Paper proposes a single task optimization for endmembers' number estimation and unmixing.
problem Endmembers' number estimation and unmixing in hyperspectral images.
method Low-rank and sparse nonnegative matrix factorization with alternating proximal algorithm.
result Effectiveness of the proposed approach verified by experiments.
Paper proposes a new method to handle spectral variability in hyperspectral unmixing.
problem Spectral variability within endmember classes affects unmixing performance.
method Adaptive bundles and double sparsity to promote sparsity on spectra and classes.
result Successfully determines variable number of classes and estimates their abundances.
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution ena…
This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that…
This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and t…
New methods for hyperspectral unmixing handle intra-class variability.
problem Intra-class variability in hyperspectral images.
method Inertia-constrained Pixel-by-pixel NMF (IP-NMF) for handling variability.
result IP-NMF outperforms state-of-the-art methods in real data.
The successive projection algorithm (SPA) has been known to work well for separable nonnegative matrix factorization (NMF) problems arising in applications, such as topic extraction from documents and endmember detection in hyperspectral images. One of the reasons is in that the algorithm is robust to noise. Gillis and…
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and …
In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind…
Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how aspects of these problems, such as misalignment of DOAS references and uncertain…
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
New estimator reduces kernel mean estimation error.
problem Kernel mean estimation in reproducing kernel Hilbert spaces.
method Corrupt data with known distributions and estimate kernel mean under the corrupted distribution.
result The marginalized kernel mean estimator achieves lower estimation error.
Enhances gradient estimates for Hermitian Monge-Ampère equations.
problem Improving estimates for Hermitian Monge-Ampère equations.
method Improves gradient estimates using Evans-Krylov and third derivatives estimates.
result Enhanced estimates for second and third order derivatives.
Paper proposes robust estimators for GANs under Wasserstein contamination.
problem Robust estimation of distributions under contamination.
method Wasserstein GAN-based estimators for location, covariance, and regression.
result Proposed estimators are minimax optimal in many scenarios.
New framework converts offline to online estimation using black-box offline estimators.
problem Convert offline estimation algorithms to online estimation algorithms.
method Oracle-Efficient Online Estimation (OEOE) framework.
result Achieves near-optimal online estimation error via black-box offline estimators.
Proposes variational autoencoder for efficient MMSE estimation.
problem Efficient parameterized MMSE estimation for noisy observations.
method Variational autoencoder models data distribution, approximates MMSE.
result Proposed estimator performs well compared to state-of-the-art.
Paper presents a robust estimator for density ratio estimation that trims outliers.
problem Vulnerability of density ratio estimation to corrupted data points.
method Automatically identifies and trims outliers in density ratio estimation; uses convex formulation and subgradient descent.
result Global optimum can be obtained via subgradient descent; parameter estimation error analyzed under high-dimensional settings.
Paper improves Fisher information estimation methods.
problem Estimating Fisher information for location parameters.
method Revisits and improves Bhattacharya estimator, introduces clipped estimator.
result Clipped estimator shows superior convergence rates in Gaussian noise.
Proposes a robust estimator for RD designs.
problem Estimating treatment effects in RD designs.
method Doubly robust estimator combining two estimators.
result Enhances robustness of treatment effect estimators.
New estimator reduces variance in discrete random variables.
problem Estimating gradients for discrete random variables with reduced variance.
method Sampling without replacement and Rao-Blackwellization.
result Our estimator is the most consistent gradient estimator across different entropy settings.
New risk-averse estimators uniquely characterize MAP and Wallace-Freeman estimators.
problem Formalizing and characterizing Bayesian point estimators.
method Formulated axioms for inference, showing unique characterizations of MAP and Wallace-Freeman estimators.
result Axioms uniquely characterize MAP and Wallace-Freeman estimators for different types of estimation problems.
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
Formalizes robustness for composite estimators using breakdown points.
problem Understanding the robustness of composite estimators under data modification.
method Formalizes robustness via breakdown points and analyzes the product of individual breakdown points for composite estimators.
result The breakdown point of a composite estimator is the product of the breakdown points of its individual estimators.
We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task maximum likelihood estimates. We derive the optimal minimum risk estimator and the minimax estimator, and show t…
Obtaining more accurate equity value estimates is the starting point for stock selection, value-based indexing in a noisy market, and beating benchmark indices through tactical style rotation. Unfortunately, discounted cash flow, method of comparables, and fundamental analysis typically yield discrepant valuation estim…
We find an unbiased estimator for MMD variance.
problem Efficiently estimating the variance of MMD estimators.
method Extending and correcting previous work, we derive an unbiased estimator for MMD variance.
result We provide a truly unbiased estimator for MMD variance with no additional computational cost.
