Related papers: Model-free bounds on Value-at-Risk using extreme v…
We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…
We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_1, \ldots, X_p$. We wish to do so while offering finite-sample guarantees about the…
We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…
We consider the problem of risk diversification of $\alpha$-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to…
Given finite-dimensional random vectors $Y$, $X$, and $Z$ that form a Markov chain in that order (i.e., $Y \to X \to Z$), we derive upper bounds on the excess minimum risk using generalized information divergence measures. Here, $Y$ is a…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
In this paper we study a model-based approach to calculating approximately optimal policies in Markovian Decision Processes. In particular, we derive novel bounds on the loss of using a policy derived from a factored linear model, a class…
A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…
This paper studies multivariate Value-at-Risk (VaR) for financial portfolios with a focus on modeling dependence structures through Archimedean copulas. Using the generator representation of Archimedean copulas, we derive explicit…
In this paper, we explore bounds on the expected risk when using deep neural networks for supervised classification from an information theoretic perspective. Firstly, we introduce model risk and fitting error, which are derived from…
Consider the problem of drawing random variates $(X_1,\ldots,X_n)$ from a distribution where the marginal of each $X_i$ is specified, as well as the correlation between every pair $X_i$ and $X_j$. For given marginals, the…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
We study off-policy reinforcement learning for controlling continuous-time Markov diffusion processes with discrete-time observations and actions. We consider model-free algorithms with function approximation that learn value and advantage…