Gradient and Laplacian estimates for complex Monge-Ampère equations found.
problem Estimating solutions to complex Monge-Ampère equations with singularities.
method Integral method applied to obtain gradient and Laplacian estimates.
result Gradient and Laplacian estimates for the solution to the singular complex Monge-Ampère equation.
Quantum method improves neural density estimation in high dimensions.
problem High-dimensional density estimation with poor performance and high computational complexity.
method Adaptive Fourier features based on quantum density matrices, integrated with neural networks.
result Competitive performance compared to state-of-the-art methods in various datasets.
We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size N into m machines, and estimates a local sparse LDA estimator on each machine using the data subset of size N/m. After the distri…
Paper proposes an online covariance estimator for sketched Newton methods.
problem Estimating the limiting covariance matrix of sketched Newton methods.
method Proposes a fully online covariance matrix estimator from Newton iterates.
result Establishes the consistency and convergence rate of the proposed estimator.
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
Deep learning outperforms traditional methods in estimating OU process parameters.
problem Parameter estimation of the Ornstein-Uhlenbeck process is challenging.
method Used a multi-layer perceptron to estimate OU process parameters compared to traditional methods like Kalman filter and maximum likelihood estimation.
result Deep learning method outperforms traditional methods in parameter estimation of the OU process.
Robust method estimates state, input, and parameters of linear systems online.
problem Joint estimation of state, input, and parameters in noisy or outlier-prone measurements.
method Combines recursive, alternating, and iteratively-reweighted least squares into a single algorithm.
result Good performance in presence of outliers and compared to state-of-the-art methods.
A new kernel method improves Poisson process intensity estimation.
problem Estimating intensity functions of inhomogeneous Poisson processes.
method Kernel method-based intensity estimator using least squares loss.
result K2IE achieves comparable predictive performance with improved efficiency. This paper evaluates different methods to estimate S&P 500 volatility.
problem Accurately estimating the volatility of the S&P 500 index.
method Historical volatility, GARCH model, and implied volatility methods were compared.
result Implied volatility is the best estimator of real volatility.
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the estimator using a few variables by l1-type penalized estimation. We see that the…
Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuo…
Study compares different covariance estimation methods for portfolio allocation.
problem Comparing methods for estimating covariance and precision matrices in portfolio allocation.
method Gaussian Graphical Model (GGM), Shrinkage, Thresholding, Random Matrix Theory (RMT) methods.
result GGM methods outperform other methods in predictive ability for portfolio allocation.
First, we analyze the variance of the Cross Validation (CV)-based estimators used for estimating the performance of classification rules. Second, we propose a novel estimator to estimate this variance using the Influence Function (IF) approach that had been used previously very successfully to estimate the variance of …
ROME improves density estimation for multi-modal, non-normal data.
problem Robust multi-modal density estimation in non-normal, highly correlated distributions.
method ROME uses clustering to segment multi-modal data into uni-modal clusters, then combines KDE estimates for each cluster.
result ROME outperforms state-of-the-art methods and is more robust to various distributions.
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from C0 estimates. Also, the method is flexible and can be applied to a large class of equations.
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
Optimal first-order methods are shown to be fundamental limits in functional estimation.
problem Optimal functional estimation under weak conditions.
method Formalization of functional estimation with black-box nuisance function estimates and derivation of minimax lower bounds.
result First-order methods are optimal under weak conditions, but higher-order methods can outperform them when nuisance function structure is known.
Proposes a new method for high-dimensional density estimation.
problem Estimating high-dimensional probability density functions efficiently.
method Tensorizing flow method combining tensor-train and flow-based generative modeling.
result Efficiently constructs an approximate density in tensor-train form and trains a flow model to match empirical distribution.
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample from the original full sample and uses it as a surrogate for subsequent computati…
A new real-time method estimates system matrices and states using Kalman filter.
problem Real-time estimation of system matrices and states using Kalman filter.
method Estimation in an observation space, time-invariant interval, and online learning framework.
result Extraordinary performance in estimating matrices for damped oscillation model.
In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous Itô semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot.
Generative method avoids function estimation for data generation.
problem Challenges in function estimation for generative models.
method Deterministic point transport with gradient descent.
result Data generation possible without function estimation.
A method for estimating the median of gradients in stochastic optimization.
problem Robust gradient estimation in stochastic optimization for various applications.
method Stochastic Proximal Point Method for median gradient estimation.
result The proposed method can converge even under heavy-tailed, state-dependent noise.
Method selects best estimator for off-policy evaluation.
problem Choosing the best estimator for off-policy evaluation.
method Generic data-driven method for estimator selection.
result Method is competitive with oracle estimator, up to a constant factor.
Method estimates section thickness and XY anisotropy in ssEM images.
problem Accurate 3D reconstructions require precise section thickness and XY anisotropy estimates.
method Non-parametric Bayesian regression of image statistics.
result Method has lower estimation error compared to existing methods.
