We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), whi…
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48 results for “data fitting error”
Analysis of different Mathematical Models for Different Case Studies Using Statistical Fittingmath.DG
Study evaluates different mathematical models for three case studies using statistical fitting.
problem Estimating outcomes in population dynamics, temperature variations, and market equilibrium.
method Applied various statistical equations (e.g., fractional exponential, sinusoidal) to three case studies.
result Optimal models differ by case study (fractional exponential for population dynamics, sinusoidal for temperature and market equilibrium).
Study shows how varying levels of supervision and orthonormality constraints affect generalization errors in subspace fitting.
problem Effects of varying levels of supervision and orthonormality constraints on generalization errors in subspace fitting.
method Flexible family of problems connecting unsupervised and supervised subspace fitting tasks, explored over a supervision-orthonormality plane.
result Generalization errors of subspace fitting problems follow double descent trends as they become more supervised and less orthonormally constrained.
Near-convex archetypal analysis improves interpretability and fitting error in NMF.
problem High data fitting error in traditional archetypal analysis.
method Introduces near-convex archetypal analysis (NCAA) that combines AA and NMF.
result NCAA achieves lower data fitting error than state-of-the-art methods.
Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some circumstances it may happen that the two lower-dimensional data sets have an inordinat…
In regression modelling approach, the main step is to fit the regression line as close as possible to the target variable. In this process most algorithms try to fit all of the data in a single line and hence fitting all parts of target variable in one go. It was observed that the error between predicted and target var…
Cross-validation estimates model performance on unseen data, not training data.
problem Understanding how cross-validation estimates prediction error and its limitations.
method Analyzing linear models and popular prediction error estimates, introducing nested cross-validation.
result Cross-validation estimates the average prediction error of models fit on other unseen training sets, not the model at hand.
When a feed-forward neural network (FNN) is trained for source ranging in an ocean waveguide, it is difficult evaluating the range accuracy of the FNN on unlabeled test data. A fitting-based early stopping (FEAST) method is introduced to evaluate the range error of the FNN on test data where the distance of source is u…
When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise fit and estimation error. We then show (2) how to use the adjust…
Paper proposes algorithms to accurately identify breakpoints in piecewise regression.
problem Identifying accurate breakpoints in piecewise regression for better data fitting.
method Proposes novel greedy algorithms to minimize error and determine optimal breakpoints.
result The proposed algorithms outperform existing methods in accuracy and efficiency.
Sparse feature selection improves batch RL efficiency.
problem High-dimensional batch RL with many features.
method Sparse linear function approximation, Lasso, group Lasso, fitted Q-evaluation, fitted Q-iteration.
result Sparse feature selection makes batch RL more sample efficient.
Traditionally in regression one minimizes the number of fitting parameters or uses smoothing/regularization to trade training (TE) and generalization error (GE). Driving TE to zero by increasing fitting degrees of freedom (dof) is expected to increase GE. However modern big-data approaches, including deep nets, seem to…
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
The Local Volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide range of implied volatility surfaces. The model is easy to calibrate and still ve…
Bayesian parameter estimation of miss-specified modelsphysics.data-an
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the model, the model error as well as the statistics of the model error. This method…
FORE evaluates occupancy ratios without requiring Bellman completeness.
problem Offline reinforcement learning occupancy ratio estimation.
method Fitted occupancy-ratio evaluation (FORE) using adjoint Bellman recursion.
result FORE achieves convergence in KL without Bellman completeness.
New method improves causal structure discovery with Prior-Fitted Networks.
problem Errors in likelihood estimation limit proper causal structure discovery.
method Amortized causal discovery with Prior-Fitted Networks.
result Significant gains in structure recovery compared to baselines.
Sparse learning with CARTstat.ML
The paper studies statistical properties of CART regression trees.
problem Understanding the statistical properties of CART regression trees.
method The paper constructs a prior distribution on split points and solves a nonlinear optimization problem to bound the Pearson correlation between the optimal decision stump and response data.
result CART with cost-complexity pruning achieves an optimal complexity/goodness-of-fit tradeoff when the depth scales with the logarithm of the sample size.
TD learning reduces prediction error in Markov chain problems.
problem Estimating value functions in Markov chains with temporal inconsistency.
method Temporal difference learning minimizes temporal inconsistency between successive estimates.
result TD learning can significantly reduce mean-squared error in value estimates.
We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled…
A new method treats all variables equally in fitting data.
problem Fitting relationships to data with multiple variables, especially when dependent and independent variables are not clearly defined.
method A general method treating all variables impartially, using geometric mean functional relationships and correlation.
result The method provides coefficients that are easily calculated from covariances or correlations, making it scale-invariant and applicable to various units.
AHS framework selects hyperparameters for FQE with error guarantees.
problem Hyperparameter selection for FQE is challenging and affects its utility.
method AHS framework defines optimality criteria without hyperparameters.
result Error bounds match empirical observations.
Improved estimators for causal inference using cross-fitting and undersmoothing.
problem Estimating expected conditional covariance in causal inference.
method Double cross-fit doubly robust (DCDR) estimators with undersmoothing for non-smooth nuisance functions.
result DCDR estimators achieve -consistency and asymptotic normality under minimal conditions.
Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly identifying a significant (but perhaps small) segment of a population in which there is a…
Two methods monitor high-dimensional processes via manifold fitting or learning.
problem Monitoring high-dimensional, dynamic industrial processes.
method Manifold fitting and learning approaches for online SPC.
result Manifold-fitting approach achieves performance competitive with classical methods.
New method stabilizes FQE by reweighting Bellman targets.
problem Stability guarantees for FQE often rely on Bellman completeness, which can fail with function approximation.
method Proposes stationary-weighted FQE, reweighting Bellman targets by stationary target-to-behavior density ratio.
result Proves finite-sample linear convergence to stationary projected Bellman fixed point without Bellman completeness.
