相关论文: The Conditional Probability Interpretation of the …
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Variable importance assessment has become a crucial step in machine-learning applications when using complex learners, such as deep neural networks, on large-scale data. Removal-based importance assessment is currently the reference…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt equation, boundary conditions, interpretation of $\psi$), I discuss how these ideas can be tested observationally. Observational predictions differ for different choices…
We use the machinery of a conditional probability space (R\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a…
Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing…
The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification…
The search for a logic capturing PTIME is a long standing open problem in finite model theory. One of the most promising candidate logics for this is Choiceless Polynomial Time with counting (CPT). Abstractly speaking, CPT is an…
We study the interpretability of conditional probability estimates for binary classification under the agnostic setting or scenario. Under the agnostic setting, conditional probability estimates do not necessarily reflect the true…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
Conditional Feature Importance (CFI) is a classical variable importance measure that accounts for the relationship between the studied feature and the others. However, CFI has not yet been studied from a theoretical perspective because the…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…
Gauge invariant local observables describing primordial scalar quantum fluctuations in Inflationary Cosmology are identified as elements of a type $II$ de Sitter crossed product algebra. This algebra is defined, after adding a reference…
We reconsider the fine-tuning problem of scalar-driven inflation arising from the need to couple the inflaton to ordinary matter in order to make reheating efficient. Quantum fluctuations of this matter induce Coleman-Weinberg corrections…
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to…
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space,…
The quantum analogue of a constraint satisfaction problem is a sum of local Hamiltonians - each local Hamiltonian specifies a local constraint whose violation contributes to the energy of the given quantum state. Formalizing the intuitive…
The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that the time evolution is…