Efficiently reduces costs for Bayesian networks in FGrn form.
problem High computational and memory costs of Bayesian networks in FGrn form.
method Detailed algorithmic and structural analysis leading to cost reduction solutions, including an online learning algorithm.
result Proposed solutions and online learning algorithm significantly reduce costs for Bayesian networks.
A Bayesian factor graph reduced to normal form consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-dive…
Study of zero-divisors in sedenions via determinant factorization.
problem Characterizing zero-divisors in the sedenion algebra.
method Factorization of determinant of left multiplication, reduction to quaternionic normal form, block computation.
result Quartic polynomial factorization of determinant, geometric model of zero-divisor locus.
We prove a mapping between dual and primal factor graph marginals for efficient estimation.
problem Efficient estimation of marginal densities in factor graphs.
method Local mappings derived from Fourier transforms of local factors, applied to Ising and Potts models.
result Marginal densities can be more accurately estimated in the dual domain.
Novel CGTF model for recommender systems and community detection from coupled graphs and tensors.
problem Lack of effective methods for analyzing multiple information repositories with graph side information.
method Coupled Graph-Tensor Factorization (CGTF) with ADMM for nonnegative factor recovery.
result CGTF model successfully detects communities even with missing graph links.
The study finds that many mapping class groups have normal generators.
problem Finding normal generators in mapping class groups.
method Provided a criterion for normal closure and applied it to show normal generators for specific classes of mapping classes.
result Many nontrivial periodic mapping classes and pseudo-Anosov mapping classes are normal generators.
We find a closed-form determinant for a specific sparse covariance matrix model.
problem Finding the determinant of a specific class of sparse positive definite matrices.
method Using Fourier transform of local factors, Normal Factor Graph Duality Theorem, and Matrix Determinant Lemma.
result We derive a closed-form expression for the determinant.
The paper improves Gibbs sampling for large graphs by minibatching.
problem High computational cost of single Gibbs sampling update step.
method Minibatching: subsampling factors to estimate their sum.
result Minibatched Gibbs can be made unbiased and converge faster.
Normal forms and symplectic reduction for gauge field theory in infinite dimensions.
problem Understanding the structure of moduli spaces in gauge field theory.
method Establishing normal forms for equivariant maps and developing singular symplectic reduction in infinite dimensions.
result The reduced phase space decomposes into smooth manifolds each with a natural symplectic structure.
The paper proves spectral convergence rates for graph Laplacian to manifold Laplace-Beltrami operator.
problem Spectral convergence of graph Laplacian to manifold Laplace-Beltrami operator.
method Analysis of Dirichlet form convergence and construction of approximate eigenfunctions via manifold heat kernel.
result Proves spectral convergence rates for Gaussian kernelized graph Laplacian.
Graph normalizing flows use neural networks for graph prediction and generation.
problem Efficiently processing and generating graph data with reduced memory usage.
method Reversible graph neural network model combining auto-encoder and normalizing flows.
result Graph normalizing flows achieve competitive results in graph generation and prediction.
Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.
problem Efficient estimation of marginal probabilities in statistical physics models.
method Local mappings based on Fourier transform of local factors, applied to Ising, Potts, and clock models.
result Local extrema of fixed points are at phase transition points, and the mapping facilitates efficient estimation.
The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
Tensor variable elimination for plated factor graphs enables exact inference in models with repeated structure.
problem Efficient inference in models with repeated structure.
method Generalized variable elimination to tensor variable elimination on plated factor graphs.
result Tractable inference for a class of plated factor graphs.
A method to reduce knowledge graph embedding models by binarizing parameters.
problem Large memory requirements for tensor factorization models in knowledge graph completion.
method Introducing a quantization function to binarize parameters of CP tensor decomposition.
result Successfully reduced model size by more than an order of magnitude while maintaining task performance.
This paper studies mean curvature flows near cylindrical singularities.
problem Understanding the behavior of mean curvature flows near cylindrical singularities.
method Proved the rescaled flow converges to a graph over a cylinder, defined nondegeneracy, and showed properties of nondegenerate singularities.
result Nondegenerate cylindrical singularities are isolated, have a mean convex neighborhood, and are type-I.
Auto-decoder synthesizes graphs from latent codes.
problem Creating new graph structures from specified distributions.
method Generative model learns latent codes from empirical distribution. Self-attention identifies likely connectivity patterns. Graph-based normalizing flows sample latent codes.
result Model outperforms state of the art by 1.5x in accuracy and 2x in speed.
We consider graphs Sigma^n in R^m with prescribed mean curvature and flat normal bundle. Using techniques of Schoen, Simon and Yau, and Ecker-Huisken, we derive an interior curvature estimate of the form |A|^2<=C/R^2 up to dimension n<=5, where C is a constant depending on natural geometric data of Sigma^n only. This g…
Paper proves convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian and robustness to outlier noise.
problem Convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian and robustness to outlier noise.
method Proves convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian with rates, and proposes an approximate and constrained matrix scaling problem to achieve the same consistency rate.
result Graph Laplacian consistency rate matches the rate for clean manifold data plus an additional term proportional to the boundedness of the inner-products of the noise vectors.
Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension …
A normal form for edge metrics is derived under the necessary conditions that the metric be normalized and exact. The normal forms for such an edge metric are shown to be in 1-1 correspondence with representative metrics for a reduced conformal infinity on the boundary. The normal form is constructed via solution of a …
DGA and DVGA learn disentangled graph representations to improve graph analysis.
problem Holistic graph auto-encoders fail to capture latent factors effectively.
method Design disentangled graph convolutional network and component-wise flow, impose independence constraints.
result Improved disentangled graph representations enhance graph analysis tasks.
