Double Q-learning has the same mean-squared error as Q-learning under certain conditions.
problem Comparing the mean-squared error of Double Q-learning and Q-learning.
method Theoretical analysis based on Lyapunov equations for both tabular and linear function approximation settings.
result The asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning under specific conditions.
The paper provides mean-square error bounds for stochastic approximation algorithms.
problem Error bounds for recursive equations with Markovian disturbances.
method Analysis of mean-square error for stochastic approximation algorithms.
result Mean-square error achieves the optimal rate of O(1/n) under certain conditions. This study calculates the maximum error of a famous estimation method.
problem Estimating rare items not seen in a sample.
method Characterizes the maximal mean-squared error of the Good-Turing estimator.
result Characterizes the maximal mean-squared error of the Good-Turing estimator.
New method optimizes tail dependence coefficient estimation.
problem Estimating tail dependence in nonparametric data.
method Optimal threshold selection combining mean squared error and copula estimation.
result Improved accuracy in tail dependence coefficient estimation.
Paper bounds prediction error for misspecified Gaussian process models.
problem Guaranteeing model confidence for nonparametric Gaussian process regression.
method Derives an upper bound for mean square prediction error using pseudo-concave optimization.
result Upper bound for mean square prediction error of misspecified models.
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…
New method finds best arm minimizing mean-squared error in correlated bandits.
problem Finding an arm that best captures information about other arms.
method Formulated correlated bandit problem, derived MSE estimator, proposed algorithm.
result Proposed algorithm identifies best arm with error probability bounds.
Cryptocurrency prices predicted using LSTM, SVM, and polynomial regression.
problem Uncertainty in crypto coin values.
method Long Short Term Memory, Support Vector Machine, Polynomial Regression models.
result Support Vector Machine with linear kernel had the smallest mean square error.
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.
A fast method for LOOCV in k-NN regression reduces computation time.
problem Efficient computation of LOOCV for k-NN regression.
method Identical LOOCV estimate to (k+1)-NN MSE on training data.
result LOOCV computation can be done with (k+1)-NN regression once.
This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…
Enhances RL for jump processes using MSBVE algorithm.
problem Challenges in continuous-time RL with jumps and noise.
method Introduces MSBVE algorithm to minimize quadratic variation error.
result MSBVE algorithm outperforms MSTDE in jump processes.
This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It…
The paper develops a method to accurately estimate the Bayes misclassification error rate.
problem Estimating the best achievable classifier performance without learning a Bayes-optimal classifier.
method Learning to benchmark using an ensemble of ε-ball estimators and Chebyshev approximation.
result The proposed method achieves an optimal mean squared error rate of O(N^(-1)) under a smoothness assumption.
The paper analyzes how data augmentation affects the test error in regression models.
problem Understanding the impact of data augmentation on the test error in regression models.
method Characterizes the test error in terms of population quantities and augmentation statistics.
result Provides a tight characterization of the test error in mean squared error.
The paper compares machine learning models for forecasting residential gas demand, highlighting the impact of temperature forecasts.
problem Forecasting residential gas demand for optimal energy planning.
method Implemented and compared five models: Ridge Regression, GP, k-Nearest Neighbour, ANN, and Torus Model.
result ANN is the best model in terms of RMSE, while GP is the best in terms of MAE.
Paper optimizes diffusion models for denoising tasks with theoretical guarantees.
problem Lack of theoretical understanding of MSE optimality in diffusion models.
method Inspired by MSE-optimal CME, proposes a novel denoising strategy for diffusion models.
result Demonstrates polynomial-time convergence to the CME under mild conditions.
Improved multi-task averaging reduces mean squared error in high-dimensional data.
problem Joint estimation of multiple distributions using independent data sets.
method Exploits similarities between tasks by shrinking naive estimators towards local averages.
result The method provides a significant reduction in mean squared error, especially in high-dimensional spaces.
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably dominates its conventional counterpart in terms of mean square deviations. We es…
ABae efficiently computes subset means with expensive predicates using stratified sampling.
problem Computing subset means with expensive predicates efficiently.
method Stratified sampling and proxy models.
result Mean squared error of O(N−1) when N is split evenly between stages. This research finds that using mean-squared error and codeword targets improves adversarial robustness.
problem Evaluating and improving the robustness of neural networks against adversarial attacks.
method Training neural networks on mean-squared error and using codeword targets as representations.
result The modified models show up to 98.7% increase in accuracy against untargeted attacks and up to 99.8% decrease in targeted attack success rates.
Network agents solve adaptive regression problems with compressed signals.
problem Solving regression problems in networks with communication constraints.
method ACTC diffusion strategy with randomized differential compression.
result Optimized resource allocation improves performance.
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention as been paid to proving lower error bounds for the SGD method. It is the key cont…
Unified framework for robust A/B testing under model misspecification.
problem Improving sample efficiency in A/B testing with model misspecification.
method Unified framework for contextual bandit and dynamic settings, proving worst-case mean squared error bounds.
result Empirically validated approach using synthetic and real-world datasets.
