Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
New algorithm selects features using Catastrophe model for better regression analysis.
problem Improving feature selection in regression analysis to enhance model performance.
method The algorithm ranks features based on their fit to the Catastrophe model and uses Akaike information criterion for ranking.
result The proposed algorithm outperforms RELIEF in various datasets.
SplitWise enhances stepwise regression by adaptively encoding numeric predictors into binary features.
problem Capturing nonlinear relationships in regression models without sacrificing interpretability.
method Adaptive encoding of numeric predictors into binary features using shallow decision trees, assessed by AIC or BIC.
result Consistently produces more parsimonious and generalizable models than traditional techniques.
We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is generated from a finite order autoregression, the Bay…
OGA and HDAIC improve high-dimensional regression with dependent data.
problem High-dimensional linear regression with dependent observations.
method Orthogonal greedy algorithm (OGA) and high-dimensional Akaike's information criterion (HDAIC).
result OGA and HDAIC achieve optimal convergence rate without knowing sparsity.
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…
We propose to use nonparametric Bernstein copulas as bivariate pair-copulas in high-dimensional vine models. The resulting smooth and nonparametric vine copulas completely obviate the error-prone need for choosing the pair-copulas from parametric copula families. By means of a simulation study and an empirical analysis…
The paper reviews and applies GLMs in actuarial analysis.
problem Analyzing actuarial situations using generalized linear models.
method Assess model adequacy using deviance and Akaike information criterion.
result Best chosen GLM model accurately predicts claims in an automobile portfolio.
In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the predictive complexity. In the large-sample-size limit of a regular model, the predicti…
Paper uses referenced thermodynamic integration for Bayesian model selection in a complex COVID-19 transmission model.
problem Bayesian model selection with uncertainty and misleading metrics.
method Referenced thermodynamic integration for intractable high-dimensional distributions.
result Favourable convergence performance in model selection for COVID-19 transmission.
Modeling air pollutants using data-driven techniques and sparse identification of nonlinear dynamics.
problem Predicting concentrations of air pollutants using hidden physical laws.
method Sparse identification of nonlinear dynamics (SINDy) for parsimonious systems of ordinary differential equations.
result More than half of the critical points are saddle points, indicating system instability.
SIC detects elbows in error curves automatically.
problem Automatic elbow detection in error curves.
method Spectral information criterion (SIC) extracts geometric features of error curves.
result SIC provides a subset of models with smaller cardinality than total possible models.
The paper derives an equation linking WAIC and WBIC for singular models.
problem In singular models, conventional criteria fail due to likelihood and posterior breakdown.
method Theoretical derivation linking WAIC and WBIC.
result An asymptotic equation linking WAIC and WBIC for singular models.
We study the dynamical behavior of high-frequency data from the Korean Stock Price Index (KOSPI) using the movement of returns in Korean financial markets. The dynamical behavior for a binarized series of our models is not completely random. The conditional probability is numerically estimated from a return series of K…
We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature for other high-frequency financial data are only approximately valid. As a conseq…
The study evaluates three IC for selecting Hawkes process model order in financial data.
problem Model selection for Hawkes process with financial data.
method Testing AIC, BIC, HQ on simulated data.
result Correct model selection success rate varies with sample size and IC type.
Study predicts stream turbidity using surrogate data and meta-model.
problem Costly turbidity sensor deployment limits monitoring networks.
method Dynamic regression (ARIMA), LSTM, GAM models; surrogate covariates (rainfall, water level, temperature, solar exposure); meta-model combining strengths of individual models.
result ARIMA and GAM models with all covariates outperform single models; meta-model yields highest accuracy.
Proposes SNML for selecting word2vec Skip-gram dimensionality.
problem Selecting optimal dimensionality for word2vec Skip-gram models.
method Information criteria (AIC, BIC, SNML) applied to SG and SG Negative Sampling models.
result SNML outperforms AIC and BIC, selecting closer optimal dimensionality.
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include K-fold cross-validation (K-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for lo…
Bayesian BIC for multi-trial data improves VAR model order selection.
problem Optimal VAR model order selection for multi-trial event-based data.
method Derive and apply Bayesian Information Criterion (BIC) for multi-trial ensemble data.
result Multi-trial BIC successfully recovers real model order and estimates small model order.
Study forecasts cardiology admissions from cath lab using ARIMA models.
problem Complexity in managing cardiology admissions from cath lab.
method Retrospective data analysis with ARIMA, Holts method, and other models.
result ARIMA (2,0,2) (1,1,1) model selected as best fit.
Paper introduces NICc for fast cluster-based validation of prediction models.
problem Validation of prediction models on clustered data.
method Derived NICc to approximate leave-one-cluster-out deviance for standard regression models.
result NICc provides more accurate model size and variable selection, especially with strong clustering.
Automates model selection for GLMs using optimization.
problem Automating model selection for generalized linear models.
method Mixed-integer conic optimization for feature subset selection and model constraints.
result Optimization of AIC and BIC criteria with multicollinearity constraints.
In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. Howe…
Efficiently estimates covariance for sparse functional data.
problem Sparse data in functional analysis.
method Random-knots and B-spline estimators for covariance function.
result Asymptotic pointwise covariance estimates for sparsified data.
Unified framework for SGMoE resolves estimation and selection issues.
problem Non-identifiability, coupled differential relations, and tight coupling in softmax-Gated models.
method Unified statistical framework with Voronoi-type loss functions and dendrograms of mixing measures.
result Consistent selection of the number of experts without model sweeps, optimal parameter rates under overfitting.
