Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
The study analyzes robustness of estimators in linear models with adversarial errors.
problem Analyzing robustness of estimators in linear models with adversarial errors.
method Develops a general theory for minimum norm interpolating estimators and RERM in linear models without conditions on errors.
result Quantitative bound for the prediction error relating it to Rademacher complexity, norm of minimum norm interpolator of errors, and subdifferential size.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
Estimates generalization error for two-layer ReLU NNs through minimum norm solutions.
problem Estimating generalization error for two-layer ReLU NNs trained by mean squared error.
method Uses minimum norm solutions and Neural Tangent Kernel (NTK) regime to derive generalization error bounds.
result Derives an a priori generalization error bound for two-layer ReLU NNs without requiring exponentially large number of neurons.
Clustering stocks reduces estimation error in global minimum variance portfolio.
problem High estimation error in covariance matrix estimation.
method Bounded clustering to limit maximum cluster size.
result Reduction in out-of-sample volatility and gap between in-sample and out-of-sample volatility.
The study analyzes how covariance estimation errors affect the global minimum-variance portfolio under heavy-tailed distributions.
problem The impact of covariance estimation errors on the global minimum-variance portfolio under heavy-tailed distributions.
method Characterization of covariance-estimation error's effect on GMVP suboptimality, derivation of regret identity and bound, application to heavy-tailed returns.
result The decision geometry of GMVP regret is invariant to a (p-1)-dimensional projection of the error matrix, with invariance to the covariance-scale direction as an exact special case.
Super-efficient automatic differentiation outperforms analytic methods in min-min optimization.
problem Optimizing functions defined as a minimum using iterative algorithms.
method Comparing automatic differentiation to analytic gradient estimation methods.
result Automatic differentiation yields an asymptotic error close to the square of the optimization error, demonstrating super-efficiency.
LoCoV reduces portfolio optimization errors from sample covariance matrices.
problem Large errors in sample covariance matrix for optimal portfolio weights.
method LoCoV (low dimension covariance voting) algorithm to reduce these errors.
result LoCoV outperforms classical methods in portfolio optimization experiments.
MPF method improves parameter estimation in probabilistic models.
problem Difficulty in fitting probabilistic models due to intractable partition function.
method Minimum Probability Flow (MPF) method for parameter estimation.
result MPF outperforms existing techniques in convergence time and accuracy.
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.
Private minimum Hellinger distance estimators maintain robustness and efficiency while ensuring privacy.
problem Ensuring privacy in robust statistical estimation.
method Derive private minimum Hellinger distance estimators satisfying Hellinger differential privacy.
result Private minimum Hellinger distance estimators retain robustness and efficiency under privacy constraints.
Defines MER for Bayesian learning, a gap between achievable and optimal performance.
problem Analyzing the best performance of Bayesian learning under generative models.
method Two methods for deriving upper bounds for MER: conditional mutual information and minimum estimation error.
result Quantifies the rate at which MER decays to zero with more data and relates it to model richness.
New method estimates minimizer and minimum value of a regression function.
problem Estimating minimizer and minimum value of a regression function from noisy data.
method Projected gradient descent with gradient estimated by regularized local polynomial algorithm, followed by a rate optimal nonparametric procedure.
result Achieves minimax optimal rates of convergence for smooth and strongly convex functions.
Inflating the minimum norm interpolator improves linear regression generalization error.
problem Highly anisotropic covariances and diverging d/n in linear regression. method Inflating the minimum ℓ2 norm interpolator by a constant greater than one. result Inflating the minimum norm interpolator improves generalization error.
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
K-Medoids(KM) is a standard clustering method, used extensively on semi-metric data.Error analyses of KM have traditionally used an in-sample notion of error,which can be far from the true error and suffer from generalization gap. We formalize the true K-Medoid error based on the underlying data distribution.We decompo…
Paper uses DFL to optimize portfolio risk and outperforms conventional methods.
problem Optimizing portfolio risk and return under uncertainty.
method Decision-focused learning (DFL) to derive global minimum variance portfolio (GMVP).
result DFL-based methods consistently deliver superior decision performance in portfolio optimization.
Exact expressions for double descent and implicit regularization in over-parameterized models.
problem Understanding the generalization error of over-parameterized models like deep neural networks.
method Surrogate random design to replace standard i.i.d. design, leading to exact expressions for mean squared error and implicit regularization.
result Exact non-asymptotic expressions for double descent and implicit regularization in over-parameterized models.
Statistical analysis of regularization in continual learning tasks.
problem Understanding how regularization affects model performance in sequential learning.
method Derivation of convergence rates, iterative update formula, and optimal hyperparameters for generalized ℓ2-regularization.
result Optimal hyperparameters balance forward and backward knowledge transfer, improving model performance.
Estimates domain truncation error for option pricing PDEs.
problem Estimating error in option pricing models with domain truncation.
method Derives an estimate of domain truncation error for a multidimensional PDE system.
result Proposes a sharper error estimate for option pricing models.