Proposes MPCA for robust PCA using mode estimation.
problem Outliers sensitivity in PCA.
method Modal Principal Component Analysis (MPCA) based on mode estimation.
result MPCA shows advantages over conventional methods.
Method estimates M-matrices in graphical models with improved accuracy.
problem Estimating M-matrices as precision matrices in Gaussian graphical models.
method Adaptive multiple-stage estimation method solving weighted ℓ1-regularized problems.
result Method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification.
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not neces…
New method resolves density ratio estimation saturation issues.
problem Error saturation in density ratio estimation methods.
method Iterated regularization to improve kernel methods.
result Achieves fast error rates on regular learning problems.
Hybrid method improves mutual information estimation from samples.
problem Estimating mutual information from joint distributions is challenging.
method Proposes a hybrid method combining discriminative and generative approaches.
result Hybrid methods yield tighter variational bounds on mutual information.
Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of cond…
Multiple regression has been the go-to method for data analysis for generations of scholars due to its transparency, interpretability, and desirable theoretical properties. However, the method's simplicity precludes the discovery of complex heterogeneities in the data. We introduce the Method of Direct Estimation and I…
New method estimates model parameters from incomplete data.
problem Estimating model parameters from incomplete data.
method Variational Gibbs Inference (VGI)
result Competitive or better performance compared to existing methods.
A new method for estimating large-scale linear models with improved precision.
problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.
The paper examines Wiener process for LID estimation methods.
problem Estimating local intrinsic dimension in high-dimensional datasets.
method Investigates recent LID estimation methods from a Wiener process perspective.
result Explains how methods behave under non-ideal conditions.
Popular deep learning uncertainty estimation methods often mislead on out-of-distribution data.
problem Misleading uncertainty estimates on out-of-distribution data.
method Analysis of Gaussian process, Bayesian neural networks, and Monte Carlo dropout methods.
result BNNs and MCDropout do not always provide high uncertainty estimates on out-of-distribution samples.
Meta-learning improves CATE estimation from limited data.
problem Estimating heterogeneous treatment effects from scarce observational data.
method Meta-learning framework decomposes CATE estimation into sub-problems, using neural networks with shared and specific parameters, and optimizing task-specific parameters in closed form.
result Meta-learning method outperforms existing approaches in few-shot CATE estimation.
Estimation of reliable whole-brain connectivity is a crucial step towards the use of connectivity information in quantitative approaches to the study of neuropsychiatric disorders. When estimating brain connectivity a challenge is imposed by the paucity of time samples and the large dimensionality of the measurements. …
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
This paper reviews SDR methods for multivariate response regression.
problem Handling sufficient dimension reduction for multivariate response regression.
method Characterizes SDR estimators as inverse or forward regression methods.
result Pooled marginal, projective resampling, distance-based, ordinary least squares, partial least squares, and semiparametric SDR estimators are discussed.
Many decisions in healthcare, business, and other policy domains are made without the support of rigorous evidence due to the cost and complexity of performing randomized experiments. Using observational data to answer causal questions is risky: subjects who receive different treatments also differ in other ways that a…
Develops methods for estimating and providing confidence bands in sparse high-dimensional additive models.
problem Estimating and providing reliable confidence bands for nonparametric components in high-dimensional additive models.
method Integrates sieve estimation into a high-dimensional Z-estimation framework, employing a multiplier bootstrap procedure.
result Constructs uniformly valid confidence bands for the target component f1 in sparse high-dimensional additive models. Study introduces new methods to estimate stock return rates.
problem Estimating the required rate of return for stocks and private companies.
method Maximum likelihood, Bayesian, and Kalman filtering methods applied to historical data.
result Suggested methods can accurately estimate the required rate of return.
We study a new parametric approach for particular hidden stochastic models such as the Stochastic Volatility model. This method is based on contrast minimization and deconvolution. After proving consistency and asymptotic normality of the estimation leading to asymptotic confidence intervals, we provide a thorough nume…
Discussing new econophysics methods for volatility and probability density estimation.
problem Estimating volatility and probability densities in econophysics.
method Reviewing recent methods for volatility and probability density estimation.
result Pioneering methods for volatility and probability density estimation in econophysics.
Recently, a method called the Mutual Information Neural Estimator (MINE) that uses neural networks has been proposed to estimate mutual information and more generally the Kullback-Leibler (KL) divergence between two distributions. The method uses the Donsker-Varadhan representation to arrive at the estimate of the KL d…
New method estimates shape distance in neural representations with limited data.
problem Measuring geometric similarity between high-dimensional network representations.
method Method-of-moments estimator with tunable bias-variance tradeoff.
result New estimator achieves lower bias than standard methods in high-dimensional settings.
Bayesian methods reduce variance in subspace identification for small data sets.
problem High variance in traditional subspace identification methods for large models or small sample sizes.
method Investigation of Bayesian estimation solutions (regularized and shrinkage estimators) for subspace identification.
result Bayesian estimators reduce estimation risk by up to 40% compared to traditional methods.