LogDet estimator improves entropy estimation in neural networks.
problem Inconsistent observations and diversified interpretation in neural networks.
method Proposes LogDet estimator for reliable entropy approximation.
result LogDet estimator overcomes distributional diversity issues.
A numerical expression in the form of an integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a curious sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. A few graphs are drawn.
Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the flexibility of the model by parameterizing the model matrix. By imposing restrictions …
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. …
Polylab is a MATLAB toolbox for multivariate polynomial modeling.
problem Efficiently modeling and manipulating multivariate polynomials across CPU and GPU.
method Unified symbolic-numeric interface, three aligned classes (MPOLY, MPOLY_GPU, MPOLY_HP), polynomial operations, differentiation, matrix computations.
result Advantages of MPOLY-HP for reduction-heavy simplification and large-scale computations, and the stochastic log-determinant variant for sparse regimes.
Novel unsupervised MIG detectors improve signal detection in cluttered environments.
problem Signal detection in nonhomogeneous clutter environments.
method Developed novel discriminative MIG detectors using HPD matrices and geometric measures.
result Improved signal detection performance compared to conventional methods.
New method computes affine normal directions efficiently for sparse polynomials.
problem Computing affine normal directions is computationally expensive in high dimensions.
method Reduces third-order tensor contraction to matrix-free formulation using log-determinant gradient.
result Scalable implementations with near-linear scaling in dimension and sparsity.
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.
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.
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
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 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.
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.
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…
We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the Rao-Blackwellization of three different estimators. Combining our estimator with REINFORCE, we ob…
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…
The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able to efficiently estimate the variance of this estimator is very helpful to vario…
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.
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.
Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a robust estimator wh…
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.
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 …
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
Estimating boundaries from point clouds with improved accuracy and rigorous error estimates.
problem Identifying the boundary of a domain from point cloud samples.
method Developed new estimators for normal vectors, distances, and boundary tests; provided error estimates.
result Efficient and accurate estimators for boundary properties on point clouds.
Study nonparametric covariance function estimation for noisy data.
problem Estimating covariance function from discrete noisy data in high dimensions.
method Adaptive learning-based estimators, including deep learning.
result Established oracle inequality and convergence rates for deep learning estimators.
We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on each part, then the second estimator on the outputs of the first estimator. And …
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.
Proposes RCL method to improve ATE estimation from observational data.
problem Error-compounding issue and extreme estimates in DML estimators.
method Robust Causal Learning (RCL) method to offset DML deficiencies.
result RCL estimators are more stable and perform better than DML estimators.
Unified plug-in approach for estimating symmetric properties of distributions efficiently.
problem Estimating symmetric properties of distributions with high accuracy and efficiency.
method Profile-maximum-likelihood (PML) based estimator.
result Achieves theoretical limit for universal symmetric property estimation.
The paper derives new gradient and Hessian estimates for nonlinear parabolic equations.
problem Estimating solutions to nonlinear weighted parabolic equations.
method Derives Li-Yau and Hamilton type gradient estimates, and Hessian estimates.
result New gradient and Hessian estimates for positive solutions of nonlinear parabolic equations.
The problem of estimating a high-dimensional sparse vector θ∈Rn from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the…
Unified theory for causal inference using various methods.
problem Estimating causal effects in ATE estimation.
method Riesz regression, covariate balancing, DRE, TMLE, matching estimator.
result Unified theory integrating multiple methods for ATE estimation.
The paper develops a new algorithm for constructing minimax estimators using online learning techniques.
problem Designing minimax estimators for probability distribution parameters.
method Viewing the problem as a zero-sum game and using online learning with non-convex losses to find a Nash equilibrium.
result The algorithm constructs both a minimax estimator and a least favorable prior.
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical cha…