arXiv research

Any Sasakian structure can be closely mimicked by embeddings into weighted spheres.

Study approximates sub-Riemannian structures with Riemannian metrics and analyzes spectral convergence.

We derive caplet volatilities for quadratic models, providing an asymptotic approximation.

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is se…

Develops methods for structured variational inference with star-structured models.

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact Kähler manifolds and we present some basic properties of it. In particular, we show that its gradient flow can be wr…

Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.

Similarity algebra extends algebraic structures with quantitative bounds.

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is ba…

Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulat…

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generaliz…

Neural and numerical methods approximate G2-structures on Calabi-Yau manifolds.

Study approximates probability measures using structured classes of functions.

The computer program SnapPea can approximate whether or not a three manifold whose boundary consists of tori has a complete hyperbolic structure, but it can not prove conclusively that this is so. This article provides a method for proving that such a manifold has a complete hyperbolic structure based on the approximat…

Theory for deep neural network approximation of score function and its derivatives.

The geometry of supermanifolds provided with $Q$-structure (i.e. with odd vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic structure ) and $S$-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of Batalin-Vilkovisky ap…

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sa…

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact Kähler manifolds and we present some basic properties of it. In particular, we show that its gradient flow can be wr…

Constructs stable Hilbert bundles on curves using Diophantine approximation.

The paper analyzes deep ReLU CNNs' approximation properties in 2D space.

Structured Nonparametric Variational Inference for Dependent Latent Modeling

In this paper, using Donaldson's heat flow, we show that the semi-stability of a Higgs bundle over a compact Kähler manifold implies the existence of approximate Hermitian-Einstein structure on the Higgs bundle.

Compact Gaussian model approximates deep ensemble predictions.

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identificat…

Innovative PGMs match neural networks, revealing precise approximations during forward propagation.

This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.

New findings on how convolutional architectures approximate time series data.

Paper learns meaningful state and action representations from MDP trajectories.

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…

Improves Bayesian neural networks inference efficiency and accuracy.

Let E_G be a principal G-bundle over a compact connected Kähler manifold, where G is a connected reductive complex linear algebraic group. We show that E_G is semistable if and only if it admits approximate Hermitian-Einstein structures.

Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wish…

NODEs can approximate a wide range of diffeomorphisms with strong guarantees.

New model OPSS allows constant approximation for maximum coverage problem.

Bayesian structure learning improved using GFlowNets.

Study shows smooth holomorphic structures can be approximated from weak connections.

Generative model captures repetitive industrial processes with varying durations and dynamics.

We simplify SSL by approximating redundant structural components with low-rank factorization.

Paper proposes Walsh-Hadamard Variational Inference for efficient approximate inference in large models.

We simplify a complex volatility model to make it easier to price options.

Library learns Bayesian networks from mixed data without discretization.

Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving approximate inference over the latent variables by minimizing a tight upper bound on …

JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.

Many predicted structured objects (e.g., sequences, matchings, trees) are evaluated using the F-score, alignment error rate (AER), or other multivariate performance measures. Since inductively optimizing these measures using training data is typically computationally difficult, empirical risk minimization of surrogate …

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field approaches have been used. However, mean field approximations assume a factorized di…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on the Tucker factorisation of tensors. The probabilistic interpretation of such ap…

Proposes a balanced multi-component and multi-layer neural network for efficient function approximation.

The paper simplifies Bayesian posterior using clustering to make inference more manageable.