New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.
problem Estimating first-and total-orders Sobol' indices accurately.
method Comparing two Monte Carlo estimators for Sobol' indices.
result New method outperforms current approach in accuracy.
Enhances sensitivity analysis for correlated inputs.
problem Estimating sensitivity indices in models with correlated inputs.
method Proposes an extension of Sobol' estimator using a linear correlation model.
result Improves accuracy in variance-based sensitivity analysis.
Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which o…
Extensions to given-data Sobol' index estimators for large models.
problem Efficiently compute Sobol' indices for models with many inputs.
method General definition, streaming algorithm, heuristic filtering.
result Comparable accuracy and lower memory usage for large models.
Sobol method applied to probabilistic networks for sensitivity analysis.
problem Measuring influence of probabilistic network nodes on a quantity of interest.
method Transforms global sensitivity analysis into marginalization inference exploiting network structure.
result Efficient computation of sensitivity indices for complex networks.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
problem Challenges in sensitivity analysis of black-box computer experiments with complex, nonlinear functional outputs.
method Functional-output orthogonal additive Gaussian process (FOAGP) with conditional orthogonality constraint.
result Demonstrates effectiveness in orthogonal effect decomposition and variance decomposition through simulations and real-world application.
New method quantifies uncertainty at class level for better decision-making.
problem Improving cost-sensitive decision-making in classification tasks.
method Label-wise decomposition of uncertainty measures based on non-categorical metrics.
result Proposed measures adhere to desirable properties and improve uncertainty quantification.
Introduces TSI, a variance-based measure for persistence barcodes.
problem Capturing structural variability in persistence barcodes.
method Variance-based scalar measure, TSI, and complementary TSigI.
result TSI captures structural variability complementary to entropy.
Multi-agent reinforcement learning (MARL) has recently received considerable attention due to its applicability to a wide range of real-world applications. However, achieving efficient communication among agents has always been an overarching problem in MARL. In this work, we propose Variance Based Control (VBC), a sim…
Paper introduces variance-based measures for second-order uncertainty quantification in classification problems.
problem Uncertainty in machine learning predictions and decision-making.
method Second-order uncertainty quantification using variance-based measures.
result Variance-based measures effectively quantify uncertainty on a class-based level and are competitive with entropy-based measures.
This paper analyzes ETFs with Taiwan exposure, finding heavy tails and asymmetric volatility.
problem Heavy tails and asymmetric volatility in Taiwan-related ETFs.
method Tail-risk diagnostics, asymmetric volatility modeling, and portfolio optimization under mean--variance and CVaR criteria.
result CVaR optimization produces more concentrated allocations, favoring SMH during the post-COVID AI-driven expansion.
Neural-SDE models improve option hedging with lower errors and robustness.
problem Improving option hedging strategies using machine learning.
method Derive sensitivity-based and minimum-variance-based hedging strategies using neural-SDE market models.
result Neural-SDE models achieve lower hedging errors and are more robust than traditional models.
New method uses interval-based metric to validate prediction uncertainty in machine learning.
problem Validation of prediction uncertainty in machine learning regression tasks is unreliable due to heavy-tailed distributions.
method Shift from variance-based metrics to interval-based Prediction Interval Coverage Probability (PICP).
result PICP method more quickly and reliably tests prediction intervals than variance-based metrics.
The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.
problem Risk-sensitive learning aims to minimize risk-averse measures of loss.
method Proposes learning bounds for empirical OCE minimizers based on Rademacher average and variance.
result Provides two learning bounds on the performance of empirical OCE minimizers.
Excluding irrelevant features in a pattern recognition task plays an important role in maintaining a simpler machine learning model and optimizing the computational efficiency. Nowadays with the rise of large scale datasets, feature selection is in great demand as it becomes a central issue when facing high-dimensional…
A new approach to sensitivity analysis without the Sobol decomposition.
problem Traditional sensitivity indices like Sobol indices have limitations.
method Introducing sensitivity measures that generalize existing indices and define interaction effects.
result Sensitivity measures can create new indices and define interaction effects.
