Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.
problem Local elliptic regularity for operators with low regularity coefficients in Sobolev-type spaces.
method Rescaling estimates and multiplication results for function spaces.
result Unified set of interior estimates and regularity inference for operators with Sobolev-type coefficients.
MIC consistently estimates dependence in large datasets.
problem Estimating dependence between variable pairs in large datasets.
method Proving consistency of MIC as an estimator.
result MIC is a consistent estimator of population statistic MIC*.
Improved portfolio optimization using Kendall-like correlation coefficients.
problem Accurate estimation of eigenvectors in data-poor regimes for portfolio optimization.
method Developed generalized correlation coefficients based on Kendall's rank correlation.
result Markowitz portfolios with lower out-of-sample risk using these coefficients.
New method for estimating high-dimensional binary time series coefficients.
problem Statistical inference for high-dimensional binary time series.
method Post-selection estimator and second-order wild bootstrap algorithm.
result Good finite-sample performance of the proposed method.
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the estimation of such processes using constrained and penalized estimators. As an applica…
Study reconstructs Faber-Schauder coefficients from antiderivative observations.
problem Reconstructing Faber-Schauder coefficients from discrete antiderivative observations.
method Piecewise quadratic spline interpolation and closed-form solution.
result Final-generation coefficients are unstable; others are robust.
The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.
problem Estimation of high-dimensional piecewise-constant regression coefficients.
method Formulated a restricted isometry condition for the fused lasso estimator and derived estimation bounds.
result The estimation error can be dominated by either the lasso or the fused lasso rate, depending on the number of non-zero coefficients and piece-wise constant segments.
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficient…
Paper proposes methods for transfer learning with random coefficient ridge regression.
problem Estimation and prediction in high-dimensional settings with related models.
method Two estimators using weighted sums of ridge estimates from target and source models.
result Explicit expression of estimation and prediction risks derived using random matrix theory.
Estimates LLC for deep linear networks up to 100M parameters.
problem Quantifying model complexity for large-scale deep learning architectures.
method Empirical estimation of LLC using a method developed for DLNs.
result LLC can be accurately measured for DLNs up to 100M parameters.
We consider the problem of predicting several response variables using the same set of explanatory variables. This setting naturally induces a group structure over the coefficient matrix, in which every explanatory variable corresponds to a set of related coefficients. Most of the existing methods that utilize this gro…
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.
Improved model-free reinforcement learning with decision-estimation coefficient.
problem Interactive decision making, including structured bandits and reinforcement learning.
method Combining Estimation-to-Decisions with optimistic estimation to achieve better regret bounds.
result Regret bounds for model-free reinforcement learning with value function approximation.
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Efficiently estimates shrinkage coefficient for RTME using LOOCV approximation.
problem Estimating optimal shrinkage coefficient for Regularized Tyler's M-estimator.
method Proposes an approximate LOOCV method to estimate α efficiently. result Significant speedup and accuracy improvement over existing methods.
In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the …
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
The paper discusses methods for interval estimation of coefficients in penalized regression models for insurance data.
problem Valid inference on coefficients after feature selection in GLM family for insurance data.
method Proposes methodologies for constructing confidence intervals of coefficients after feature selection in GLM family.
result Valid inference on coefficients after feature selection in GLM family for insurance data.
Study Fourier estimator for spot volatility with unbounded coefficients and jumps.
problem Estimating spot volatility with unbounded coefficients and jumps in price process.
method Fourier estimator for spot volatility, convergence analysis for unbounded coefficients and jumps.
result Convergence of trigonometric polynomial to volatility's path, almost sure convergence of reconstructed volatility.
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators, where performance is evaluated using a matrix-weighted two-norm of the defect of …
We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this …
Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.
problem Functional predictor selection and estimation of smooth functional coefficients in high-dimensional multivariate functional data.
method Functional group-sparse regression methods in a generic Hilbert space of infinite dimension.
result Consistency of estimation and selection (oracle property) under infinite-dimensional Hilbert spaces.
Characterizes braid types and estimates twist coefficients.
problem Understanding braid types and their properties.
method Birman-Ko-Lee left canonical form of braids.
result Characterization of almost strongly quasipositive braids and estimates of fractional Dehn twist coefficient.
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level. The iterat…
A new method estimates the learning coefficient using empirical loss.
problem Estimating the learning coefficient in complex models.
method Numerical estimation using Empirical Loss.
result Our method outperforms existing techniques in terms of bias and variance.
Efficiently estimates sparse linear regression with heavy-tailed data and outliers.
problem Sparse estimation of linear regression coefficients with heavy-tailed covariates and noises, including outliers.
method Efficient computation of robust estimator with nearly optimal error bound.
result Nearly optimal error bound for robust sparse estimation.
