Related papers: Quantum Bayesian implementation

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…

Online learning via Bayes' theorem allows new data to be continuously integrated into an agent's current beliefs. However, a naive application of Bayesian methods in non stationary environments leads to slow adaptation and results in state…

Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

We introduce a cooperative Bayesian optimization problem for optimizing black-box functions of two variables where two agents choose together at which points to query the function but have only control over one variable each. This setting…

Classical reinforcement learning assumes the agent interacts with a fixed environment whose behavior does not depend on the agent's policy. This assumption breaks down in non-realizable settings where other actors might anticipate the…

LLMs excel at predictive tasks and complex reasoning tasks, but many high-value deployments rely on decisions under uncertainty, for example, which tool to call, which expert to consult, or how many resources to invest. While the usefulness…

Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…

Bayesian learning is ubiquitous for implementing classification and regression tasks, however, it is accompanied by computationally intractable limitations when the feature spaces become extremely large. Aiming to solve this problem, we…

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…

Due to increased awareness of data protection and corresponding laws many data, especially involving sensitive personal information, are not publicly accessible. Accordingly, many data collecting agencies only release aggregated data, e.g.…

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…

Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts…

We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…

In this article, we propose to use the formalism of quantum mechanics to describe and explain the so-called "abnormal" behaviour of agents in certain decision or choice contexts. The basic idea is to postulate that the preferences of these…