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or w-prior) which unifies objective Bayes and information-based inference. The w-prior is chosen to make the marginal probability an unbia…
New method speeds up model selection for complex scientific tasks.
problem Exhaustive model selection is computationally infeasible for large model spaces.
method Branch-and-bound algorithm with non-monotonic criteria.
result Guaranteed identification of optimal models with significant computational speedups.
New estimator for prediction error using AMP algorithm for sparse penalties.
problem Estimating prediction error for penalized linear regression models.
method Approximate message passing (AMP) algorithm for calculating generalized degrees of freedom.
result Asymptotically unbiased estimator for Gaussian distributed predictors.
Bayesian methods improve OoD detection in deep networks.
problem Detecting Out-of-Distribution (OoD) inputs in deep neural networks.
method Three Bayesian inference approaches applied to VAE weights.
result Improved OoD detection scores over benchmarks.
The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard quadratic penalty is exactly analogous to the energy of a stretched string, with the p…
The ℓ-1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the ℓ-1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path …
Paper proposes a novel method to accurately determine the number of experts in Gaussian-gated Gaussian MoE models.
problem Challenges in model selection for MoE models, especially with covariates.
method Introduces a novel extension using dendrograms of mixing measures to estimate the true number of mixture components.
result Achieves optimal convergence rates for parameter estimation and accurately approximates the regression function.
Bayesian method improves PCA and MUSIC for unknown number of sources.
problem Estimating the number of sources in PCA and MUSIC algorithms.
method Bayesian inference for computing the exact MAP estimate of the number of sources.
result Bayesian method outperforms AIC in estimating the number of sources.
A new strategy selects k in k-NN regression without hold-out data.
problem Choosing optimal k in k-NN regression without hold-out data.
method Iterative procedure over k, minimum discrepancy principle.
result Minimax-optimal over smoothness function classes.
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.
GWRBoost improves GWR for better spatial relationship quantification.
problem Underfitting in GWR for complex data and lack of explainable quantification.
method Geographically weighted gradient boosting model using localized additive model and gradient boosting optimization.
result Significant improvement in RMSE and AICc compared to classic GWR.
The study finds that firm membership in flagship indices and TCFD endorsement are strong predictors of a wider Disclosure-Performance Gap.
problem The Aggregate Confusion hypothesis and the measurement of greenwashing in environmental disclosures.
method The study uses a Disclosure-Performance Gap (DPG) model to measure the divergence between voluntary environmental disclosures and realised emissions performance for 200 large European firms. The model selection process involved multiple stages and robust standard errors.
result Firm membership in flagship indices and TCFD endorsement are strong predictors of a wider gap, while renewable energy use and environmental capital expenditure significantly narrow the gap.
Develops new Markov processes with switching rates and past dependence.
problem Modeling processes with dynamic switching rates and path dependence.
method Introduces a new class of Markov jump processes with regime switching and path dependence. Derives distributional properties and maximum likelihood estimates.
result Maximum likelihood estimates of the process parameters are derived in closed form and have asymptotic normality.
A new method for averaging model predictions using minimum divergence.
problem Improving model averaging methods, especially in small samples.
method Minimum divergence framework for model weight calculation.
result Empirically outperforms standard model averaging methods.
Study disproves a generalized numerical criterion for certain pairs.
problem Generalized numerical criterion for pairs
method Provided counterexamples
result Negative answer to the generalized numerical criterion problem
New polynomial criterion for periodic knots identified.
problem Identifying periodic knots efficiently.
method Examined HOMFLY-PT and Kauffman polynomials of periodic links.
result Criterion is stronger than existing methods.
Adjustment reduces bias in widely applicable Bayesian information criterion.
problem Overestimation of widely applicable Bayesian information criterion.
method Identified and adjusted an overestimating term in the criterion.
result Asymptotically unbiased estimator of log marginal likelihood.
New algorithms optimize a soft-robust criterion in reinforcement learning, reducing conservatism.
problem Computing robust policies for high-stakes decisions with limited data.
method Soft-robust criterion using risk measures, two algorithms for optimization.
result Our algorithms produce less conservative solutions than existing methods.
Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.
problem Establishing improved logarithmic Sobolev inequalities and monotonicity of Tsallis entropy.
method Proving a one-parameter family of weighted Bakry-Émery Γ2 criterion inequalities and a modified inequality. result Yields a family of sharp Sobolev inequalities and monotonicity of Tsallis entropy.
The paper provides a sliceness criterion for stably odd knots.
problem Sliceness of stably odd knots
method Analyzes cobordisms and free knots to derive a sliceness criterion
result A sliceness criterion for stably odd knots
New criterion improves predictive evaluation in weighted inference scenarios.
problem Improving predictive evaluation in scenarios with different likelihoods for estimation and evaluation.
method Developed the posterior covariance information criterion (PCIC) to handle weighted likelihood inference.
result PCIC is asymptotically unbiased for quasi-Bayesian generalization error in weighted inference.
Criterion for stopping conjugacy class enumeration in triangle groups.
problem Enumerating all conjugacy classes in cocompact triangle groups.
method Encoding by P. Dehornoy and T. Pinsky; stopping criterion based on geometric length.
result Stopping criterion for the generation of conjugacy classes in cocompact triangle groups.