Unified framework for generating set-valued outputs.
problem Handling unordered set outputs with varying sizes.
method Sequential Set Generation (SSG) framework.
result SSG outperforms baseline methods in experiments.
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48 results for “Set-valued Outputs”
In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framewo…
Unified framework for set-valued classification tackles ambiguous multi-class datasets.
problem Ambiguous multi-class datasets in modern statistics.
method Unified statistical framework encompassing various set-valued classification formulations.
result Infinite sample optimal strategies and plug-in principle for data-driven algorithms.
Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.
problem Online learning with set-valued feedback, where labels are sets rather than single labels.
method Introduced new combinatorial dimensions (Set Littlestone and Measure Shattering) to characterize learnability.
result Characterized deterministic and randomized online learnability, and established bounds for various learning settings.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
problem Defining and analyzing set-valued stochastic integrals for Lévy processes.
method Extending classical definitions to convoluted integrals with square-integrable kernels, and proving properties of set-valued convoluted stochastic integrals.
result Set-valued convoluted stochastic integrals can be explosive and take extended vector values.
Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.
problem Investigates set-valued risk measures for processes and vectors.
method Utilizes equivalence of risk measures for processes and vectors and their penalty function formulations.
result Provides new dual representation for risk measures for processes in the set-valued framework.
This work establishes properties on diffeological structures for set-valued maps and measures.
problem Establish rigorous properties on diffeological structures for set-valued maps and measures.
method Using diffeologies, the authors link various structures including set-valued maps, relations, gradients, measures, and shape analysis.
result Established rigorous properties on sample diffeologies.
This work extends set-valued risk measures to discrete time, using difference inclusions and equations.
problem Defining set-valued dynamic risk measures in discrete time.
method Investigates discrete time setting with difference inclusions and difference equations.
result Provides insights for continuous time representations of set-valued dynamic risk measures.
Set-valued risk measures on with for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Sc…
The paper tackles fair set-valued classification under demographic parity constraints.
problem Set-valued classification can amplify discriminatory bias, especially in multiclass settings.
method Proposes two strategies: an oracle-based method and a proxy method, both aiming to satisfy demographic parity and expected size constraints.
result Established distribution-free convergence rates and excess-risk bounds for both methods.
Paper improves conformal prediction for imprecise training data.
problem Applying conformal prediction to partially labeled data.
method Generalizes conformal prediction for set-valued training and calibration data.
result Validates the proposed method and shows it outperforms baselines.
Unified framework for generalized Venn and Venn-Abers calibration for reliable prediction.
problem Asymptotic guarantees of popular distribution-free methods in model calibration.
method Unified framework extending Vovk's approach to generic loss functions, transforming predictors into set-valued predictions.
result Finite-sample set predictions shrink to a single conditionally calibrated prediction, capturing epistemic uncertainty.
Revisits superhedging under proportional costs in continuous time markets.
problem Superhedging in markets with proportional transaction costs.
method Set-valued stochastic analysis, continuous trading schemes, dynamic risk measure.
result Dynamic set-valued risk measure with multi-portfolio time-consistency.
Finding hidden-feature depending laws inside a data set and classifying it using Neural Networkcs.LG
The logcosh loss function helps neural networks learn set-valued functions better.
problem Learning set-valued functions with neural networks.
method Using artificial neural networks with logcosh loss.
result Neural networks with logcosh loss can classify samples based on set-valued functions.
New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading …
Researchers develop multi-utility representations for incomplete preferences linked to risk measures.
problem Handling incomplete preferences induced by set-valued risk measures.
method Established dual representations of set-valued risk measures to create parsimonious and well-behaved multi-utility representations.
result Unified dual representations of set-valued risk measures, linking them to scalar risk measures.
We consider the problem of retrieving the most relevant labels for a given input when the size of the output space is very large. Retrieval methods are modeled as set-valued classifiers which output a small set of classes for each input, and a mistake is made if the label is not in the output set. Despite its practical…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for assets with transaction costs or illiquidity and possible trading constraints are considered on a finite probability space. The set of capital requirements at each time and state is c…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the exchange rules in the a…
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…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be made in a basket of currencies or assets. Time consistency of scalar risk measu…
The paper introduces a new risk statistic considering the time value of money.
problem Traditional risk statistics do not fully account for the time value of money.
method Introducing set-valued risk statistics with the time value of money.
result The new risk statistic provides a more accurate quantification of portfolio risk.
New methods identify and score systemic risk measures accurately.
problem Identifying and scoring systemic risk measures accurately.
method Constructing oriented selective identification functions to induce a mixture representation of strictly consistent scoring functions.
result Demonstrated the applicability of the constructed functions through a comprehensive simulation study.
New approach shows continuity and compactness of martingale measures.
problem Stability of martingale optimal transport problem.
method Set-valued map theory and lower-upper hemicontinuity.
result Lower and upper hemicontinuity of the set of martingale measures.
