Related papers: A Posteriori Probabilistic Bounds of Convex Scenar…

This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…

Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…

With an increasing use of data-driven models to control robotic systems, it has become important to develop a methodology for validating such models before they can be deployed to design a controller for the actual system. Specifically, it…

Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about…

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…

The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions -- (i) the existence of a variable (or set of…

Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…

We suggest guaranteed, robust a posteriori error bounds for approximate solutions of the reaction-diffusion equations, modeled by the equation $-\Delta u+\sigma u= f$ in $\Omega$ with any $\sigma={\mathrm{const}}\ge 0$. We also term our…

Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…

We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An…

An advantage of methods that base inference on a posterior distribution is that credible regions are readily obtained. Except in well-specified situations, however, there is no guarantee that such regions will achieve the nominal…

Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data…

Multi-model prediction efforts in infectious disease modeling and climate modeling involve multiple teams independently producing projections under various scenarios. Often these scenarios are produced by the presence and absence of a…

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential)…

We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…

As the complexity of control systems increases, the need for systematic methods to guarantee their efficacy grows as well. However, direct testing of these systems is oftentimes costly, difficult, or impractical. As a result, the test and…