Related papers: Observable Geometry of Singular Statistical Models
We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study…
Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are ``identifiable,'' indicating that model parameters may not be uniquely…
We propose graph-based predictable feature analysis (GPFA), a new method for unsupervised learning of predictable features from high-dimensional time series, where high predictability is understood very generically as low variance in the…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
These notes provide a pedagogical introduction to the role of transversality theory in the analysis of statistical degeneracies within the framework of distributional statistical models. The classical question of when a statistical model is…
In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…