Related papers: Hidden Equations of Threshold Risk
A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the…
Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples is difficult and highly subjective through standard…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We consider a random process as a solution of stochastic differential equations with dependence of the coefficients on small parameter $\varepsilon$ and we suppose that the drift coefficients of these equations are unbounded on the…
Hidden-variable resultant methods are a class of algorithms for solving multidimensional polynomial rootfinding problems. In two dimensions, when significant care is taken, they are competitive practical rootfinders. However, in higher…
In a compound decision problem, consisting of $n$ statistically independent copies of the same problem to be solved under the sum of the individual losses, any reasonable compound decision rule $\delta$ satisfies a natural symmetry…
A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions $P_0$ and $P_1$, we find a lower bound for the risk of…
Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
Risk and utility functionals are fundamental building blocks in economics and finance. In this paper we investigate under which conditions a risk or utility functional is sensitive to the accumulation of losses in the sense that any…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…
We study the asymptotic distribution of critical values of random holomorphic `polynomials' s_n on a Kaehler manifold M as the degree n tends to infinity. By `polynomial' of degree n we mean a holomorphic section of the nth power of a…
Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are…