The paper registers noisy curves using M-estimation for rotation and scaling parameters.
problem Registration of noisy curves with rotation and scaling parameters.
method M-estimation procedure for estimating rotation and scaling parameters.
result Consistency and asymptotic normality of the estimators proved.
The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation. The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors; we name the resulting estimator as t…
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions …
This paper presents a novel scaling method for unbiased risk estimation.
problem Challenges in risk assessment due to limited data, non-stationarity, and heavy tails.
method Develops a statistical framework for efficient risk scaling, extending beyond the square-root-of-time rule.
result Ensures robust and conservative risk estimation, applicable to small sample settings.
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level. The iterat…
Paper introduces multi-scale methods to improve CATE estimation from EO data.
problem Challenges in balancing fine-grained and contextual information in EO-based causal inference.
method Multi-Scale Representation Concatenation, combining Vision Transformer and Causal Forests.
result Multi-scale approach captures effect heterogeneity better than single-scale models.
Temporal Normalizing Flows enhance density estimation of time-dependent data.
problem Accurate and robust density estimation of time-dependent stochastic data.
method Leveraging normalizing flows for temporal data, tNFs estimate multi-scale distributions without prior scale knowledge.
result Temporal Normalizing Flows improve density estimation of time-dependent data, including multi-scale distributions.
We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns.
Many real-world regression problems demand a measure of the uncertainty associated with each prediction. Standard decision forests deliver efficient state-of-the-art predictive performance, but high-quality uncertainty estimates are lacking. Gaussian processes (GPs) deliver uncertainty estimates, but scaling GPs to lar…
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse representation. There have been several studies for improving this problem such…
Paper tackles leverage effect estimation from noisy data.
problem Estimating leverage effect from high-frequency data with microstructure noise.
method Holistic multi-scale framework operating directly on leverage effect, using Subsampling-and-Averaging Leverage Effect (SALE) and Multi-Scale Leverage Effect (MSLE) estimators.
result Holistic multi-scale framework achieves substantial efficiency gains over existing benchmarks.
New method for high-dimensional regression with unknown scale parameter.
problem High-dimensional linear regression with unknown scale parameter.
method Penalized Huber M-estimator with adaptive Lepski's method. result The method effectively calibrates scale in high-dimensional robust regression.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.
Bayesian model tackles high-dimensional inverse problems efficiently.
problem Estimating spatially-varying parameters in expensive models.
method Multiscale Bayesian inference with deep generative models and MCMC.
result Efficient estimation of global and local parameter features.
In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov-switching multifractal model (MSM). In order to see how well the estimated models captur…
eDCF estimates intrinsic dimension using local connectivity.
problem Challenges in estimating intrinsic dimension due to scale dependence.
method eDCF: a novel, scalable, and parallelizable method based on Connectivity Factor (CF).
result eDCF consistently matches leading estimators with comparable MAE and higher exact intrinsic dimension match rates.
Paper proposes MWDE for estimating finite location-scale mixtures.
problem Estimating finite location-scale mixtures using MLE is problematic.
method Investigates minimum Wasserstein distance estimators (MWDE).
result MWDE is consistent and provides a numerical solution.
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution avail…
Ordinal embedding methods estimate perceptual scales from relative judgments.
problem Measuring subjective sensation using relative judgments.
method Ordinal embedding from machine learning applied to method of triads.
result Ordinal embedding allows estimating perceptual scales from few judgments, non-monotonous functions, and multi-dimensional scales.
Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.
problem Optimizing estimation of Kernel Stein Discrepancy from samples.
method Identifying and comparing minimax scales for U-statistic and V-statistic.
result Hilbert-Schmidt norm of Stein covariance operator gives optimal scale.
This work introduces a protocol to automatically select the correct range of scales for meaningful Intrinsic Dimension estimation.
problem The Intrinsic Dimension (ID) varies with scale in real-world datasets, leading to erroneous results.
method The protocol selects the correct range of scales by ensuring constant density of data points.
result The method provides a robust and scale-adaptive approach to estimating meaningful Intrinsic Dimension.
New algorithms estimate Jacobian matrices for large-scale machine learning.
problem Efficiently computing search directions for large nonlinear least squares.
method Exploit low-rank structure in Hessian to estimate Jacobian matrices.
result Two algorithms perform well compared to state-of-the-art methods.
Automated spectral clustering algorithm discovers clusters without parameter tuning.
problem Automatic spectral clustering for multi-scale data.
method Heuristic iterative eigengap search with global and local scaling.
result Discover different patterns with accuracy >90% in most cases.
Novel algorithm speeds up log-determinant estimation for large matrices.
problem Efficiently estimating log-determinants of large positive definite matrices under memory constraints.
method Hierarchical algorithm based on block-wise computation of LDL decomposition.
result Accurate estimation of NTK log-determinants from a tiny fraction of the full dataset.
New method speeds up learning of complex dynamical systems.
problem Efficiently learning large-scale dynamical systems from finite data.
method Random projections (sketching) to boost kernel-based Koopman operator estimators.
result The proposed estimators maintain accuracy while significantly reducing computation time.
