Related papers: A Remark on the Structure of Expectiles

Systemic risk is the risk that a company- or industry-level risk could trigger a huge collapse of another or even the whole institution. Various systemic risk measures have been proposed in the literature to quantify the domino and…

Quantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while have distinguished features. In this project, our primary goal is to develop stable and practical…

There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…

We introduce a new formulation of structural causal models for extremes, called the extremal structural causal model (eSCM). Unlike conventional structural causal models, where randomness is governed by a probability distribution, eSCMs use…

We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

We present a conceptual framework that unifies a variety of evaluation metrics for different structured prediction tasks (e.g. event and relation extraction, syntactic and semantic parsing). Our framework requires representing the outputs…

In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing…

Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable;…

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…

A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…

We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a…

We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…

The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…

A dynamical model consists of a continuous self-map $T: \mathcal{X} \to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f: \mathcal{X} \to \mathbb{R}$. This paper considers the fitting of a…

Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…

We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…

We provide tight upper and lower bounds on the expected minimum Kolmogorov complexity of binary classifiers that are consistent with labeled samples. The expected size is not more than complexity of the target concept plus the conditional…

Plotting a learner's average performance against the number of training samples results in a learning curve. Studying such curves on one or more data sets is a way to get to a better understanding of the generalization properties of this…

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction…