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
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48 results for “numerical criterion”
Criterion for solvability of complex 2-Hessian equation on compact Kähler manifolds.
problem Solvability of complex 2-Hessian equation on compact Kähler manifolds.
method Nakai--Moishezon-type criterion associated with the complex 2-Hessian equation.
result Criterion equivalent to existence of a smooth 2-admissible representative in complex dimension three.
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…
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.
New criterion for solving inverse Hessian equations, including J-equation.
problem Existence of solutions to inverse Hessian equations, including J-equation.
method Stability of pairs in the sense of Paul, formulated in terms of GIT criterion.
result New numerical criterion for existence of solutions to inverse Hessian equations.
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.
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…
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.
Criterion for realizing groups on Enriques manifolds.
problem Realizing groups on Enriques manifolds.
method Using recent developments in Birman-Hilden theory and Nielsen realization for hyper-Kähler manifolds.
result Numerical criterion for realizing groups on Enriques manifolds.
We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…
Selection of tuning parameters in bridge regression models via Bayesian information criterionstat.ME
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be v…
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum …
Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterionmath.OC
New approach to optimal dividend control with mean-variance criterion.
problem Balancing expected dividends and variability in a singular control framework.
method Game-theoretic approach to find time-consistent equilibrium strategies.
result Verification theorem for MV singular dividend control problem.
A new Bayesian optimization method tackles constrained optimization with uncertainties.
problem Optimizing functions with uncertain constraints.
method Bayesian optimization with a new acquisition criterion.
result The new criterion optimizes both objective function improvement and constraint reliability.
A new criterion selects models in overparameterized settings.
problem Model selection for overparameterized models with more parameters than data.
method Establishes Bayesian duality and introduces the Interpolating Information Criterion.
result The Interpolating Information Criterion selects models in overparameterized settings.
On the modified -equationmath.DG
The paper studies the modified J-equation on Kähler manifolds.
problem Solvability of the modified J-equation on compact Kähler manifolds.
method Characterization of solvability via coercivity of the modified J-functional; Nakai-Moishezon criterion formulation and verification.
result Extension of existence criteria for extremal Kähler metrics.
Let X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria guaranteeing various positivity conditions for the log-canonical divisor K_X+D. …
Quantum strategy optimizes wealth growth in a double-or-nothing game.
problem Optimizing wealth growth in a quantum double-or-nothing game.
method Numerical determination of the optimal quantum strategy.
result The quantum strategy outperforms the classical Kelly criterion.
Let X be a projective manifold. We prove that the Mabuchi Energy of X is bounded below on all degenerations in B (the space of Bergman metrics) if and only if it is bounded below uniformly on B.
Proposes a method to solve deep neural networks' local minimum problem.
problem Local minimum problem in deep neural networks training.
method Transforms cross-entropy loss into risk-averse error criterion, adjusts RSI, and uses convexity region.
result Trained deep learning machine is expected to be inside a global minimum's attraction basin.
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.
This paper introduces a more efficient method for estimating level sets with a stopping criterion.
problem Efficiently estimating regions where a function exceeds a threshold without exhaustive evaluations.
method Acquisition strategy with a stopping criterion for -accurate level set estimation.
result The method satisfies -accuracy with a confidence level of and guarantees on lower bounds of performance metrics.
Paper optimizes portfolios for absolute return funds with constraints.
problem Optimizing portfolios with constraints for absolute return funds.
method Stochastic control framework with numerical solution using kernel-based collocation method.
result Leverage is necessary to achieve the target level.
We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula for the generalised futaki invariant interms of weights and multiplicities of t…
Study quantifies model risk in dynamic portfolio selection using KL divergence.
problem Model risk in financial portfolio selection under uncertainty.
method Defined model risk as KL divergence loss, solved nonlinear equations for optimal robust strategy.
result Optimal robust strategy can be obtained semi-analytically in worst case scenario.