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…
A new copula estimation method using classification.
problem Estimating copula density from joint and marginal distributions.
method Train a classifier to distinguish joint density from product of marginals.
result Empirically outperforms existing copula estimators.
Paper improves Li-Yau gradient estimates for heat equation solutions.
problem Improving Li-Yau gradient estimates for heat equation solutions.
method Obtained new Li-Yau type gradient estimates with time-dependent parameters.
result Improved Li-Yau gradient estimates for heat equation solutions.
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.
TAKDE optimizes kernel density estimation for real-time dynamic processes.
problem Real-time density estimation in applications like computer vision and signal processing.
method Derives asymptotic mean integrated squared error (AMISE) upper bound for 'sliding window' kernel density estimator and proposes TAKDE as a novel, theoretically optimal estimator.
result TAKDE outperforms other dynamic density estimators in terms of test log-likelihood and runtime.
Paper bridges score estimation to parameter and density estimation in DDPMs.
problem Efficiently estimating scores for generative models.
method Introduces a framework linking score estimation to parameter and density estimation.
result Denoising score-matching in DDPMs is asymptotically efficient for parameter estimation.
New method estimates density-derivative-ratios directly for clustering and ridge estimation.
problem Accurately estimating ratios of density derivatives.
method Direct estimation of density-derivative-ratios without density estimation.
result Developed methods significantly outperform existing techniques, especially for high-dimensional data.
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local X-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …
New estimator improves reliability of KL divergence estimation.
problem Estimating KL divergence reliably and efficiently.
method Proposes a new estimator using Reproducing Kernel Hilbert Space.
result Proposed estimator is consistent and more reliable for small datasets.
New method for fast volatility estimation robust to change points.
problem Robust high-frequency volatility estimation with change points.
method ℓ1-regularized power variation estimators using LARS for sparse estimation and dynamic programming for change point refinement.
result Minimax rates achieved for volatility estimators, providing accurate and smooth forecasts.
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.
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
Private estimation of many quantiles using differential privacy.
problem Estimating quantiles of a distribution privately.
method Two approaches: 1) Private estimation of empirical quantiles, 2) Uniform density estimation.
result There is a tradeoff between estimating quantiles at specific points and uniformly estimating the quantile function.
New estimator improves mutual information estimation.
problem Estimating mutual information in data science and machine learning.
method Proposes a new estimator that uses a preliminary estimate of the data distribution.
result A preliminary estimate helps in estimating mutual information more accurately.
Kernel estimator improves spectral risk measure estimation.
problem Estimating spectral risk measures accurately.
method Kernel-based estimation of L-statistics for SRMs.
result Kernel estimator is strongly consistent and asymptotically normal.
Paper proposes robust LAD estimators for 2D sinusoidal model, proving consistency and normality.
problem Estimation of parameters in 2D sinusoidal models with outliers or heavy-tailed noise.
method Least absolute deviation (LAD) estimators for robust parameter estimation.
result Strong consistency and asymptotic normality of LAD estimators for 2D sinusoidal model parameters.
New empirical Bayes estimator outperforms soft-thresholding for high-dimensional sparse vectors.
problem Estimating high-dimensional sparse vectors from noisy observations.
method Empirical Bayes shrinkage estimator using a Bernoulli-Gaussian prior.
result Hybrid estimator outperforms soft-thresholding in compressed sensing applications.
Combines multiple OPE estimators into a more accurate and efficient estimate.
problem Offline evaluation of recommender systems using biased data.
method Meta-analysis of correlated OPE estimators, accounting for inter-estimator correlation.
result Improved statistical efficiency and accuracy in estimating policy value.
Unified framework for efficient estimation of unnormalized models.
problem Estimation of unnormalized models with statistical efficiency.
method Unified estimation framework combining density-ratio matching and nonparametric estimators.
result Asymptotic variance of proposed estimators is the same as MLE.
Paper introduces estimator response curve to assess mutual information estimators.
problem Assessing the performance of mutual information estimators.
method Utilizes estimator response curve to test various measures of association.
result Suboptimal estimators perform worse than optimal ones in real-world data.
Optimal and safe semi-supervised learning estimator for high-dimensional data.
problem Improving regression parameter estimation with unlabeled data in high-dimensional settings.
method Established minimax lower bound, proposed optimal and safe semi-supervised estimators.
result Optimal semi-supervised estimator achieves the minimax lower bound.