This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single integral is then computed with efficiently implemented numerical techniques. The perf…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “Integral Squared Error”
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 …
Improved LOO cross-validation for function approximation.
problem Estimating the Integrated Squared Error (ISE) for function approximation.
method Weighted Leave-One-Out cross-validation based on Gaussian Process.
result Significantly more precise ISE estimation compared to unweighted LOO.
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our al…
Novel approach integrates Multivariate Square-root Lasso into Synthetic Control for high-dimensional data.
problem Challenges in practical implementation and computational efficiency of Synthetic Control method for high-dimensional disaggregated data.
method Integrates Multivariate Square-root Lasso into Synthetic Control framework.
result Demonstrates superior computational efficiency without compromising estimation accuracy.
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.
A method for noise reduction in functional time series using FPCA.
problem Noise contamination in functional time series.
method Extending FPCA to separate signal and noise components.
result Optimal projection minimizes mean integrated squared error.
We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, an…
Optimizes sliding window approach for tracking Gaussian densities.
problem Improving tracking performance of Gaussian density estimation.
method Theoretical analysis of sliding window Gaussian Kernel Density Estimators.
result Empirical evidence shows improved tracking performance with optimal weight sequence.
The paper improves error bounds for Bayesian quadrature in noisy settings.
problem Improving error bounds for Bayesian quadrature in noisy settings.
method Develops a two-step meta-algorithm to relate average-case quadrature error to -function approximation error.
result Provides new average-case results for various kernels and noise settings.
Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.
problem Efficiently implementing Gaussian process acquisition functions for expensive simulations.
method Proposed a truncated eigenbasis representation for closed-form evaluation of IMSE acquisition function.
result Significantly lower prediction error and reduced computation time compared to benchmarks.
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…
This paper introduces a class of k-nearest neighbor (-NN) estimators called bipartite plug-in (BPI) estimators for estimating integrals of non-linear functions of a probability density, such as Shannon entropy and Rényi entropy. The density is assumed to be smooth, have bounded support, and be uniformly bounded from…
Signature volatility models are analyzed for existence, arbitrage, completeness, and hedging-error decomposition.
problem Existence, arbitrage, completeness, and hedging-error decomposition of signature volatility models.
method Global existence and uniqueness of strong solutions, asset-pricing, market completeness, and hedging-error decomposition derived through structural results.
result Signature volatility models are structurally sound with existence, arbitrage, completeness, and hedging-error decomposition.
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.
Counterexample shows Ito integrand needn't be locally square integrable.
problem Ito integrand's square integrability condition is not always met.
method Provided a counterexample to Ito's Lemma's integrability condition.
result Ito integrand needn't be locally square integrable.
We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show that we can select tuning parameters by minimizing the estimated risk. We study t…
Hybrid model outperforms benchmarks in financial forecasting.
problem Robust asset price forecasting in finance.
method Combining LSTM with Neural Levy Processes using Grey Wolf Optimizer and ANN calibration.
result Hybrid model outperforms base LSTM and other models.
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or O(n*log(n)) for constructing a classifier, where n is the number of sampling instances.…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio , where and encode the smoothness and dimension of the integrand. However, an empirical investigation re…
We study the asymptotic behaviour of doubly periodic instantons with square-integrable curvature. Then, we establish the equivalence given by the Nahm transform between the doubly periodic instantons with square integrable curvature and the wild harmonic bundles on the dual torus.
Machine learning improves American option pricing accuracy.
problem Complexities of American options and traditional models' limitations.
method Monte Carlo simulations combined with machine learning algorithms (Least Square Method, LSTM, GRU).
result GRU model outperforms LSTM in predicting bid prices, enhancing accuracy and stability.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
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.
This work examines consistency issues in Gaussian Mixture Model reduction algorithms.
problem Consistency issues in Gaussian Mixture Model reduction algorithms.
method Discussion of the importance of dissimilarity measure choice and consistency of GMR algorithms.
result Most existing GMR algorithms are not consistent with a unique measure, leading to suboptimal reduced GMs.
