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11 results for Determinacy

Study on robust utility maximization with nonconcave utility functions under projective determinacy.

problem Investor's optimal investment strategy under model ambiguity and nonconcave utility.
method Projective functions of the path and sets of priors, upper-semicontinuous utility.
result Existence of optimal investment strategy under PD.

We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries - in parti…

2016-04-25abs ↗pdf ↗

A new framework CyGen models joint distributions using cyclic conditionals.

problem Modeling a joint distribution using only two conditional models without relying on an uninformative prior.
method Developed a general theory for operable equivalence criteria for compatibility and sufficient conditions for determinacy. Proposed CyGen framework and methods to achieve compatibility and determinacy.
result CyGen better fits data and captures more representative features compared to models using an uninformative prior.

Empower efficient representation of distributions through moment-preserving methods.

problem Representing high-dimensional probability measures efficiently and accurately.
method Empower efficient representation of distributions through moment-preserving methods.
result Empowers efficient and accurate representation of high-dimensional probability measures.

Study on homeomorphism groups of manifolds using set theory.

problem Relationship between set theory and homeomorphism groups of manifolds.
method First-order rigidity, type versus conjugacy, axiom of constructibility, projective determinacy.
result Under V=L, homeomorphism groups of manifolds are first-order rigid and conjugacy class is determined by type.

Geometric regularisation improves statistical models by avoiding degeneracy loci.

problem Non-identifiability, singular information, and moment indeterminacy in statistical models.
method Develops the geometric regularisation of distribution-kernel pairs (T,φ)(T, \varphi) using Whitney, Thom, and Mather theorems.
result Finite-dimensional weak transversality theorem for generic kernels, avoiding degeneracy strata of high codimension.

The paper explores indeterminacy in latent factor projections and its implications for data representation.

problem Indeterminacy in latent factor projections and its implications for data representation.
method Analyzes the fundamental problem of indeterminacy in latent factor projections and discusses its implications for data representation.
result Latent factor determinacy across all facets is achieved when the feature-dimension grows to infinity.