New method approximates partition function of graphical models using gauge functions and polynomials.
problem Computing the partition function of graphical models is computationally challenging.
method Combines gauge function technique with real stable polynomials to approximate partition function.
result Belief Propagation estimations in the sequence do not decrease and low-bound the partition function.
We show that Caratheodory's conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one umbilic in the graphs of functions f: R^2-->R whose gradient decays uniformly faster than 1/r. The divergence theorem then yields a pair of integral equations for the norm…
Normal forms for equivariant maps in infinite dimensions established.
problem Establishing normal forms for equivariant maps in infinite-dimensional manifolds.
method Inspired by Lyapunov-Schmidt reduction and Kuranishi method, uses Slice Theorem for Fréchet manifolds.
result Abstract moduli spaces of equivariant maps are locally modeled on quotient by a compact group.
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise naturally when working with factor graphs. Belief propagation is a widely deplo…
We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimiz…
Extract common latent factors from graphs for better representation learning.
problem Graph-level representation learning challenges due to limited labeled data and poor negative sample selection.
method Graph-wise Common Latent Factor Extraction (GCFX) using deepGCFX model.
result Improved graph-level and node-level tasks performance compared to state-of-the-art methods.
Study ancient solutions on graphs with unbounded Laplacians, generalizing previous results.
problem Understanding ancient solutions on graphs with unbounded Laplacians.
method Generalizing Colding and Minicozzi's theorem and Hua's result to graphs with unbounded Laplacians.
result The dimension of the space of ancient solutions of polynomial growth is bounded by the dimension of harmonic functions with the same growth.
The paper examines deformations of simple dotted graphs made of circles.
problem Investigating reducibility of admissible dotted graphs.
method Analyzes deformations of admissible dotted graphs consisting of standard circles.
result Identifies specific conditions under which certain dotted graphs can be reduced.
FDR criterion simplifies complex causal graphs to a standard front-door setting.
problem Complex causal graphs make identification of causal effects difficult and computationally infeasible.
method Front-door reducibility (FDR) criterion and FDR-TID algorithm.
result Many graphs can be simplified to a standard front-door setting, making causal effect identification simpler and more interpretable.
GANF uses normalizing flows to detect anomalies in multiple time series.
problem Detecting anomalies in multiple time series with interdependencies.
method Bayesian network integration with normalizing flows for unsupervised anomaly detection.
result GANF effectively detects anomalies and identifies distribution drift in time series data.
New theory for partial disentanglement from sparse graphs.
problem Disentangling latent factors from sparse causal graphs.
method Generalization of disentanglement theory to any graph, using consistency equivalence.
result Partial disentanglement captures expected factor entanglement based on graph structure.
Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's …
Normal forms and isotropic embeddings via Euler-like vector fields.
problem Proving normal forms results for geometric structures.
method Construction of Euler-like vector fields compatible with geometric structures.
result Illustrated in various examples, including Morse-Bott, Weinstein, and Zung's theorems.
Sharp curvature bounds for minimal graphs over unit disk.
problem Proving sharp curvature bounds for minimal graphs.
method Analyzing minimal graphs over unit disk, using Heinz constant and Hopf constant.
result Improved estimate for curvature of minimal graphs and sharp inequality.
The thesis shows how automorphisms of hyperbolic groups can be represented by train track maps.
problem Representing automorphisms of hyperbolic groups using train track maps.
method Using graphs of groups and Bestvina-Handel's irreducible train track maps, the thesis constructs relative train track maps.
result Outer automorphisms of finitely-generated word hyperbolic groups satisfy a dynamical trichotomy.
We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in quant trading with much shorter holding horizons is suboptimal: 1) longer horizon …
Paper introduces Categorical Normalizing Flows for better handling of categorical data.
problem Limited application of normalizing flows on categorical data due to lack of intrinsic order.
method Categorical Normalizing Flows use continuous transformations to model latent relations in categorical data, optimizing both continuous representation and model likelihood.
result GraphCNF, a permutation-invariant generative model, outperforms state-of-the-art on molecule generation.
A new method for machine learning updates reduces complexity and improves robustness.
problem Stochastic gradient updates are inefficient and sensitive to feature scaling.
method Incremental Gauss-Newton Descent (IGND) reduces the need for matrix operations and improves robustness.
result IGND improves robustness to sensitivity scaling and can be competitive with common stochastic optimizers.
Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid sends a curve to another curve, then the image of this curve after each factor o…
BR-SNIS reduces bias in self-normalized IS without increasing variance.
problem Bias in self-normalized IS.
method Iterated sampling-importance resampling (ISIR) to form a bias-reduced estimator.
result Significant reduction in bias without increasing variance.
Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factoriza…
The study defines and constructs hypersurfaces in a product of two space forms.
problem Characterizing hypersurfaces in a product of two space forms.
method Explicit construction using parallel families of hypersurfaces and isoparametric hypersurfaces.
result Classification of hypersurfaces with constant mean curvature and constant product angle function.
IPGDN learns disentangled node representations in graphs.
problem Learning disentangled node representations in graph convolutional networks (GCNs).
method IPGDN uses neighborhood routing mechanism and HSIC to enforce independence among latent representations.
result IPGDN outperforms state-of-the-arts in graph classification, clustering, and visualization.
Let φ(G) be the minimum conductance of an undirected graph G, and let 0=λ_1 <= λ_2 <=... <= λ_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, φ(G) = O(k) λ_2 / \sqrt{λ_k}, and this performance guarantee is achieved by the spectral partitioning algorithm. …
We study very small trees from the point of view of reducing systems of free factors, which are analogues of reducing systems of curves for a surface lamination; a non-trivial, proper free factor $F \leq \FN$ reduces T if and only if F acts on some subtree of T with dense orbits. We characterize those trees, call…