arXiv research

Parametric UMAP learns a mapping from data to embeddings.

Researchers provide explicit parametrizations for Sasakian space forms.

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model …

This work introduces benchmarks for evaluating nanophotonic structures in design simulations.

The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.

Study real projective structures on a specific Coxeter orbifold.

We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual information which is used to create a non-parametric test for multivariate conditional i…

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, …

Proposes a new algorithm for graph-based semi-parametric contextual bandits.

Study contact structures on lens spaces, classifying rational knots.

Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a Markov factor graph model, this exploration process is called structure discover…

Probabilistic Quantum Memory (PQM) is a data structure that computes the distance from a binary input to all binary patterns stored in superposition on the memory. This data structure allows the development of heuristics to speed up artificial neural networks architecture selection. In this work, we propose an improved…

Graphical models for covariance matrices improve structure learning.

Study provides guarantees for kernel clustering under non-parametric mixtures.

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…

We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain Monte Carlo to move between solutions. In contrast, we assume that the number of hi…

One of the main challenges in the parametrization of geological models is the ability to capture complex geological structures often observed in the subsurface. In recent years, generative adversarial networks (GAN) were proposed as an efficient method for the generation and parametrization of complex data, showing sta…

The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.

New neural network models extreme value distributions with preserved shape constraints.

Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.

The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on trivial 1-dimensional central extensions of semisimple Lie algebras. In particular, we develop the general theory of such structures and study related families of functions in involution. We also show that th…

Thurston related $\mathbb{C}{\rm P}^1$-structures (complex projective structures) and equivariant pleated surfaces in the hyperbolic-three space $\mathbb{H}^3$, in order to give a parameterization of the deformation space of $\mathbb{C}{\rm P}^1$-structures. In this note, we summarize Thurston's parametrization of $\ma…

Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, includi…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the present paper is to provide a short overview of some results and open problems on s…

This is the second of two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R x (S^1 x S^2) as defined by a certain natural pair of almost complex structure and symplectic form. The first article in this series described the local structure of the moduli spaces and gave existe…

In this paper, we present an infinite hierarchical non-parametric Bayesian model to extract the hidden factors over observed data, where the number of hidden factors for each layer is unknown and can be potentially infinite. Moreover, the number of layers can also be infinite. We construct the model structure that allo…

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the {em marginal likelihood/} of the data given a candidate struct…

Proposes a flexible framework for implied volatility surfaces with random parameters.

Meta-materials simulation sped up with energy surrogates.

Optimal learning for parametric prophet inequalities with exponential-type distributions

A graph-based method for two-sample testing across connected nodes.

Paper relaxes assumptions for non-parametric estimation in pairwise learning.

DAG-FOCI learns causal relationships without parametric assumptions.

Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.

Flexible copula model using implicit generative neural networks.

A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A two-parametric family of complex connections is studied on a conformal Kähler manifo…

Develops flexible non-parametric ACFs using B-spline kernels.

A new approach to unsupervised learning using recognition-parametrised models.

Study identifies specialist representations from generalist models without parametric constraints.

Descending phase retrieval algorithms show a phase transition with increasing sample complexity.

New method estimates causal effects with multi-valued, time-varying treatments.

We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost co…

Unified analysis for nonlinear parametric models in Bayesian optimization.

Study algebraic relations of Vassiliev invariants for families of knots.

One of the fundamental problems in supervised classification and in machine learning in general, is the modelling of non-parametric invariances that exist in data. Most prior art has focused on enforcing priors in the form of invariances to parametric nuisance transformations that are expected to be present in data. Le…

Neural model improves option pricing by calibrating additive process term structure.

In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem directly from it, allowing to discard the dataset from the memory. This is useful w…

New method uses adversarial training for structural model estimation.