Related papers: Probability assignment in a quantum statistical mo…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…
In stochastic modeling, the excess entropy -- the mutual information shared between a process's past and future -- represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated…
The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
Consider a continuous time particle system $\eta^t=(\eta^t(k),k\in \mathbb{L})$, indexed by a lattice $\mathbb{L}$ which will be either $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, a segment $\{1,\cdots, n\}$, or $\mathbb{Z}^d$, and taking its…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown of monotonicity of thermodynamic functions. By adopting an entropy-based formulation of quantum thermodynamics, we use the…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…