We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
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48 results for “consistency conditions”
The paper establishes conditions for Bayesian consistency in supremum metric.
problem Ensuring Bayesian consistency in the supremum metric.
method Using a triangle inequality and weak convergence, the paper establishes conditions for Bayesian consistency.
result Demonstrates supremum consistency with weaker conditions than previously used.
Enhanced -consistency bounds derived under relaxed conditions.
problem Quantifying the relationship between zero-one estimation error and surrogate loss estimation error.
method Relaxing the condition on the surrogate loss conditional regret and presenting a general framework for establishing enhanced -consistency bounds.
result Derivation of more favorable -consistency bounds in various scenarios.
Enhanced consistency bounds derived for classification under a new noise condition.
problem Enhanced consistency bounds for classification under a new noise condition.
method Model Margin Noise (MM noise) assumption, derived enhanced H-consistency bounds.
result Enhanced H-consistency bounds under MM noise condition, interpolates between linear and square-root regimes.
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…
Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of ``cocycle condition'' of the minimal penalty function. We prove also the supermartingale property for general time consistent dynamic risk measures. Whe…
MTSCI uses diffusion models to impute multivariate time series data with consistency.
problem Imputation of missing values in multivariate time series data.
method MTSCI employs a contrastive complementary mask and mixup mechanism to ensure intra-consistency and inter-consistency.
result MTSCI achieves state-of-the-art performance on multivariate time series imputation tasks.
Universal consistency and rates of convergence of multiclass prototype algorithms in metric spacescs.LG
Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.
problem Multiclass classification in metric spaces, focusing on universal consistency and convergence rates.
method Novel Proto-NN and hybrid rules for multiclass classification in metric spaces, analyzing convergence rates.
result Proto-NN is universally consistent and simpler to implement, with similar computational advantages.
The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
problem Finding upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
method Using spectral decompositions and consistency conditions derived from quadruple overlap integrals in terms of triple overlap integrals.
result Derives upper bounds on eigenvalues, nearly saturated by the Bolza surface.
The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a dual representation of dynamic cash-subadditive convex risk measures (that can al…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characteriza…
The simplicial condition and other stronger conditions that imply it have recently played a central role in developing polynomial time algorithms with provable asymptotic consistency and sample complexity guarantees for topic estimation in separable topic models. Of these algorithms, those that rely solely on the simpl…
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All metrics (resp. transports) consistent with a given transport (resp. metric) are e…
The paper defines and characterizes conditional nonlinear expectations.
problem Defining and characterizing conditional nonlinear expectations.
method Embedding in decision theory, using state-dependent preferences, and continuous utility representation.
result Consistent backward conditional projections are characterized by the Sure-Thing Principle.
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both com…
New rule universally consistent for online learning with non-ergodic data.
problem Online learning with non-ergodic data processes.
method Developed an online learning rule for processes on (X,Y) pairs.
result Generalizes past results to non-ergodic processes on (X,Y).
A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter, and consistency of the estimator is established in the well specified case. In ex…
We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs for certain p…
Active learning seeks to build the best possible model with a budget of labelled data by sequentially selecting the next point to label. However the training set is no longer \textit{iid}, violating the conditions required by existing consistency results. Inspired by the success of Stone's Theorem we aim to regain cons…
This paper rethinks confidence calibration under covariate shifts.
problem Calibration methods struggle with covariate shifts and unstable importance weighting.
method Derives Expectation consistency condition and proposes Expectation consistency loss (ECL).
result ECL loss is compatible with various types of calibration and has the same sample complexity as ECE.
New method simplifies checking consistency of differentiable loss functions.
problem Verifying consistency of differentiable loss functions is difficult.
method Developed a new approach called strong indirect elicitation (strong IE) to simplify checking consistency.
result Strong IE is equivalent to calibration for strongly convex, differentiable surrogates.
Paper establishes MLE consistency for market microstructure models.
problem Estimating parameters in partially observed diffusion models.
method Tractable sufficient condition for MLE consistency based on stationary distribution.
result Maximum likelihood estimators are consistent for market microstructure parameters.
Aggregation distorts causal discovery results but recovery is possible with partial linearity or prior.
problem Understanding how temporal aggregation affects causal discovery in aggregated data.
method Functional consistency and conditional independence consistency methods.
result Causal discovery results may be distorted by aggregation, but recovery is possible with certain conditions.
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
The paper proves consistency of GVI posteriors under minimal conditions.
problem Consistency of generalized variational inference posteriors.
method Proves consistency using -convergence theory.
result GVI posteriors are consistent and collapse to the population-optimal parameter value.
Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivitystat.ML
New methods for better uncertainty prediction in ML.
problem Insufficient calibration in machine learning regression.
method Conditional calibration with respect to input features (adaptivity).
result Consistency and adaptivity are complementary, and good consistency does not guarantee good adaptivity.
Lasso proves consistent model selection for high-dimensional Ising models.
problem Model selection consistency of Lasso for high-dimensional Ising models.
method Theoretical analysis of Lasso with and without post-thresholding for Ising models.
result Lasso without post-thresholding is model selection consistent in the whole paramagnetic phase with .
Proposes a new method for rank-consistent ordinal regression without weight-sharing constraints.
problem Ordinal response variables in real-world prediction problems are often ignored by conventional classification losses.
method CORN framework using conditional training sets and the chain rule for conditional probability distributions.
result Improves performance substantially compared to the CORAL reference approach without weight-sharing restrictions.
Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on with image space in the power set of . In the convex case, multiportfolio time consistency is equivalent to a cocycle condition on…
High signal to noise ratio (SNR) consistency of model selection criteria in linear regression models has attracted a lot of attention recently. However, most of the existing literature on high SNR consistency deals with model order selection. Further, the limited literature available on the high SNR consistency of subs…
Algorithm estimates nonparametric mixtures from grouped data.
problem Estimating identifiable nonparametric mixture models from grouped observations.
method Oracle inequality for weighted kernel density estimators and general consistency result.
result Consistent estimation of mixture components from grouped observations.
Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.
problem Identifying causal structure in nonparametric settings.
method Reframed GES algorithm with a neural conditional dependence measure.
result Optimality and consistency of the reframed GES algorithm under standard assumptions.
Self-Consistent Asset Pricing Modelsphysics.soc-ph
We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implie…
We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al.…
The paper extends static Systemic Risk Measures to a conditional setting.
problem Investigating how static Systemic Risk Measures can be adapted to a conditional framework.
method Providing a general dual representation result, analyzing Conditional Shortfall Systemic Risk Measures, and providing explicit formulas for exponential preferences.
result Explicit formulas for Conditional Shortfall Systemic Risk Measures and a time consistency property.
Generalizes sigma model with Lie algebroid structure and geometric conditions.
problem Consistency of constraints and gauge symmetry in topological sigma models.
method Analysis of geometric conditions and constraints in Hamiltonian and Lagrangian formalisms.
result Identifies universal compatibility condition between Lie algebroid and multi-symplectic structure.
New conditions for ACD model consistency and normality.
problem Random number of durations in ACD model.
method Additional sufficient conditions for consistency and normality of QMLE.
result Finite mean of durations is required for consistency and normality.
The paper bounds eigenvalues and integrals of eigenfunctions on hyperbolic manifolds.
problem Eigenvalues and integrals of eigenfunctions on compact hyperbolic manifolds.
method Spectral decompositions and consistency conditions derived from quadruple overlap integrals.
result Upper bounds on Laplacian eigenvalues and triple overlap integrals.
Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistencystat.ML
Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a partition. The estimator predicts the empirical conditional expectation over the cel…
This paper is dedicated to the consistency of systemic risk measures with respect to stochastic dependence. It compares two alternative notions of Conditional Value-at-Risk (CoVaR) available in the current literature. These notions are both based on the conditional distribution of a random variable Y given a stress eve…
Paper improves BN structure learning from incomplete data.
problem Learning BN structure from incomplete data.
method Node-Average Likelihood (NAL) approach.
result NAL proves consistent and identifiable for conditional Gaussian BNs.
Paper corrects Max-Margin loss for multi-label tasks.
problem Max-Margin loss inconsistency in multi-label classification.
method Introduced Restricted-Max-Margin loss.
result Consistent loss for multi-label tasks under milder conditions.
Classical scaling is shown to be optimal under various noisy conditions.
problem Consistency of classical scaling under general noise conditions.
method Established using finite fourth moments of noise, derived convergence rates, and matching minimax lower bounds.
result Classical scaling achieves minimax optimality in recovering true configuration from noisy dissimilarities.
The paper explores conditions for predicting optimization performance.
problem Lack of formal theoretical guarantees linking prediction and optimization performance.
method Exploring conditions for asymptotic convergence and exact quantification of optimization performance.
result Explicit theoretical relationship between prediction and optimization performance.
Modified relative universality for unbiasedness and consistency in dimension reduction.
problem Gap in proof of unbiasedness and Fisher consistency in relative universality.
method Modified definition of relative universality using ǫ-measurability.
result Established unbiasedness and Fisher consistency rigorously.
Gaussian OBFS proves strong consistency in feature selection with correlations.
problem Feature selection consistency in the presence of correlations.
method Proves strong consistency of Gaussian OBFS under mild conditions.
result Identifies selected features and rates of convergence for different feature types.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.