Related papers: Pandora with Inaccurate Priors
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…
In this study, the effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information. We employed a toy two-party protocol in which Bob by using a…
Colleges and universities are increasingly turning to algorithms that predict college-student success to inform various decisions, including those related to admissions, budgeting, and student-success interventions. Because predictive…
We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which…
Goals for planning problems are typically conceived of as subsets of the state space. However, for many practical planning problems in robotics, we expect the robot to predict goals, e.g. from noisy sensors or by generalizing learned models…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…
Missing covariates in regression or classification problems can prohibit the direct use of advanced tools for further analysis. Recent research has realized an increasing trend towards the usage of modern Machine Learning algorithms for…
The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to…
This study is aimed at answering the famous question of how the approximation errors at each iteration of Approximate Dynamic Programming (ADP) affect the quality of the final results considering the fact that errors at each iteration…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…
Decision makers often need to rely on imperfect probabilistic forecasts. While average performance metrics are typically available, it is difficult to assess the quality of individual forecasts and the corresponding utilities. To convey…
We study a longstanding question of Aaronson and Kuperberg on whether there exists a classical oracle separating $\mathsf{QMA}$ from $\mathsf{QCMA}$. Settling this question in either direction would yield insight into the power of quantum…
Reliable uncertainty estimation is crucial for perception systems in safe autonomous driving. Recently, many methods have been proposed to model uncertainties in deep learning based object detectors. However, the estimated probabilities are…
We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this…
Classical Krylov subspace projection methods for the solution of linear problem $Ax = b$ output an approximate solution $\widetilde{x}\simeq x$. Recently, it has been recognized that projection methods can be understood from a statistical…
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of…
Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…