相关论文: Mathematical Basis for Physical Inference

We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely…

Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is…

Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…

The quantum reference frames program is based on the idea that reference frames should be treated as quantum physical systems. In this work, we combine these insights with the emphasis on operationality, understood as refraining from…

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…

Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even when the detector is modeled unitarily. Experimental data are represented in a Boolean event algebra of mutually exclusive records, while…

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Ar{\i}kan style constructions. This paper, which is presented in two…

Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…

The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

We undertake a reconstruction of the epistemic significance of research on operational theories in quantum foundations. We suggest that the space of operational theories is analogous to the space of possible worlds employed in the possible…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

This note presents a rigorous introduction to a selection of distributions along with their Fourier transforms, which are commonly encountered in signal processing and, in particular, magnetic resonance imaging (MRI). In contrast to many…

The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…

A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or…

The formalism of particle number on a spatial domain for mean field wave functions with pairing is revisited to account for the case where finite dimensional basis are used. The formulas differ from the ones previously used in the…

Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis…