In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model…
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48 results for “Measurement Model”
Performance evaluation of predictive AI models to support medical decisions: Overview and guidancecs.LG
The study evaluates AI model performance measures for medical use.
problem Selecting appropriate performance measures for AI models in medical practice.
method Assessed 32 performance measures across five domains for binary outcomes.
result 17 measures are both proper and reflect decision-analytic performance.
The paper bounds payoffs and option prices in discrete models.
problem Measuring risk in discrete models and incomplete markets.
method Analytical and simulated bounds for payoff functions and option prices.
result Analytical and simulated bounds for European and American options.
Assessing Financial Model Riskq-fin.RM
Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk…
Bayesian approach to robust risk measures under model uncertainty.
problem Representing robust risk measures as a single probability measure.
method Introducing two types of risk measures and analyzing their relation to robust risk measures.
result Robust risk measures can be represented by a mixture probability measure, a Bayesian approach.
Generative models solve medical imaging inverse problems without needing paired data.
problem Reconstructing medical images from partial measurements.
method Score-based generative models trained on medical images, then sampling to reconstruct images consistent with measurements and physical model.
result Comparable or better performance in CT and MRI tasks, with improved generalization to unknown measurement processes.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
The paper assesses quality measures for machine learning models using cross-validation.
problem Evaluating the accuracy and robustness of quality measures for machine learning models.
method Cross-validation approach to estimate prediction error and quantify explained variation. Confidence bounds and local quality measures derived from residuals.
result The reliability and robustness of quality measures are assessed through numerical examples and confidence bounds.
Correlated Random Measuresstat.ML
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process based c…
Model Spaces for Risk Measuresq-fin.RM
We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk measure respecting the underlying ambiguity profile. We particularly emphasise li…
Improved measure of predictive uncertainty for machine learning models.
problem Current measure of predictive uncertainty assumes BMA predictive distribution is equivalent to true model's distribution.
method Introduced a new measure based on information theory to correct the assumption.
result Our measure behaves more reasonably in synthetic tasks and is advantageous in real-world applications.
Paper tackles measure estimation in barycentric coding model.
problem Estimating an unknown measure in the barycentric coding model.
method Geometric, statistical, and computational insights; quadratic optimization problem; empirical i.i.d. samples algorithm.
result Proves precise rates of convergence for algorithm, ensuring statistical consistency.
The study examines methods to correct measurement error in nutritional epidemiology studies.
problem Measurement error in nutritional studies leads to biased and underconfident estimates.
method The article reviews various bias-correction models for exposure variables in nutritional epidemiology.
result Bias-correction methods are essential for accurate inference in nutritional studies.
Signal retrieval from a series of indirect measurements is a common task in many imaging, metrology and characterization platforms in science and engineering. Because most of the indirect measurement processes are well-described by physical models, signal retrieval can be solved with an iterative optimization that enfo…
Study nationwide measures' impact on COVID-19 using models and machine learning.
problem Analyzing the impact of nationwide COVID-19 measures.
method Compartmental model and machine learning tools.
result Comparison of deterministic model and machine learning forecasts.
Parametrized measure modelsmath.DG
We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space which does not assume that all measures of the model have the same null sets. This is given by a diffferentiable map from the parameter manifold into the set of finite measures or probability me…
Paper characterizes monotonic mean-deviation risk measures.
problem Developing consistent risk measures from mean-deviation models.
method Applying a risk-weighting function to the deviation part of a mean-deviation model.
result Characterizes monotonic mean-deviation measures as consistent risk measures.
Paper introduces a new, tractable measure of model complexity.
problem Need for a reliable measure of model complexity.
method Mathematically rigorous measure based on gradient similarities.
result Generalizes to various model types and insights into double descent.
Paper proposes a new model for multivariate risk measures using Wasserstein barycenters.
problem Estimating robust multivariate risk measures in financial markets.
method Wasserstein barycenters of probability measures, copulas, Value at Risk models.
result The new model provides realistic VaR forecasts in both common and volatile periods.
Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is made using a novel pseudo-marginal Metropolis-Hastings sampler for normalized comp…
This post introduces model calibration and evaluation measures, highlighting issues with a common measure.
problem Ensuring model confidence accurately reflects true outcomes.
method Explains common calibration definition, ECE, and its drawbacks.
result New evaluation measures needed for comprehensive model calibration.
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.
Paper clusters microstructure measures for better stock return prediction.
problem Finding the best microstructure measures for predicting stock returns.
method Clustering model of market microstructure features studied in 10-second time-frequency.
result Identifies the most effective microstructure measures for accurate stock return prediction.
Paper proposes efficient method for estimating risk measures in complex models.
problem Accurately estimating distortion risk measures in computationally expensive models.
method Integrates importance sampling and machine learning for efficient Monte Carlo estimation.
result Demonstrates significant reduction in computational cost for estimating risk measures.
We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing …
The author suggests using non-Euclidean geometry for psychometric models.
problem Current psychometric models lack geometric insights.
method Illustrates how non-Euclidean geometry can be applied to psychometrics.
result Geometric concepts may improve psychometric model understanding.