Factorized information criterion (FIC) is a recently developed approximation technique for the marginal log-likelihood, which provides an automatic model selection framework for a few latent variable models (LVMs) with tractable inference algorithms. This paper reconsiders FIC and fills theoretical gaps of previous FIC…
In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and non-Lipschitz problem, we develop a non-monotone alternating updating method based o…
We consider the problem of maximizing a real-valued continuous function using a Bayesian approach. Since the early work of Jonas Mockus and Antanas Žilinskas in the 70's, the problem of optimization is usually formulated by considering the loss function (where denotes the best function value ob…
The economic equities maximization criterion (MFPE) leads to the choice of financial portfolio, which maximizes the ratio of the expected value of the insurance company on the capital. This criterion is presented in the framework of a non-life insurance company and is applied within the framework of the French legislat…
Bayesian nonparametrics improves data-driven risk optimization under distributional uncertainty.
problem Improving out-of-sample performance in machine learning models due to distributional uncertainty.
method Combining Bayesian nonparametric theory and decision-theoretic preferences to propose a robust optimization criterion.
result The proposed robust optimization procedure provides favorable statistical guarantees and tractable approximations.
Optimal reinsurance contracts for multiple dependent risks are derived without specific dependency assumptions.
problem Finding optimal reinsurance contracts for multiple dependent risks without assuming their dependency structure.
method Assumes maximal expected utility criterion and independent negotiation of reinsurance for each risk. Derives optimality conditions and shows that under mild assumptions, optimal contracts are classical (non-randomized) type.
result Optimal reinsurance contracts exist and can be classical (non-randomized) type under mild assumptions.
The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.
problem Defining angular momentum at null infinity and ensuring its continuity across different cross-sections.
method Introducing cross-section continuity as a criterion and proving it for specific angular momentum definitions.
result The Chen-Wang-Yau definition of angular momentum satisfies cross-section continuity, while the Compere-Nichols modification does not.
K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, in particular in cases involving non-i.i.d. data. This paper analyzes …
One of the longstanding open problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. We propose automated mode…
Develops an actor-critic algorithm for risk-sensitive Markov decision processes.
problem Risk-sensitive cost criterion in Markov decision processes.
method Actor-critic algorithm with function approximation.
result Asymptotic convergence of the actor-critic algorithm.
Deep Knockoffsstat.ME
This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion i…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is well-studied, under frameworks such as independent component analysis and constrained matrix…
Resolution and Scale Independent Function Matching Using a String Energy Penalized Spline Priorstat.ML
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…
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.
Proposes a more robust rating scale for banks.
problem Inconsistent rating scale validation leading to higher capital requirements.
method Develops a new rating scale that is statistically distinguishable and robust.
result Reduces the calibration probability of default, saving capital requirements.
A new method for automatic gradient tree boosting using information theory.
problem Automatic selection of tree complexity and number in gradient boosting.
method Optimism of greedy leaf splitting procedure modeled as a Cox-Ingersoll-Ross process, leading to an information criterion for model selection.
result The method achieves significant speedups (10-1400) compared to xgboost without sacrificing predictive power.
It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the…
Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor's wealth and the factors. These formulas enable fast computation of a wide range of i…
Bayesian optimization uses triangulation candidates for better performance.
problem Non-convex and multi-modal optimization challenges in Bayesian optimization.
method Proposes using Delaunay triangulation candidates for discrete search over continuous optimization.
result Triangulation candidates outperform numerically optimized and random alternatives.
This paper analyzes a game between insurer and reinsurer under ambiguity and risk aversion, optimizing reinsurance and investment strategies.
problem Optimizing reinsurance and investment strategies in a game between insurer and reinsurer under ambiguity and risk aversion.
method Stackelberg game, -maxmin mean-variance criterion, Heston's stochastic volatility, Hamilton-Jacobi-Bellman equations, Riccati differential equations.
result Excess-of-loss reinsurance is optimal for the insurer, and the equilibrium strategies are determined by specific equations.
Paper introduces a novel approach to generalize models without validation data.
problem Achieving generalization in machine learning without validation data.
method Introduces a new risk measure and a novel criterion for training models.
result Demonstrates that the new approach outperforms popular methods in generalization and estimation tasks.
New test for SGD in binary classification reduces computation time.
problem Determining optimal stopping for SGD in binary classification.
method Proposes a new, simple, computationally inexpensive termination criterion for SGD.
result Termination criterion reduces expected misclassification probability.
New method improves matrix completion accuracy, especially in noisy data.
problem Noisy matrix completion in recommendation systems and signal processing.
method Residual Spectral Matching criterion and pseudo-gradient algorithms.
result Improved numerical performance in noisy data environments.