Improved stock volume prediction using Kalman Filters with various hidden states.
problem Improving accuracy of intraday trading volume prediction.
method Extended Kalman Filter with various hidden states for different stocks, using cross-validation to determine optimal state number.
result Demonstrated improved accuracy through comparison experiments and numerical analysis.
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…
RPNN-EOFs model improves time series forecasting accuracy.
problem Improving time series forecasting accuracy for complex systems.
method Combines higher-order neural networks with error-output feedbacks.
result RPNN-EOFs outperformed other models in forecasting the Mackey-Glass time series.
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
Transformer model with mixed-frequency data improves stock volatility prediction.
problem Improving stock volatility prediction using mixed-frequency data.
method Transformer model trained on mixed-frequency data (GARCH-MIDAS model for frequency alignment).
result Transformer model reduces mean square error from 1.00 to 0.86.
Estimating mean from one-bit samples of symmetric log-concave distributions.
problem Estimating the mean of a symmetric log-concave distribution with limited one-bit measurements.
method Analyzes mean squared error in three settings: centralized, adaptive, and distributed, with and without quantization.
result One round of adaptivity is sufficient to achieve optimal mean-square error in the adaptive setting.
Paper predicts EEG features from acoustic features using RNN and GAN.
problem Predicting EEG features from acoustic features.
method Recurrent Neural Network (RNN) and Generative Adversarial Network (GAN).
result Lower RMSE and normalized RMSE values compared to generating acoustic features from EEG features.
Paper provides statistical guarantees for GNNs in link prediction.
problem Link prediction accuracy in graph neural networks.
method Proposes a linear GNN architecture (LG-GNN) and derives statistical guarantees.
result LG-GNN produces consistent estimators for edge probabilities and has better detection of high-probability edges.
Convolutional neural network improves MRE image reconstruction.
problem Reconstructing MRE images from displacement data is computationally intensive and costly.
method Proposes a CNN architecture to directly map MRE displacement data into elastograms, introducing a secondary loss for training.
result CNN-generated images compare favorably with nonlinear inversion methods.
We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up t…
Unified framework for finite-sample RL algorithms using Lyapunov theory.
problem Finite-sample convergence guarantees of asynchronous RL algorithms.
method Reformulate RL algorithms as Markovian SA, develop Lyapunov analysis.
result Mean-square error bounds and convergence for various RL algorithms.
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For d covariates, there are 2d basis coefficients to estimate, which renders conventional approaches computationally prohibitive …
A new method for approximating softmax and Gaussian kernels with reduced error.
problem Approximating softmax and Gaussian kernels with low error.
method Simplex Random Features (SimRFs) and SimRFs+.
result SimRFs provide the smallest MSE among weight-independent geometrically-coupled PRF mechanisms.
We derive a mapping between MSE and CCC, revealing counterintuitive insights.
problem Missing mapping between mean square error and concordance correlation coefficient.
method Derive mathematical formula connecting MSE and CCC, analyze graphical implications.
result Formula uncovers counterintuitive insights and precise range for CCC given MSE.
ALRC clips learning rates to stabilize neural network training.
problem Stability issues in training with small batch sizes and high learning rates.
method Adaptive learning rate clipping (ALRC) to limit losses.
result ALRC decreases errors in unstable training conditions.
Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (…
Probability calibration trees improve accuracy of probability estimates.
problem Improving accuracy and calibration of probability estimates from classifiers.
method Probability calibration trees modify logistic model trees to learn different models in regions of the input space.
result Probability calibration trees outperform isotonic regression and Platt scaling in terms of root mean squared error.
The paper proposes a method to improve forecast combination accuracy using portfolio theory.
problem Improving forecast accuracy by combining multiple forecasts.
method Generates forecast combinations using a portfolio analogy, allowing negative weights for hedging.
result Demonstrates improved performance in weighted random forest forecasts.
Combines experimental and historical data for robust policy evaluation.
problem Policy evaluation with mixed data sources, especially experimental vs historical.
method Linear integration of estimators from experimental and historical data, optimized for MSE minimization.
result Proposed estimators outperform traditional methods in ridesharing company data.
Study large deviations rates for SGD with strongly convex functions.
problem High probability metrics with SGD.
method Large deviations theory, generic gradient noise, strongly convex functions.
result Upper large deviations bound for SGD with strongly convex functions.
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution. However, no finite sample statistical guarantees and no computationally efficient o…
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
Paper analyzes convergence of two time-scale stochastic approximation using martingale approach.
problem Analyzing convergence of two time-scale stochastic approximation algorithms.
method Uses martingale approach to establish convergence conditions and rates.
result Establishes different rates of convergence for fast and slow subsystems.
The article derives a formula for predicting claims uncertainty using the GCC method.
problem Claims reserving uncertainty in non-life insurance modeling.
method Generalized Cape Cod (GCC) method, derived an analytical formula for MSEP.
result Derives an analytical formula for the mean squared error of prediction (MSEP) of the GCC method.