This paper presents an automatic approach for selecting optimal meta-models for sensitivity analysis in complex systems.
problem Efficient surrogate models for high-dimensional problems in virtual prototyping.
method Automatic selection of meta-models, variable space reduction, and advanced sensitivity measures.
result Optimal meta-models and subspace identification for accurate probabilistic analysis.
Variance plays a crucial role in risk-sensitive reinforcement learning, and most risk measures can be analyzed via variance. In this paper, we consider two law-invariant risks as examples: mean-variance risk and exponential utility risk. With the aid of the state-augmentation transformation (SAT), we show that, the two…
Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.
problem Efficiently estimating cross-partial derivatives and sensitivity indices in complex models.
method Using randomized points and constraints, the paper develops estimators with optimal convergence rates and low bias.
result The estimators achieve optimal rates of convergence and do not suffer from the curse of dimensionality.
This paper simplifies conditional Sobol' indices calculation using PCE bases.
problem Computational inefficiency and lack of consistency in evaluating conditional Sobol' indices.
method Analytical extraction of conditional Sobol' indices via basis decomposition of PCE expansions.
result Derives closed-form expressions for conditional Sobol' indices.
A novel clustering method using a subset of data for better performance.
problem Improving clustering efficiency with limited data.
method Proposes a sampling subset approach for variance-based k-clustering.
result The method achieves competitive results with only 7% of the dataset, outperforming existing methods in 80% of tasks.
Method quantifies sensitivity of reliability analysis to uncertainty sources.
problem Computational expense in reliability analysis of complex models.
method Gaussian process surrogate model, active learning, sensitivity analysis.
result Reduces main source of error in estimating rare event probabilities.
Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.
problem Accurately estimating Sobol' indices with limited data.
method Integrates sparse, gradient-enhanced regression with Poincaré chaos expansions for derivative-based sensitivity analysis.
result Accurately estimated Sobol' indices using limited data.
Study improves MACD trading strategy with volume and price adjustments.
problem Signal lag and false signals in traditional MACD trading rules.
method Develops VP-MACD framework with sensitivity calibration.
result Proposed framework outperforms baseline MACD in profitability and risk-adjusted return.
This study introduces axioms to assess regression uncertainty measures.
problem Limited formal justification and evaluations of uncertainty measures in regression settings.
method Introduces axioms and analyzes entropy- and variance-based measures in a predictive exponential family context.
result Provides a principled foundation for reliable uncertainty assessment in regression.
Invariant detects sliceness of virtual knots with specific chord indices.
problem Detecting sliceness in virtual knots with chord indices.
method Constructs an invariant using sliceness obstruction and sensitivity to Δ-move.
result Invariant detects sliceness and is sensitive to chord indices.
A new indicator measures project risk from activity durations.
problem Managing project risks throughout the lifecycle.
method Activity Risk Index (ARI) based on Schedule Risk Baseline.
result Identifies activities contributing most to project uncertainty.
This paper improves generative models by using data scaling and theoretical analysis.
problem Challenges in selecting noise distributions for stable learning in generative models.
method Introduces Scale-GAN, which uses data scaling and variance-based regularization.
result Data scaling controls the bias-variance trade-off and improves stability and accuracy.
Paper proposes a cost-sensitive conformal training method with provably controllable learning bounds.
problem Uncertainty quantification and learning bounds in conformal prediction.
method Cost-sensitive conformal training algorithm that minimizes the expected size of prediction sets using rank weighting.
result Theoretical analysis shows tightness between weighted objective and expected size of conformal prediction sets.
The paper develops methods to analyze sensitivity in stochastic models using surrogate models.
problem Quantifying the impact of input variability on stochastic simulators with randomness.
method The authors propose using generalized lambda models to emulate response distributions of stochastic simulators and estimate sensitivity indices.
result The proposed method can estimate sensitivity indices even with strong heteroskedasticity and small signal-to-noise ratio.
Global sensitivity analysis improves BNN hyperparameter selection for accurate uncertainty quantification.
problem Difficulties in obtaining accurate uncertainty quantification with Bayesian Neural Networks (BNNs).
method Global sensitivity analysis of BNN performance under varying hyperparameter settings.
result Many hyperparameters interact to affect both predictive accuracy and uncertainty quantification.
