An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables. The undirected graphical model selection (UGMS) problem is to es…
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48 results for “junction trees”
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
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…
Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies predominantly on local search heuristics such as Expectation Maximization. Using te…
A new method for selecting high quality itemsets from a large collection.
problem Selecting a small, high-quality subset of patterns from a larger collection of itemsets.
method Using decomposable families of itemsets and a junction tree structure.
result The method provides high quality results and is computationally efficient.
A new framework for efficient Bayesian network inference.
problem High-dimensional Bayesian networks are hard to infer due to computational scaling.
method Directed convex subgraphs and minimal d-decomposition tree for decomposition, enabling parallel computation.
result The method reduces computational cost and enables parallel computation.
We seek to automate the design of molecules based on specific chemical properties. In computational terms, this task involves continuous embedding and generation of molecular graphs. Our primary contribution is the direct realization of molecular graphs, a task previously approached by generating linear SMILES strings …
Study on network flow singularities, focusing on Type-0 singularities.
problem Understanding singularities in network flow evolution.
method Analysis of curvature evolution and junction behavior.
result Bounded curvature for Type-0 singularities in network flow.
A new neural network model for molecular graphs that learns efficiently and accurately.
problem Learning on molecular graphs with cycles and complex structures.
method Hierarchical inter-message passing using raw graph and junction tree representations.
result The model outperforms classical GNNs in detecting cycles and is efficient to train.
A market-maker-based prediction market lets forecasters aggregate information by editing a consensus probability distribution either directly or by trading securities that pay off contingent on an event of interest. Combinatorial prediction markets allow trading on any event that can be specified as a combination of a …
Constructs perturbations of a minimal surface with triple junctions.
problem Minimal surfaces with triple junctions in curved spaces.
method Constructs stationary perturbations with given boundary conditions.
result Constructs minimal surfaces with triple junctions in .
Self-Expanding Solutions to the Mean Curvature Flow for Multiphase Surfaces with Regular Junctionsmath.DG
Study proves existence of expanding solutions for multiphase surfaces with regular junctions.
problem Existence of self-similar expanding solutions for multiphase surfaces with regular junctions.
method Proves existence of solutions for a multiphase surface with regular junctions using mean curvature flow.
result Multiple self-similar expanding solutions exist for the initial condition of a multiphase surface with regular junctions.
Uniformizes surfaces with boundaries, focusing on triple junctions.
problem Uniformization of surfaces with boundaries, especially triple junctions.
method Extends conformal structure results to triple junction surfaces.
result Weak uniformization results for triple junction surfaces.
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string junctions is naturally related to the Lie algebra structures of the associated singular…
The paper proves a regularity theorem for Brakke flows near triple junctions.
problem Understanding the structure of triple junctions in Brakke flows.
method Establishes the ε-regularity theorem for k-dimensional Brakke flows near static, multiplicity-one triple junctions.
result The regular structure of triple junctions persists under weak mean curvature flow.
Paper studies curvature of stable surfaces meeting at a common boundary.
problem Stable multiple junction surfaces and their curvature estimates.
method Derived estimate of curvature for stable multiple junction surfaces.
result Bernstein Theorem holds for stable multiple junction surfaces in certain cases.
We study junctions of Wilson lines in refined SU(N) Chern-Simons theory and their local relations. We focus on junctions of Wilson lines in antisymmetric and symmetric powers of the fundamental representation and propose a set of local relations which realize one-parameter deformations of quantum groups $\dot{U}_{q}(\m…
We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the evolution.
This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all the measurements to have been collected before processing begins. We propose an…
New geometric approach realizes 5D bulk theories with 4D edge modes.
problem Realizing novel higher-dimensional junctions of theories coupled to localized edge modes.
method M-theory on singular, asymptotically conical G2-holonomy orbifolds.
result Geometric approach shows how bulk generalized symmetries are inherited in the boundary system.
We prove that there are no networks homeomorphic to the Greek "theta" letter (a double cell) embedded in the plane with two triple junctions with angles of degrees, such that under the motion by curvature they are self-similarly shrinking. This fact completes the classification of the self-similarly shrinking net…
Finite singular times for symmetric network curvature flow.
problem Formation of singularities in network curvature flow.
method Curvature flow of networks with symmetric initial data and two triple junctions.
result The set of singular times is finite.