This paper addresses parameter estimation for wave equations with Markovian switching.
problem Parameter estimation for wave equations with abrupt changes.
method Bayesian statistical framework using discrete sparse Bayesian learning.
result Strong performance in parameter estimation for variable coefficient PDEs.
New loss function improves accuracy of MRI parameter estimation.
problem Systematic errors in parameter estimates at low SNR.
method Developed and implemented negative log Rician likelihood (NLR) loss.
result NLR loss shows higher accuracy in parameter estimation than MSE loss at low SNR.
The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-ℓ1-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces …
Improved 3D LiDAR data classification using product coefficients.
problem Enhancing accuracy in 3D LiDAR data classification.
method Introducing product coefficients derived from measure theory as additional features in the classification process, alongside PCA.
result Significant improvement in classification accuracy with product coefficients.
Bayesian approach improves network lasso for multi-task learning.
problem Improving the determination of relational coefficients in network lasso.
method Proposes a Bayesian approach to solve multi-task learning problems using network lasso.
result Objective determination of relational coefficients through Bayesian estimation.
We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results…
Proposes a Varying-Coefficient MoE model for analyzing dynamic data.
problem Inadequate constant coefficients in MoE models for dynamic settings.
method Varying-Coefficient Mixture of Experts (VCMoE) model with varying coefficients in gating and expert models.
result Established identifiability and consistency of the VCMoE model.
New algorithm recovers model coefficients and supports from noisy data.
problem Simultaneous estimation and support recovery in linear models with Gaussian noise.
method Projection-based algorithm for STG regularized minimization problem, proving convergence and support recovery guarantees.
result New algorithm outperforms existing methods in support recovery for various data setups.
New method calibrates asynchronous, error-prone covariates for longitudinal data.
problem Estimation biases and slow convergence in analyzing time-varying covariates with measurement error.
method Functional calibration approach based on functional principal component analysis.
result Asymptotically unbiased and consistent estimators for time-invariant coefficients; optimal convergence rate for time-varying coefficients.
This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correl…
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank minrelation coefficient. We define a minrelation of X to Y (or equivalently a majrela…
For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.
New method for MTL with varying sparsity patterns across tasks.
problem Jointly training multiple linear models with differing sparsity patterns.
method Mixed-integer programming formulation and scalable algorithms.
result Our methods leverage shared support information to improve variable selection.
LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.
problem Analyzing trade-offs between privacy and utility in estimation problems.
method Equivalence of LDP constraints to contraction coefficients of E_γ-divergence, using f-divergences and estimation-theoretic tools.
result LDP guarantees can be expressed in terms of contraction coefficients of arbitrary f-divergences.
Proposes a model for time-varying regression coefficients.
problem Uncertainty in forecasting due to changing correlations over time.
method Adopting state space literature, models how regression coefficients change over time.
result Accurate estimates for continuous outcomes but fails for binary outcomes.
Simplifies NL models by approximating them as LPV systems and identifying NL subterms.
problem Complex NL models are hard to interpret and impractical.
method Linear approximation around operating points, sparse estimation in RKHS, LPV model reduction.
result Identifies NL subterms and their input spaces in sparse additive NL models.
Estimates mixing coefficients of geometrically ergodic Markov processes from a single sample path.
problem Estimating mixing coefficients of geometrically ergodic Markov processes.
method Proposes methods to estimate β-mixing coefficients from a single sample path under standard smoothness conditions. result Obtains a rate of convergence of order \(\mathcal{O}(\log(n) n^{-[s]/(2[s]+2)})\) for the expected error of the estimator.
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate settings, studies its relationship with Bayes risk and mutual information, proposes an efficient importance sampling estimator.
result UNL as a measure of dependence between group labels and variables of interest, interpretable measure of partition-covariate dependence in clustering.
Direct measurements of Gini coefficients by conventional arithmetic calculations are a poor estimator, even if paradoxically, they include the entire population, as because of super-additivity they cannot lend themselves to comparisons between units of different size, and intertemporal analyses are vitiated by the popu…
Bayesian method discovers PDEs with variable coefficients robustly.
problem Discovering PDEs from noisy data is challenging.
method Bayesian sparse learning with tBGL-SS and Gibbs sampler.
result Method enhances robustness and model selection criteria.
Paper addresses high-dimensional linear regression with missing data, proposing efficient and nearly unbiased estimators.
problem High-dimensional linear regression with blockwise missing covariates and partially observed responses.
method Proposes a computationally efficient estimator and nearly unbiased debiased estimators using blockwise imputation and estimating equations.
result Asymptotically valid confidence intervals and statistical tests constructed based on debiased estimators.
Novel method estimates complex nonlinear systems with stochastic differential equations.
problem Handling complex nonlinear dynamical systems with strong learning guarantees.
method Estimates drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations.
result Strong theoretical guarantees including finite-sample bounds for various metrics.