Algorithm estimates nonparametric mixtures from grouped data.
problem Estimating identifiable nonparametric mixture models from grouped observations.
method Oracle inequality for weighted kernel density estimators and general consistency result.
result Consistent estimation of mixture components from grouped observations.
ML-VAE learns disentangled representations from grouped data.
problem Learning disentangled representations from grouped observations with minimal supervision.
method Multi-Level Variational Autoencoder (ML-VAE) that separates latent representation at group and observation levels.
result ML-VAE learns meaningful disentanglement of grouped data and enables manipulation of latent representation.
The paper uses symmetry groups to simplify observability analysis of PDEs.
problem Observability of nonlinear PDEs with input and output.
method Differential-geometric representation and symmetry groups to transform solutions.
result Conditions for existence of symmetry groups that preserve input and output trajectories.
Bayesian approach groups observations with similar effects for better inference.
problem Estimating heterogeneity across observations in political science.
method Structured sparsity framework integrated into Bayesian regression analysis.
result Method outperforms state-of-the-art methods for heterogeneous effects estimation.
Study of isometries in spacetimes without observer horizons.
problem Understanding the symmetries of spacetimes without specific boundaries.
method Analysis of isometry groups in causal spacetimes without observer horizons.
result The group of time orientation-preserving isometries acts properly on the spacetime.
New dynamics derived from Lie groups using 2nd order tangent groups.
problem Deriving dynamics on complex Lie groups.
method Using double cross product groups and 2nd order Euler-Lagrange equations.
result 2nd order Lagrangian dynamics on double cross product groups derived.
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are themselves drawn from a probability measure P over probability measures. When estimating …
Two quandles from Coxeter groups studied, showing similarities in automorphism groups.
problem Understanding quandles from Coxeter groups and their automorphism groups.
method Defined two families of quandles from Coxeter quandles and Pin groups, analyzed their automorphism groups.
result Similarity in inner automorphism groups of the two quandles.
New model clusters cells and individuals, revealing genetic influences on cell types.
problem Clustering nested data with group-level and observation-level variables.
method Nested Atoms Model (NAM), Bayesian nonparametric approach.
result Identifies clusters of genetically similar individuals with homogeneous cell-type profiles.
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot observables (i.e. traces of holonomies along knots) essentially vanish, but yet, th…
Estimates heterogeneous treatment effects by grouping conditional average treatment effects.
problem Non-randomized experiments suffer from selection bias.
method Doubly-robust estimator, machine learning for propensity score and conditional mean functions, linear projection model, Neyman-orthogonal moments.
result Lower absolute errors and smaller bias compared to benchmark estimator.
SymmPI predicts unobserved values under group symmetries, improving over existing methods.
problem Quantifying uncertainty in predictions under group symmetries.
method Distributional equivariant transformations to preserve symmetries.
result SymmPI provides valid coverage and performs favorably in simulations and empirical data.
The study finds non-trivial elements in moduli spaces of curvature metrics.
problem Identifying non-trivial elements in moduli spaces of curvature metrics.
method Constructing elements in homotopy groups of moduli spaces of positive curvature metrics.
result Non-trivial elements found in moduli spaces of positive curvature metrics.
Proposes a new RNN model for grouped sequential data with varying time intervals.
problem Implicitly models fixed time intervals between observations and lacks group-level effects.
method Mixed membership framework for RNN, learning group-level base parameter.
result Demonstrates dynamic topic modeling with evolving topic distributions over time.
Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using l1/l2 regularization upon the activation possibilities of hidden unit…
Study shows Morse elements are common in acylindrically hyperbolic groups.
problem Understanding generic elements in acylindrically hyperbolic groups.
method Analyzing Morse elements and outer automorphisms.
result Morse elements are common in acylindrically hyperbolic groups.
Lickorish has constructed large families of contractible 4--manifolds that have knotted embeddings in the 4--sphere and has also shown that every finitely presented perfect group with balanced presentation occurs as the fundamental group of the complement of a knotted contractible manifold. Here we make a few observati…
We show that the topological groups Diff+1(I) and Diff+1(S1) of orientation-preserving C1-diffeomorphisms of the interval and the circle, respectively, admit finitely generated dense subgroups. We also investigate the question of genericity (in the sense of Baire category) of such finite to…
In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that "generic" finitely generated groups have no smooth volume preserving actions on compact manifolds while also producing many finitely presented, torsion free groups with the same pr…
For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.
Artin groups have a special structure that helps prove a complex mathematical conjecture.
problem Proving the Farrell-Jones isomorphism conjecture for Artin groups.
method Identifying an inductive structure in Artin groups and applying it to the conjecture.
result The Farrell-Jones isomorphism conjecture is proven for certain Artin groups.
EbC learns equivariant embeddings from unlabeled group actions.
problem Learning equivariant embeddings from unlabeled group actions.
method Equivariance by Contrast (EbC) method to learn equivariant embeddings from observation pairs (y,g⋅y). result High-fidelity equivariance in latent space for diverse groups.
In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.
New findings on compactness and fundamental groups of certain spacetime manifolds.
problem Understanding the compactness and fundamental groups of Zx manifolds. method Defined observer-refocusing spacetimes and used contact geometry to prove compactness and finite fundamental groups.
result Analytic Zx manifolds are Ylx manifolds for some l>0. We observe that a sharp result on the exponential growth rate of the number of primitive elements exists for the free group on two generators.
