Related papers: The Optimal 'AND'
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown…
Estimating the mutual information from samples from a joint distribution is a challenging problem in both science and engineering. In this work, we realize a variational bound that generalizes both discriminative and generative approaches.…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…
This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance…
The prior independent framework for algorithm design considers how well an algorithm that does not know the distribution of its inputs approximates the expected performance of the optimal algorithm for this distribution. This paper gives a…
Clinical trial simulation (CTS) is critical in new drug development, providing insight into safety and efficacy while guiding trial design. Achieving realistic outcomes in CTS requires an accurately estimated joint distribution of the…
Information divergences allow one to assess how close two distributions are from each other. Among the large panel of available measures, a special attention has been paid to convex $\varphi$-divergences, such as Kullback-Leibler,…
We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…
This paper presents a decision-theoretic approach to statistical inference that satisfies the likelihood principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
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…
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
In many statistical settings, two types of data are available: coupled data, which preserve the joint structure among variables but are limited in size due to cost or privacy constraints, and marginal data, which are available at larger…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In…
We discuss optimal prediction for families of probability distributions with a locally compact topological group structure. Right-invariant priors were previously shown to yield a posterior predictive distribution minimizing the worst-case…