This paper solves parameter estimation with ordered ℓ2 regularization using ADMM.
problem Scaling up ordered ℓ2 regularization for large-scale data. method Alternating Direction Method of Multipliers (ADMM) for ordered ℓ2 regularization. result ADMM-Oℓ2 outperforms or matches state-of-the-art methods in parameter estimation. This thesis examines the accuracy of scaling VaR estimates for longer holding periods.
problem The accuracy of VaR estimates for longer holding periods using the square root of time rule.
method Examined VaR scaling for longer holding periods using empirical analysis.
result Scaling can provide good estimates of VaR but may lead to significant losses over time.
Study identifies and estimates causal LSNM models, proving feature maps are consistent.
problem Identifying causal direction in LSNM models.
method Proposed two estimators: feature maps and neural networks.
result Feature maps estimator is consistent and concave.
New method improves model calibration efficiency and accuracy.
problem Improving model calibration for better probability estimates.
method Scaling-binning calibrator method that reduces variance and ensures calibration.
result 35% lower calibration error than histogram binning and guarantees true calibration.
Study finds the number of modes in Gaussian kernel density estimators scales with sqrt(β log β).
problem Determining the number of clusters in Transformers.
method Used Kac-Rice formula and Edgeworth expansion to prove scaling.
result The expected number of modes scales as Θ(√(β log β)).
New method estimates bidirectional causal effects in large-scale systems.
problem Estimating bidirectional causal effects in systems with mutual dependence and heteroskedasticity.
method Heteroskedasticity-based identification with online kernel learning and random Fourier features.
result Superior accuracy and stability compared to single equation and polynomial approximations.
The paper improves boundary detection and density estimation on noisy data.
problem Detecting boundary points and estimating density on noisy data from compact manifolds.
method Doubly stochastic scaling of the Gaussian heat kernel via Sinkhorn iterations.
result The new estimates of boundary points and density outperform standard methods, especially under noise.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
New algorithms optimize risk for large datasets, improving efficiency.
problem Optimizing risk for large datasets with robust methods.
method Proposed algorithms for distributionally robust optimization with CVaR and χ² divergence uncertainty sets.
result Algorithms require independent gradient evaluations of training set size and parameters, suitable for large-scale applications.
New method estimates multiscaling exponents for financial risk assessment.
problem Estimating multiscaling properties in financial time series.
method Generalized Hurst Exponent (GHE) and RNSGHE method.
result MSVaR method improves VaR forecasts for multiscaling financial data.
Bayesian model averaging improves causal effect estimation by averaging over multiple models.
problem Estimating causal effects under linear Structural Causal Models (SCMs).
method Bayesian model averaging using Gaussian scale mixture distributions for computational efficiency.
result Bayesian model averaging is optimal for causal effect estimation.
A new method resolves permutation issues in shuffled linear regression for large-scale applications.
problem Estimating latent features through linear transformation with unknown permutations.
method Spectral matching method to align spectral components of measurement and feature covariances.
result Achieves accurate estimates in shuffled LS and LASSO settings with sufficient samples.
New method estimates and samples high-dimensional probability distributions avoiding optimization and approximation curse.
problem Estimating high-dimensional probability distributions from data samples.
method Hierarchic probability flow from coarse to fine scales, defined by conditional probabilities across scales.
result Sampling hierarchic models avoids critical slowing down at phase transitions and generates turbulence and dark matter images.
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in thr…
Enhances Fourier estimator performance for asynchronous event-data.
problem Improving correlation and covariance estimation on event-data.
method Implement and test NUFFT methods with different averaging kernels.
result Demonstrates improved performance and relationship between averaging scales.
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmet…
Study on learning properties of scale-dependent kernels controlling stability and error.
problem Understanding the learning properties of scale-dependent kernels in nonparametric ridge-less least squares.
method Combines probabilistic results with interpolation theory to analyze stability and error.
result Different regimes of learning error depending on sample size and data dimension.
Estimates model performance from compute budget for distillation.
problem Risk mitigation in large-scale distillation.
method Distillation scaling law based on compute budget allocation.
result Maximizes student performance with compute-optimal allocation.
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is u…
A new data set helps estimate continental-scale population distributions.
problem Lack of comprehensive, publicly available data for population estimation.
method Comprehensive data set combining satellite imagery and open-source data.
result Provides a valuable resource for developing population estimation methods.
Proves uniqueness of Ricci flow with scaling invariant estimates.
problem Proving uniqueness of Ricci flow with scaling invariant curvature bound.
method Solving Ricci-harmonic map heat flow in unbounded curvature background.
result Complete Ricci flow starting from uniformly non-collapsed, non-negatively curved manifold is unique in dimension three.
Paper develops robust methods for large-scale testing without tuning parameters.
problem Heavy-tailed data in high-dimensional settings.
method Revisits Hodges-Lehmann estimator for robust inference without tuning parameters.
result Develops confidence intervals and controls false discovery proportion.