Recently, Ross showed that it is possible to recover an objective measure from a risk-neutral measure. His model assumes that there is a finite-state Markov process X that drives the economy in discrete time. Many authors extended his model to a continuous-time setting with a Markov diffusion process X with state space…
Unified framework for learning quantum models from limited measurements.
problem Sample complexity and measurement shots in classical learning of quantum models.
method Unified learning framework considering probabilistic quantum measurements.
result Asymmetrical effects and interplay of sample size and measurement shots on learning performance.
Paper identifies latent factors from noisy measurements using tensor decomposition.
problem Identification of latent factors from noisy, correlated measurements.
method Tensor decomposition of third order cross moments, Kruskal theorem, Kotlarski identity, generalized Kruskal rank.
result Full distribution of latent factors and measurement errors identified without injective measurements.
The paper proposes a framework for information-theoretic predictive uncertainty measures.
problem The need for reliable estimation of predictive uncertainty in machine learning.
method Revisiting core concepts, categorizing predictive uncertainty measures based on model and approximation of true distribution.
result Identification of conditions under which certain predictive uncertainty measures excel.
Framework for transitioning financial models from risk-neutral to real-world measure.
problem Transitioning financial models from risk-neutral to real-world measure to better reflect market dynamics and investor preferences.
method Leveraging probability theory, specifically Girsanov's theorem, to incorporate real-world dynamics into financial models.
result Validation of the robustness and practical relevance of the methodology through case studies involving financial forecasts and stress tests.
Learning Interpretability for Visualizations using Adapted Cox Models through a User Experimentstat.ML
In order to be useful, visualizations need to be interpretable. This paper uses a user-based approach to combine and assess quality measures in order to better model user preferences. Results show that cluster separability measures are outperformed by a neighborhood conservation measure, even though the former are usua…
We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility models of Ornstein-Uhlenbe…
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, -optimal martingale measures, bilateral Esscher…
Study recovers community structure from coarse graph measurements.
problem Community recovery from low-resolution graph measurements.
method Formalized coarsening process of graph measurements, developed conditions for perfect recovery.
result Simple and closed-form asymptotic conditions for perfect recovery of coarse graph communities.
Investor sentiment improves model accuracy but complexity doesn't always boost predictive power.
problem Determining the optimal complexity of investor sentiment measures in asset pricing models.
method Comprehensive review of 71 papers from 2000-2021, analyzing various sentiment measures and models.
result Higher complexity of sentiment measures does not necessarily improve predictive power.
Paper introduces new risk measures for default risk and model uncertainty.
problem Model uncertainty and default risk in rating systems.
method Introduces default risk measures and discusses their properties and impacts.
result Different default risk measures and margins of conservatism affect risk-weighted assets.
The paper develops a robust signal estimation method for noisy measurements from generative models.
problem Signal estimation from noisy non-linear measurements with adversarial corruptions.
method Generalized Lasso approach with sub-Gaussian measurements and adversarial noise consideration.
result The method requires $O\left(\frac{k}{ε^2}\log L
ight)$ samples for -error recovery, robust to adversarial noise.
This paper critiques the Standardized Measurement Approach (SMA) for operational risk and recommends maintaining Advanced Measurement Approach (AMA).
problem Weaknesses and failures of the Standardized Measurement Approach (SMA) in operational risk.
method Critical review and analysis of SMA and AMA approaches.
result SMA is unstable, insensitive to risk, and implicitly related to systemic risk in the banking sector.
Study proposes local effective dimension to measure model capacity and generalization error.
problem Capturing the generalization power of machine learning models.
method Proposes local effective dimension as a capacity measure.
result Local effective dimension bounds the generalization error and correlates well with it.
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for equivalent and non-equivalent p…
Proposes a new model to handle noisy data in scientific research.
problem Measurement error in noisy data settings.
method Measurement error BART (meBART) integrates measurement error in Bayesian additive regression trees.
result meBART provides more accurate parameter estimation, robust uncertainty quantification, and superior predictive performance.
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed a…
Study proposes worst+gap measure for better DG evaluation.
problem Lack of comprehensive exploration of average measure in DG evaluation.
method Introduced worst+gap measure and compared it with average measure.
result Worst+gap measure provides a more accurate approximation of true DG performance.
Paper develops a fractal dimension-based generalization measure.
problem Developing a robust generalization measure for machine learning models.
method Analyzes decision boundaries using fractal dimension concept.
result Developed a generalization measure based on fractal dimension.
Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functionseess.SY
Unified control theory and machine learning for safety in uncertain systems.
problem Safety guarantees for systems with measurement model uncertainty.
method Measurement-Robust Control Barrier Functions (MR-CBFs) for control synthesis.
result MR-CBFs ensure safety in perception systems with measurement model uncertainty.
Proposes Neural Complexity (NC) for predicting and explaining generalization in deep neural networks.
problem Challenges in specifying a suitable complexity measure for deep neural networks to predict and explain generalization.
method A meta-learning framework that learns a scalar complexity measure through interactions with many heterogeneous tasks.
result Trained NC model can be added to standard training loss to regularize any task learner.