estimates the leading eigenvector with limited precision.
problem Estimating the leading eigenvector in a streaming setting with limited precision.
method Oja's algorithm with linear and nonlinear stochastic quantization.
result A batched version of the quantized variants achieves the lower bound on quantization error up to logarithmic factors.
Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of low-precision fixed-point computations, we observe the rounding scheme to play a cruc…
Active learning selects samples for labeling to build accurate models with minimal labeled data.
problem Costly acquisition of labeled data in supervised learning.
method Adaptive selection of unlabeled data samples for labeling.
result Efficient model building with minimal labeled data.
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.
New metric evaluates generative models across domains, diagnosing fidelity, diversity, and generalization.
problem Evaluating generative models in diverse domains with limited metrics.
method Introduces a 3D evaluation metric (α-Precision, β-Recall, Authenticity) for domain-agnostic diagnostics. result Unified metric characterizes fidelity, diversity, and generalization, diagnosing model performance.
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
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.
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-comp…
It is well-known that the precision of data, hyperparameters, and internal representations employed in learning systems directly impacts its energy, throughput, and latency. The precision requirements for the training algorithm are also important for systems that learn on-the-fly. Prior work has shown that the data and…
Paper stabilizes bandit learning with regularization, improving inference under adaptive sampling.
problem Challenges in statistical inference with adaptive sampling.
method Refined stability condition for online algorithms, using regularized stochastic-mirror-descent-style methods.
result Derives precise regret bounds and asymptotic normality, showing necessity of regularization for valid inference.
This work analyzes a two-stage algorithm for single index models, showing precise asymptotics of gradient descent.
problem Learning single index models with non-convex optimization.
method Spectral initialization followed by gradient descent, with detailed analysis of dynamics and asymptotics.
result Gradient descent converges to long-time fixed points in the large system limit, representing mean field behavior.
We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial correlations. In the limited-data scenario, where the covariance matrix would be rank-defi…
Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
problem Limitations of inverse covariance matrix in non-Gaussian settings.
method Exploits local dependence function to define generalized precision matrix (GPM) for multivariate t-Student distribution.
result GPM leads to statistically significant lower out-of-sample variances in minimum-variance portfolios.
Given a compact closed subset M of a line segment in R3, we construct a sequence of minimal surfaces Σk embedded in a neighborhood C of the line segment that converge smoothly to a limit lamination of C away from M. Moreover, the curvature of this sequence blows up precisely on M, and the limit…
The paper improves PCS approximation for ranking and selection under limited simulation budgets.
problem Improving finite sample performance in Ranking and Selection.
method Develops a Bahadur-Rao type expansion for PCS, proposes a novel FCBA policy.
result FCBA policy achieves superior PCS performance compared to traditional methods.
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-comp…
For spherically symmetric distributions, efficient quantisation can be achieved with moderate sample sizes.
problem Optimal quantisation in high dimensions requires large sample sizes, making it impractical.
method Uniformly distributed random quantisers on a sphere of suitable radius achieve exceptional performance.
result For moderate sample sizes, quantisation error can be efficiently computed and approximated.
Adaptive Prespecification improves precision in randomized trials.
problem Selecting optimal covariates for precision in randomized trials.
method Adaptive Prespecification using V-fold cross-validation and influence curve-squared loss function.
result Substantial gains in precision, equivalent to 20-43% reductions in sample size for the same power.
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.