New method reveals insights about stochastic optimization methods using modified equations.
problem Understanding the qualitative behavior of stochastic optimization algorithms.
method Developed a class of stochastic differential equations to approximate the dynamics of stochastic optimization methods.
result Mean-square stability of the modified equation provides qualitative insights about stochastic coordinate descent.
Paper improves volatility estimation using a Queue-Reactive model.
problem Volatility estimation from high-frequency data is biased by microstructure noise.
method Uses Queue-Reactive model of limit order book to improve volatility estimation.
result Unified and alternation estimators lead to optimal mean squared error for integrated volatility.
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
Paper uses LSTM neural networks to forecast commodity prices.
problem Forecasting accuracy of traditional methods like ARIMA.
method Long Short-Term Memory (LSTM) neural networks complement traditional methods.
result Forecast averaging of LSTM and ARIMA models improves forecast accuracy.
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.
Extends phase retrieval methods to handle sensing vector errors.
problem Phase retrieval with errors in sensing vectors.
method Total Least Squares (TLS) framework applied to gradient descent.
result Gradient descent can efficiently solve TLS phase retrieval.
Develops nonparametric regression for non-smooth functions using fractional Laplacian.
problem Non-smooth regression functions in high dimensions.
method Fractional Laplacian eigenmaps for -fractional Sobolev spaces.
result Upper bound on estimation error of $n^{- rac{2s}{2s+d}}$.
Optimizes calibration error estimators for better classifier trustworthiness.
problem Lack of guidance on selecting and tuning calibration error estimators.
method Reformulates calibration estimation as a regression problem with i.i.d. input pairs.
result Demonstrates the effectiveness of optimized calibration estimators on image classification tasks.
Paper introduces statistical learning for point processes.
problem Statistical learning for point processes in general spaces.
method Combines bivariate innovations and point process cross-validation.
result Statistical learning approach outperforms state of the art.
Lower Bounds and a Near-Optimal Shrinkage Estimator for Least Squares using Random Projectionsmath.OC
Improved estimator for least squares using random projections achieves smaller error.
problem Improving the accuracy of least squares solutions for large-scale problems.
method James-Stein estimator applied to Gaussian sketching of least squares problems.
result Upper and lower bounds match when SNR is small and data matrix is well-conditioned.
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …
Principal binets generalize curvature line surfaces to square lattices and are a discrete integrable system.
problem Discretizing curvature line surfaces on square lattices.
method Showed principal binets as a multi-dimensional consistent system.
result Principal binets generalize to higher-dimensional square lattices and are integrable.
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are me…
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.
We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing …
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…
Estimates surface count with prescribed foliations.
problem Counting square-tiled surfaces with specific foliations.
method Effective estimate with power saving error term.
result Strengthens asymptotic counting formulas.
Efficiently estimates private least squares with linear error growth.
problem Private estimation of ordinary least squares with bounded residuals and leverage.
method Scaled noise added to a stable nonprivate estimator of the regression vector.
result Near-optimal accuracy guarantee with linear error growth in dimension.
This paper concerns error bounds for recursive equations subject to Markovian disturbances. Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) and Reinforcement Learning (RL), and many of these algorithms can be interpreted as special cases of stochastic approximation (SA). It is argued tha…
Deep neural networks estimate regression functions on manifolds.
problem Estimating regression functions on manifolds from data.
method Fully connected deep neural networks with ReLU activation, analyzing convergence rates.
result Estimates achieve a rate of convergence dependent on manifold dimension, not predictor dimension.
Paper solves a complex portfolio selection problem with time-inconsistent preferences.
problem Time-inconsistent preferences in portfolio selection.
method Unified framework with minimal assumptions, proving existence and uniqueness of solution.
result Existence and uniqueness of square-integrable solution for the integral equation.
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 solves outlier robust mean estimation near breakdown point.
problem Estimating mean in presence of adversarial outliers.
method Sum-of-Squares approach to optimize error rate efficiently.
result Achieves optimal error rate for all ε ∈ [0, 1/2).