Memorizing without overfitting: Bias, variance, and interpolation in over-parameterized modelsstat.ML
New insights into bias and variance in over-parameterized models.
problem Understanding bias and variance in over-parameterized models.
method Analytic expressions derived from statistical physics for two minimal models.
result Over-parameterized models can overfit even in noiseless conditions.
This paper presents an alternative approach to p-values in regression settings. This approach, whose origins can be traced to machine learning, is based on the leave-one-out bootstrap for prediction error. In machine learning this is called the out-of-bag (OOB) error. To obtain the OOB error for a model, one draws a bo…
In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for regularization, we develop an approach re-fitting the results of standard methods towards the input d…
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how…
Deep Learning-Based Estimation and Goodness-of-Fit for Large-Scale Confirmatory Item Factor Analysisstat.ML
New deep learning methods improve estimation and GOF assessment for large-scale IFA.
problem Estimating and assessing goodness-of-fit for large-scale confirmatory IFA models.
method Extended deep learning algorithm for parameter estimation and simulation-based tests for GOF assessment.
result Proposed methods provide comparable estimates and detect latent dimensionality misspecification.
Study improves model fit by transferring info from related datasets.
problem Improving model fit on target data using source data.
method Proposes a transfer learning algorithm for GLMs, derives error bounds, and introduces detection of informative sources.
result Theoretical and practical improvements over classical methods in high-dimensional GLM settings.
The paper describes fitting submanifolds to data using Sussmann's orbit theorem.
problem Fitting an immersed submanifold to random samples.
method Uses Sussmann's orbit theorem to ensure submanifold fitting. Reconstruction involves encoding times and decoding via flows of vector fields.
result A high-probability bound on excess risk for the reconstruction error.
Examines performance metrics for ML models in engineering.
problem Identifying proper assessment metrics for ML models.
method Analyzes commonly-used metrics for regression and classification.
result Identifies key performance metrics for ML models.
LLMs are vulnerable to task-irrelevant data changes, limiting their use for data fitting.
problem LLMs' sensitivity to task-irrelevant variations in data representation.
method Analysis of LLMs' performance and attention patterns under various data manipulations.
result LLMs are sensitive to task-irrelevant variations, leading to significant prediction errors.
A new method for combining multiple data views in supervised learning.
problem Combining multiple data views in supervised learning, especially in biology and medicine.
method Cooperative learning combines squared error loss with an agreement penalty to encourage predictions from different data views to agree.
result Cooperative learning achieves higher predictive accuracy on simulated and real multiomics data.
New test improves clustering accuracy for Gaussian mixtures.
problem Improving clustering accuracy for Gaussian mixtures.
method Relative fit test for Gaussian Mixture Models.
result New test provides provable error control and higher power.
Two new algorithms improve Q* approximation in batch RL with linear error propagation.
problem Improving Q* approximation in batch reinforcement learning.
method Two novel algorithms that estimate Bellman error directly, without quadratic dependence.
result Linear-in-horizon error propagation for batch RL algorithms.
We predict generalization error across model and dataset sizes.
problem Understanding the dependency of neural network generalization error on model and dataset size.
method Model scaling concept applied to construct a functional form of generalization error.
result The constructed functional form accurately predicts generalization error across scales.
Memorize to Generalize: on the Necessity of Interpolation in High Dimensional Linear Regressionstat.ML
Optimal machine learning requires interpolating training data in high-dimensional linear regression.
problem Achieving optimal predictive risk in overparameterized linear regression models.
method Analyzing proportional asymptotics of random design and label noise variance.
result Optimal performance in linear regression requires fitting training data to higher accuracy than inherent noise.
Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of…
A new method calibrates value predictions in offline RL to improve reliability.
problem Difficulty in long-horizon value prediction in offline reinforcement learning.
method Bellman calibration, a weak reliability criterion, and Iterated Bellman Calibration.
result Finite-sample guarantees show that Bellman calibration error is controlled at nonparametric rates.
New GLS estimator handles high-dimensional data with autocorrelated errors.
problem High-dimensional regressions with autocorrelated errors.
method LASSO regression, autoregressive model fitting, and whitening.
result The method outperforms unadjusted LASSO in estimating errors driven by autoregressive processes.
Analyzes bias-variance in overparameterized linear models using random features.
problem Understanding bias-variance trade-off in overparameterized models.
method Zero-temperature cavity method and random matrix theory.
result Three phase transitions in the linear random features model.
Proposes a method to learn policies from offline data with reduced bias.
problem Learning policies from offline data with reduced bias and complexity constraints.
method Cross-fitted debiasing device for policy learning from offline data.
result Achieves regret for complex policy classes with a product-of-errors nuisance remainder.
DP models misspecify LF dependencies, leading to significant performance errors.
problem Misspecification of LF dependencies in DP models.
method Theoretical bounds and empirical analysis of modeling errors.
result Modeling errors can be substantial, even with sensible LF structures.
Data mining and machine learning techniques such as classification and regression trees (CART) represent a promising alternative to conventional logistic regression for propensity score estimation. Whereas incomplete data preclude the fitting of a logistic regression on all subjects, CART is appealing in part because s…
MEC: Machine-Learning-Assisted Generalized Entropy Calibration for Semi-Supervised Mean Estimationstat.ML
MEC improves efficiency and robustness in semi-supervised inference.
problem Efficient inference with limited labeled data and robust uncertainty quantification.
method Machine-Learning-Assisted Generalized Entropy Calibration (MEC) using cross-fitted, calibration-weighted PPI.
result MEC achieves semiparametric efficiency bounds under weaker assumptions and provides near-nominal coverage.