Related papers: Robust Probability Updating
As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space'', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine…
As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine…
When dealing with incomplete data in statistical learning, or incomplete observations in probabilistic inference, one needs to distinguish the fact that a certain event is observed from the fact that the observed event has happened. Since…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this…
Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization,…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
Conformal prediction is a simple and powerful tool that can quantify uncertainty without any distributional assumptions. Many existing methods only address the average coverage guarantee, which is not ideal compared to the stronger…
Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
This paper studies a robust utility maximization problem for intractable claims under distributional ambiguity, where the distribution of the claim cannot be inferred from market information and its dependence with tradable assets is…