Method infers multi-layer networks from gene expression data.
problem Inference of multi-level networks from gene expression data.
method Extension of latent graphical lasso method leveraging group structure.
result Efficacy in retrieving multi-layer network structure from synthetic data.
For fixed subgroups Fix(φ) of automorphisms φ on hyperbolic 3-manifold groups π1(M), we observed that rk(Fix(φ))<2rk(π1(M)) and the constant 2 in the inequality is sharp; we also classify all possible groups Fix(φ).
Study invariant Lipschitz bandits, improving regret bounds.
problem Optimizing decisions under symmetry in online settings.
method Integrates side observations using group orbits into UniformMesh algorithm.
result Improved regret bound for invariant Lipschitz bandit class.
oi-VAE interprets complex data groups with nonlinear relationships.
problem Interpreting deep generative models for nonlinear group factor analysis.
method oi-VAE combines structured VAE with sparsity-inducing prior for nonlinear latent-to-observed relationships.
result oi-VAE yields meaningful interpretability in motion capture and MEG data.
MGpi model predicts social actions in group interactions.
problem Social interaction among multiple agents and groups.
method Deep neural network with Kinesic-Proxemic-Message gate for social signal gating.
result Achieves state-of-the-art performance in group identification.
Machine learning accurately distinguishes Sato-Tate groups for hyperelliptic curves.
problem Arithmetic of hyperelliptic curves and Sato-Tate conjecture.
method Bayesian classifier and machine learning techniques applied to L-functions of hyperelliptic curves.
result Machine learning can distinguish Sato-Tate groups with high accuracy and speed.
Study develops a new method for creating fair models.
problem Ensuring equal outcomes for different protected groups.
method Introduces a new group-fair constraint based on transport maps.
result Develops a novel algorithm FTM for training group-fair models.
Method estimates group structure in panel data using variance information.
problem Estimating group structure in panel data with unknown groups.
method Proposes a method to estimate unobserved groupings for panel data models using variance information.
result Superior performance compared to existing methods in simulations and empirical applications.
The paper studies non-trivial homotopy groups of moduli spaces of metrics with positive Ricci curvature.
problem Understanding the homotopy groups of moduli spaces of metrics with positive Ricci curvature.
method Uses gluing results from Perelman to establish infinite order elements in homotopy groups.
result Shows infinite order elements in the homotopy group π_{4k}M_{x_0}^{\mathrm{Ric}>0}(S^n) for odd dimensions n.
Upper bound found for rank gradient using simplicial volume.
problem Rank gradient of fundamental groups.
method Stable integral simplicial volume.
result Upper bound established for rank gradient.
Classifies and clusters event time data using non-homogeneous Poisson process models.
problem Classifying and clustering event time data from multiple observations.
method Modeling rate functions using spline basis expansion, estimating coefficients using maximum likelihood, and assigning observations to groups based on likelihood.
result The classification and clustering approaches perform well on both synthetic and real-world data.
New method identifies causal relationships without strong assumptions.
problem Causal Representation Learning (CRL) is ill-posed due to representation and causal discovery issues.
method Identifiability based on grouping of observational variables, self-supervised estimation framework.
result Practical identifiability conditions without temporal structure, interventions, or weak supervision.
Explains connections between free groups and positive definite functions.
problem Understanding positive definite functions on free groups.
method Expository survey of known results and new perspectives.
result New relationships between free groups and positive definite functions.
When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that observations from the mixture model are grouped, such that observations in the same gro…
New challenges in causal inference with big data.
problem Extending causal inference to incrementally available observational data.
method Formal definition of continual treatment effect estimation, solutions to challenges.
result New methods for handling challenges in causal inference with observational data.
Autoencoder learns group representations from actions, improving future prediction accuracy.
problem Learning internal models of interactions with the real world.
method Homomorphism autoencoder with group representation trained on equivariance-derived loss.
result Agents can predict future actions with improved accuracy.
Derives geometrically a description of a 3-manifold's second homotopy group.
problem Describing the second homotopy group of a 3-manifold using kernels of homomorphisms.
method Geometric derivation of Lei and Wu's result.
result Geometric derivation of the second homotopy group description.
PD_3-groups split as HNN extensions, revealing homology class properties.
problem Understanding PD_3-groups splitting as HNN extensions.
method Analyzing PD_3-groups splitting as HNN extensions and examining homology classes.
result The Poincaré dual of the homology class of a PD_3-group in the kernel of an epimorphism is revealed.
We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from observing that automorphisms of the free group strongly resemble s…
We consider topological T-duality of torus bundles equipped with S^{1}-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S^{1}-valued functions which are constant along the torus fibres. We observe that such a reduction is exactly the additional datum needed for the const…
Criterion for periodic orbits convergence proved.
problem Periodic orbits convergence criterion.
method Criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups.
result Criterion for periodic orbits convergence proved.
New hyperbolic groups exhibit unusual finiteness properties.
problem Finding groups with specific finiteness properties.
method Fibre product construction and homomorphisms to Z and Z2. result Examples of hyperbolic groups with kernels of type Fk but not Fk+1. The paper explores metrics on tree moduli spaces and a new topological group.
problem Continuous metrics on tree moduli spaces.
method Proposes and analyzes continuous piecewise-smooth metrics.
result Observes a new abelian topological group structure.