arXiv research

This paper reviews methods for constructing confidence intervals for error rates in 1:1 matching tasks.

Optimum-statistical collaboration improves black-box optimization efficiency.

The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.

StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.

Study proposes a statistical testing framework for evaluating clustering pipelines.

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of meas…

New method optimizes PCA for better prediction and variance.

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…

The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution. However, no finite sample statistical guarantees and no computationally efficient o…

Statistical analysis of regularization in continual learning tasks.

Statistical uncertainty of different filtration techniques for market network analysis is studied. Two measures of statistical uncertainty are discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some import…

This study analyzes how well GANs approximate distributions from small samples.

New framework assesses extreme errors in machine learning models.

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…

Bayesian method improves clinical trial efficiency.

Study shows MDA's effectiveness even when more components are assumed than in actual data.

Statistical mechanics reveals phase transitions in $\varepsilon$-SVR error.

Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non-trivial observational e…

Consistently checking the statistical significance of experimental results is one of the mandatory methodological steps to address the so-called "reproducibility crisis" in deep reinforcement learning. In this tutorial paper, we explain how the number of random seeds relates to the probabilities of statistical errors. …

Study validates ML-UQ calibration statistics using simulated reference values.

New methods bound estimation error in high-dimensional statistical problems.

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspe…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators, where performance is evaluated using a matrix-weighted two-norm of the defect of …

Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization me…

New $L_1$ regularization controls neural network generalization error and sparsifies input dimensions.

New algorithm accelerates single-pass SGD for generalized linear prediction.

Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood. In this work, we make the first attempt to theoretically understand the deep Q-network (DQN) algorithm (Mnih et al., 2015) from both algorithmic and statistical perspectives. In specific, we focus on …

Derives asymptotic generalization error for large-margin classifiers.

New synthetic data analysis reveals high type 1 error rates.

We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of refining time-grids to reduce statistical approximation errors in an adaptive and…

WAEs offer a statistical understanding of density estimation and error bounds.

In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…

Paper tackles fairness in CCA by minimizing correlation disparity error.

Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.

Develops statistical guarantees for neural networks with regularization.

New method predicts and optimizes matrix recovery from noisy measurements.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

Revisits CP tensor decomposition for noisy, non-orthogonal data.

In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling probabilities. The sampling dependent error bound (i) allows us to better understand the …

The paper analyzes two ISGD modes for statistical inference, deriving error bounds and confidence intervals.

Estimates kernel eigenvalues for compositional dot-product kernels.

New statistical mechanics analysis shows edge pruning outperforms node pruning in neural networks.

Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the model, the model error as well as the statistics of the model error. This method…

This work analyzes CoT prompting methods from a statistical estimation perspective.

This work analyzes the generalization properties of learned reconstruction methods for inverse problems.

Neural networks estimate statistical divergences with performance guarantees.

The paper provides bounds on estimation error in a distributed online learning setting.