In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be described by a Bayesian network that evolve dynamically over time and the observ…
A parametrization of hypergraphs based on the geometry of points in is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or M…
Energy-efficient sampling for machine learning using magnetic tunnel junctions.
problem Costly and inefficient random sampling in machine learning.
method Energy-efficient algorithm using stochastic magnetic tunnel junctions for uniform Float16 sampling.
result Higher energy efficiency than state-of-the-art algorithms, with a minimum factor of 9721.
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface opera…
We view molecular optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be optimized in different ways, there are multiple viable translations for each input graph…
Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants. In particular, it is known that using BP on a single-cycle graph or tree reweighted BP on an arbitrary graph will give the …
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
The goal of this project is to introduce and present a machine learning application that aims to improve the quality of life of people in Singapore. In particular, we investigate the use of machine learning solutions to tackle the problem of traffic congestion in Singapore. In layman's terms, we seek to make Singapore …
We consider the motion by mean curvature of an -dimensional graph over a time-dependent domain in , intersecting at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic equation with a free boundary, and derive a continuation criteri…
Study 6D localized matter spectrum on singular Calabi-Yau 3-folds.
problem Determining 6D localized charged matter spectrum on singular spaces.
method Using string junctions and monodromy to compute massless string junctions.
result Agreement with 6D anomaly cancellation in all cases considered.
The paper proves stability and convergence of minimal networks under curvature motion.
problem Stability and convergence of minimal networks under curvature motion.
method Proved Lojasiewicz-Simon gradient inequalities for minimal networks.
result Motion by curvature starting from networks close to minimal ones exists for all times and smoothly converges.
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional indepe…
We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation and asymptotic behavior of the flow.
XIMP improves molecular property prediction by integrating multiple graph representations.
problem Graph neural networks struggle in data-scarce regimes and fail to surpass traditional methods.
method Cross-graph inter-message passing with multiple graph abstractions.
result XIMP outperforms state-of-the-art baselines across diverse molecular property tasks.
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smoot…
Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe limitations that largely restrict their applicability and affect their performance. In…
In this paper, we prove Lorentzian positive mass theorem for spacetimes with distributional curvature. To do so, we introduce distributional curvature and generalized Arnowitt-Deser-Misner (ADM) momentum. As an application, we discuss a junction of spacetimes.
Minimal elastic networksmath.AP
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties of the minimal configurations.
Degenerate elastic networksmath.OC
We minimize a linear combination of the Willmore and the length functional among networks in belonging to a given class determined by the number of curves, the order of the junctions and the angles between curves at the junctions. Since this class lacks compactness, we characterize the set of limits of s…
Model predicts anti-cancer drug responses using gene and molecular data.
problem Expensive and time-consuming cancer drug discovery and tailoring.
method Uses variational autoencoders and multi-layer perceptrons to encode gene expression and drug data.
result High average of 0.83 and 0.845 in predicting drug responses for breast and pan-cancer cell lines, respectively.
A new method for CT-DCEGs simplifies inference for asymmetric processes.
problem Inference in asymmetric state space problems with continuous time evolution.
method An extension of CEG propagation for CT-DCEGs, employing junction tree inference.
result CT-DCEGs are preferred over DBNs and continuous time BNs for asymmetric processes.
Researchers use active subspaces to quantify uncertainty in deep generative models for molecular design.
problem Uncertainty quantification in deep generative models for molecular design due to high parameter space.
method Leveraging active subspaces to approximate posterior distribution over low-dimensional parameters.
result The proposed UQ scheme effectively estimates epistemic uncertainty in high-dimensional parameter space without altering model architecture.
Proves existence and uniqueness of curvature motion for regular networks.
problem Existence and uniqueness of motion by curvature for regular networks.
method Proves existence and uniqueness using $W^{2- rac{2}{p}}_p$ initial data and investigates regularization effects.
result Proves existence and uniqueness of motion by curvature for regular networks.
We study the curvature flow of planar nonconvex lens-shaped domains, considered as special symmetric networks with two triple junctions. We show that the evolving domain becomes convex in finite time; then it shrinks homothetically to a point. Our theorem is the analog of the result of Grayson for curvature flow of clo…
Surface tension of multi-phase flow with multiple junctions governed by the variational principlemath.NA
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, …
Co-PLNet combines point and line predictions to improve wireframe parsing accuracy and efficiency.
problem Separate line and point predictions lead to inconsistent wireframes.
method Co-PLNet uses a Point-Line Prompt Encoder to convert early point detections into spatial prompts, which guide line refinement.
result Co-PLNet achieves better accuracy and robustness in wireframe parsing compared to existing methods.