Set-valued prediction in hierarchical classification with constrained representation complexitycs.LG
Paper relaxes set-valued prediction in hierarchical classification by considering representation complexity.
problem Uncertainty in class labels in hierarchical multi-class classification problems.
method Introduces representation complexity for predicted sets, proposes three methods for inference.
result Recursive tree search method is computationally more efficient.
Paper proposes set-valued prediction for historical POS tagging.
problem Difficult POS tagging in historical corpora due to lack of native speakers and sparse data.
method Set-valued prediction approach to allow uncertainty in tagging.
result Set-valued prediction improves POS tagging precision and robustness.
We extend the classical risk minimization model with scalar risk measures to the general case of set-valued risk measures. The problem we obtain is a set-valued optimization model and we propose a goal programming-based approach with satisfaction function to obtain a solution which represents the best compromise betwee…
Extends sublinear expectations to random sets, identifying extremal and constructing methods.
problem Extending sublinear expectations to random sets.
method Identifying extremal expectations and presenting general construction methods.
result Identification of extremal sublinear and superlinear expectations.
Characterizes learnability of forgiving 0-1 loss functions in multiclass settings.
problem Understanding when multiclass learning with forgiving 0-1 loss functions is possible.
method Introduces a new combinatorial dimension based on Natarajan Dimension to determine learnability.
result A hypothesis class is learnable if and only if the Generalized Natarajan Dimension is finite.
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk m…
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…
The study uses neural networks to classify and predict coronavirus data.
problem Classifying and predicting coronavirus data from input variables.
method Artificial neural networks with logcosh loss function to classify branches of set-valued mappings.
result Successfully classified and predicted coronavirus data for each German district.
Introduces epistemic deep learning for better uncertainty estimation in neural networks.
problem Uncertainty quantification in deep neural networks.
method Random-set convolutional neural networks with belief function-based loss functions.
result Epistemic approach produces better performance in uncertainty estimation.
Clinician-in-the-Loop Decision Making: Reinforcement Learning with Near-Optimal Set-Valued Policiescs.LG
A new RL approach learns near-equivalent actions for healthcare decisions.
problem Finding optimal actions in healthcare settings where actions may be near-equivalent.
method Temporal difference learning with a near-greedy heuristic for action selection.
result The proposed algorithm discovers meaningful near-equivalent actions and converges well.
Kernel tests for set-valued data improve hypothesis testing accuracy.
problem Testing distributions of sets with varying sizes, noise, and nuisance variability.
method Interpreting sets as samples from latent distributions and using kernel methods for testing.
result Kernel tests outperform traditional methods in synthetic and real-world experiments.
Proposes a method to estimate acceptance regions for many classes, including new ones.
problem Lack of methods to handle new classes in set-valued classification.
method Generalized Prediction Set (GPS) approach to estimate acceptance regions.
result Achieves a good balance between accuracy, efficiency, and anomaly detection.
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of a…
Study vector-valued robust control under uncertainty.
problem Dynamic stochastic control with multi-objective criteria under model uncertainty.
method Robust minimax approach, set-valued framework, dynamic programming principle.
result Derived weak and strong versions of dynamic programming principle for vector-valued control problems.
This work examines aggregation functions in Deep Set learning.
problem The sensitivity of Deep Set networks to aggregation function choices.
method Investigation of alternative aggregation functions, including learnable recurrent ones.
result Learnable aggregations improve performance, reduce hyper-parameter sensitivity, and generalize better.
ICP improves text infilling and POS tagging with valid confidence sets.
problem Statistical reliability of machine learning predictions.
method Inductive conformal prediction algorithms for text infilling and POS tagging.
result Valid set-valued predictions with small size for real-world applications.
A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.
Develops a framework for modeling set-valued data in continuous-time.
problem Handling sequences where each event is associated with a set of items.
method General framework for modeling set-valued data, developed inference methods, and importance sampling techniques.
result Orders-of-magnitude improvements in efficiency for probabilistic queries over direct sampling.
BCCP uses bandit feedback to provide reliable predictions with limited labeled data.
problem Limited labeled data and bandit feedback challenge online set-valued classification.
method BCCP uses stochastic gradient descent to train model and make set-valued inferences with unbiased estimation of true label.
result BCCP offers coverage guarantees on a class-specific granularity.
New risk measures for financial networks avoid external capital, reducing systemic risk.
problem Systemic risk in financial networks is underestimated by traditional methods.
method Developed set-valued, intrinsic risk measures for financial networks.
result Systemic intrinsic risk measures are more stable and avoid reliance on external capital.
This paper solves optimal consumption-investment problems with time-varying preferences.
problem Optimal consumption-investment problems under time-varying incomplete preferences.
method Develops a martingale-type solution in a topological vector space, using stochastic processes and scalarization methods.
result Optimal investment policies are set-valued, with selectors decomposed into four components.
Paper presents a new approach to a strategic insider equilibrium problem in continuous time.
problem Continuous time Kyle-Back model between insider and market marker.
method Uses forward-backward stochastic differential equations (FBSDEs) for characterization of equilibria.
result Characterizes all equilibria through FBSDEs and shows uniqueness of equilibrium without Markovian restrictions.