The paper examines prediction and estimation risks of ridgeless least squares under general error assumptions.
problem Prediction and estimation risks of ridgeless least squares under realistic error structures.
method Analysis of prediction and estimation risks under general regression error assumptions, including clustered or serial dependence.
result The benefits of overparameterization extend to time series, panel, and grouped data.
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distanc…
Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyis entropy estimator, called information potential (IP), is a popular MEE cost i…
Bayes Error Rate estimators are evaluated for accuracy and sample requirements.
problem Evaluating the accuracy and sample requirements of Bayes Error Rate estimators.
method Monte Carlo simulations with synthetic data and real-world scenarios.
result k-Nearest Neighbor (kNN) is the most accurate non-parametric estimator.
Minimum-norm solutions generalize well in over-parametrized neural networks.
problem Generalization error in over-parametrized neural networks.
method Analyzing three models: random feature model, two-layer neural network, and residual network.
result Generalization error for minimum-norm solutions is comparable to Monte Carlo rate, up to logarithmic terms.
Study tightens bounds for interpolating noisy data using minimum l1-norm.
problem Predicting noisy data with minimum l1-norm interpolation.
method Provided matching upper and lower bounds for prediction error.
result Tight consistency up to negligible terms for d≫n. The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the available analytical performance guarantees are mostly asymptotic. This paper p…
Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.
problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.
A new estimator for asynchronous tick data shows better correlation estimates.
problem Estimating correlation from asynchronous tick data.
method Derive a minimum-variance estimator and a fast linear-time estimator.
result The fast tickwise estimator has smaller estimation errors than the usual method.
Study on LMMSE estimation with model mismatch, quantifying MSE trade-offs.
problem Model mismatch in LMMSE estimation with undermodeling.
method Analyzing the average MSE of LMMSE estimation with random regressors.
result Performance improvement depends on sufficient samples and model complexity.
Risk-aware MMSE improves stability in volatile scenarios.
problem In MMSE estimators, volatility of error is unconstrained, leading to significant performance differences.
method Introduces risk-aware MMSE by constraining expected predictive variance.
result Risk-aware MMSE provides better performance, especially in skewed, heavy-tailed distributions.
Robust estimation methods find global minima efficiently via quasi-gradients.
problem Efficiently solving robust estimation problems with non-convex optimization.
method Identifying generalized quasi-gradients to guarantee low-regret algorithms.
result Generalized quasi-gradients ensure efficient approximation of global minima.
The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been…
Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distri…
Paper introduces a new method for error estimation in classification tasks with limited data.
problem Challenges in designing accurate classifiers and evaluating their performance with limited training data.
method Introduces a novel Bayesian MMSE estimator for optimal Bayesian transfer learning (OBTL) using Monte Carlo importance sampling.
result Proposed OBTL error estimation scheme outperforms standard methods, especially in small-sample settings.
We break dimension dependence in sparse distribution estimation with communication constraints.
problem Estimating sparse distributions with limited communication.
method Novel localization schemes and tree-based estimation.
result Achieve dimension-free convergence rate independent of dimension d. New proof shows how to identify DAGs with weakly increasing errors.
problem Identifying the true DAG in models with weakly increasing error variances.
method Minimum-trace DAG method and hill climbing algorithm with R2R neighborhood.
result Hill climbing algorithm without strict local optima under weakly increasing error variances.
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the…
We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in terms of the approximation ability and capacity of the involved hypothesis space w…
Conventional multiuser detection techniques either require a large number of antennas at the receiver for a desired performance, or they are too complex for practical implementation. Moreover, many of these techniques, such as successive interference cancellation (SIC), suffer from errors in parameter estimation (user …
New algorithms improve robust estimation in contaminated Gaussian models.
problem Simultaneous estimation of location and variance matrix in contaminated Gaussian models.
method Tractable adversarial algorithms with spline discriminators for robust estimation.
result Achieve minimax optimal rates or near-optimal rates under Huber's contamination model.
Study robust distribution estimation with Wasserstein distance, achieving optimal risk.
problem Robust distribution estimation under adversarial corruption.
method Combining partial OT and minimum distance estimation, proving structural properties and deriving a novel dual form.
result Achieves minimax-optimal robust estimation risk in many settings.
Study uses DNN to accurately estimate daily ET o in various climates.
problem Precise estimation of reference evapotranspiration (ET o ) for irrigation and water management.
method Investigated artificial neural network (ANN) and deep neural network (DNN) models using six meteorological inputs.
result DNN models, especially P-DNN-SeLU, achieve high accuracy in daily ET o estimation.
In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the cr…
In this paper, we present a deep learning (DL) algorithm for channel estimation in communication systems. We consider the time-frequency response of a fast fading communication channel as a two-dimensional image. The aim is to find the unknown values of the channel response using some known values at the pilot location…
We study least squares linear regression over N uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features p is at most the sample size n, the estimator under consideration coincides with the principal component regression estimator; when p>n, the esti…
The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the literature. The original MEE only focuses on minimizing the Renyi's quadratic entropy …
We consider learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters based on the generalized Dantzig selector. Under suitable sample size and resampli…