arXiv research

Paper improves conformal prediction for imprecise training data.

Unified framework for set-valued classification tackles ambiguous multi-class datasets.

The paper tackles fair set-valued classification under demographic parity constraints.

Paper relaxes set-valued prediction in hierarchical classification by considering representation complexity.

Paper proposes set-valued prediction for historical POS tagging.

New set-valued star-shaped risk measures introduced for better risk assessment.

Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.

ICP improves text infilling and POS tagging with valid confidence sets.

The study uses neural networks to classify and predict coronavirus data.

The paper defines and analyzes set-valued stochastic integrals for Lévy processes.

Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.

This work establishes properties on diffeological structures for set-valued maps and measures.

Unified framework for generalized Venn and Venn-Abers calibration for reliable prediction.

Introduces epistemic deep learning for better uncertainty estimation in neural networks.

Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ 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…

Proposes a method to estimate acceptance regions for many classes, including new ones.

BCCP uses bandit feedback to provide reliable predictions with limited labeled data.

Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensi…

MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.

Revisits superhedging under proportional costs in continuous time markets.

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 …

The logcosh loss function helps neural networks learn set-valued functions better.

Researchers develop multi-utility representations for incomplete preferences linked to risk measures.

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ 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 $L^p(Ω,\mathcal F, P; R^d)$ with image space in the power set of $L^p(Ω,\mathcal F_t,P;R^d)$. 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…

Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are not readily applicable to set-valued outputs because of the growth rate of the o…

Develops a framework for modeling set-valued data in continuous-time.

New approach shows continuity and compactness of martingale measures.

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …

The paper tackles multi-label ranking with uncertain probabilities.

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…

PAC-Bayes theory improves ICP efficiency and coverage.

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.

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…

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 time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In fact, the risk statistics established by this method is closer to financial realit…

Identification and scoring functions are statistical tools to assess the calibration and the relative performance of risk measure estimates, e.g., in backtesting. A risk measures is called identifiable (elicitable) it it admits a strict identification function (strictly consistent scoring function). We consider measure…

A new RL approach learns near-equivalent actions for healthcare decisions.

Paper improves prediction sets for distribution shifts without labels.

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…

Transformers can approximate Bayesian inference efficiently.

Study vector-valued robust control under uncertainty.

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.

In cases of uncertainty, a multi-class classifier preferably returns a set of candidate classes instead of predicting a single class label with little guarantee. More precisely, the classifier should strive for an optimal balance between the correctness (the true class is among the candidates) and the precision (the ca…

The paper offers a method to create prediction sets with uncertainty control.