Study adapts AI research methods to analyze image augmentation impacts on neural network operations.
problem Understanding how image augmentation affects neural network performance and sensitivity.
method Adapted treatment-control paradigm, uses variance decomposition, Sobol indices, and Shapley values for sensitivity analysis.
result Visualizes and quantifies sensitivity to different image augmentation parameters.
A framework for sensitivity measures using scoring functions.
problem Constructing sensitivity measures for any elicitable functional.
method Score-based sensitivities constructed via consistent scoring functions.
result Demonstrated intuitive and desirable properties of score-based sensitivities.
A new method ranks and selects features without model fitting.
problem Feature importance measures algorithm-specific and need improvement.
method Integrates global sensitivity analysis with forward selection and backward elimination.
result Demonstrates clear advantage over state-of-the-art methods.
New sampling bounds improve uniform coverage verification in machine learning.
problem Conservative bounds in classical coverage analyses at small failure probabilities.
method Variance-based analysis of uniform random sampling on a d-dimensional unit hypercube. result Sample complexity bound with logarithmic dependence on failure probability.
PCA is often used in anomaly detection and statistical process control tasks. For bivariate data, we prove that the minor projection (the least varying projection) of the PCA-rotated data is the most sensitive to distributional changes, where sensitivity is defined by the Hellinger distance between distributions before…
This work presents deep asymmetric networks with a set of node-wise variant activation functions. The nodes' sensitivities are affected by activation function selections such that the nodes with smaller indices become increasingly more sensitive. As a result, features learned by the nodes are sorted by the node indices…
We investigate the topics of sensitivity and robustness in feedforward and convolutional neural networks. Combining energy landscape techniques developed in computational chemistry with tools drawn from formal methods, we produce empirical evidence indicating that networks corresponding to lower-lying minima in the opt…
We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dyn…
This paper proposes a new AED framework for multi-metric experiments with fixed budget.
problem Statistical power challenges in testing multiple metrics simultaneously.
method Two-phase structure: adaptive exploration followed by validation. SHRVar algorithm with relative-variance-based sampling.
result Achieves provable error probability that decreases exponentially.
Stock market indices are one of the most investigated complex systems in econophysics. Here we extend the existing literature on stock markets in connection with nonextensive statistical mechanics. We explore the nonextensivity of price volatilities for 34 major stock market indices between 2010 and 2019. We discover t…
Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.
problem Performing global sensitivity analysis on black-box models with dependent inputs.
method Proposes a novel framework based on probability theory, functional analysis, and combinatorics to handle dependencies.
result Any square-integrable, real-valued function of random elements with mild dependence assumptions can be uniquely additively decomposed.
In unsupervised machine learning, agreement between partitions is commonly assessed with so-called external validity indices. Researchers tend to use and report indices that quantify agreement between two partitions for all clusters simultaneously. Commonly used examples are the Rand index and the adjusted Rand index. …
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
Study shows heavy-tailed distributions affect reliability of machine learning calibration statistics.
problem Reliability of calibration statistics for machine learning regression tasks is affected by heavy-tailed uncertainty and error distributions.
method Examined two calibration error estimation methods (CE and ZMS) and found ZMS to be less sensitive to heavy-tailed distributions.
result Heavy-tailed distributions make MSE and MV unreliable, but ZMS remains a reliable approach.
Active learning method improves sensitivity analysis of complex models.
problem Limited model evaluations in global sensitivity analysis.
method Gradient-based active learning with Gaussian process.
result Improves sensitivity analysis accuracy with reduced evaluations.
We present a proxy dataset of vital signs with class labels indicating patient transitions from the ward to intensive care units called Ward2ICU. Patient privacy is protected using a Wasserstein Generative Adversarial Network to implicitly learn an approximation of the data distribution, allowing us to sample synthetic…
The paper examines stability of ReLU networks in tangent space and activation regions.
problem Stability and sensitivity of ReLU networks to small changes.
method Tangent sensitivity measure for ReLU networks, focusing on stability induced by individual examples.
result Tangent sensitivity correlates with the distribution of activation regions and generalization gap.