arXiv research

Algorithm estimates nonparametric mixtures from grouped data.

We would like to learn a representation of the data which decomposes an observation into factors of variation which we can independently control. Specifically, we want to use minimal supervision to learn a latent representation that reflects the semantics behind a specific grouping of the data, where within a group the…

Bayesian approach groups observations with similar effects for better inference.

Study of isometries in spacetimes without observer horizons.

We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler-Lagrange equations on the 2nd order tangent group from the 1st order Euler-Lagrange equ…

Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this paper, we use this property for the observability analysis of nonlinear PDEs with input and output. Based on a differential-geometric representation of the nonlinear system, we derive conditions for the existence of special …

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.

New model clusters cells and individuals, revealing genetic influences on cell types.

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…

SymmPI predicts unobserved values under group symmetries, improving over existing methods.

The study finds non-trivial elements in moduli spaces of curvature metrics.

Study shows Morse elements are common in acylindrically hyperbolic groups.

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 $l_1/l_2$ regularization upon the activation possibilities of hidden unit…

The paper proposes an estimator to make inference of heterogeneous treatment effects sorted by impact groups (GATES) for non-randomised experiments. The groups can be understood as a broader aggregation of the conditional average treatment effect (CATE) where the number of groups is set in advance. In economics, this a…

Models for sequential data such as the recurrent neural network (RNN) often implicitly model a sequence as having a fixed time interval between observations and do not account for group-level effects when multiple sequences are observed. We propose a model for grouped sequential data based on the RNN that accounts for …

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 $Diff_{+}^{1}(\mathbb{S}^1)$ of orientation-preserving $C^1$-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…

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.

Complex systems may contain heterogeneous types of variables that interact in a multi-level and multi-scale manner. In this context, high-level layers may considered as groups of variables interacting in lower-level layers. This is particularly true in biology, where, for example, genes are grouped in pathways and two …

For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.

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.

EbC learns equivariant embeddings from unlabeled group actions.

Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to multiple independent observations of event time data, observed on a common inter…

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.

For fixed subgroups $Fix(φ)$ of automorphisms $φ$ on hyperbolic 3-manifold groups $π_{1}(M)$, we observed that $\text{rk}(Fix(φ))<2\text{rk}(π_{1}(M))$ and the constant 2 in the inequality is sharp; we also classify all possible groups $Fix(φ)$.

New findings on compactness and fundamental groups of certain spacetime manifolds.

Study invariant Lipschitz bandits, improving regret bounds.

Study develops a new method for creating fair models.

Machine learning accurately distinguishes Sato-Tate groups for hyperelliptic curves.

Deep generative models have recently yielded encouraging results in producing subjectively realistic samples of complex data. Far less attention has been paid to making these generative models interpretable. In many scenarios, ranging from scientific applications to finance, the observed variables have a natural groupi…

Method estimates group structure in panel data using variance information.

Toward enabling next-generation robots capable of socially intelligent interaction with humans, we present a $\mathbf{computational\; model}$ of interactions in a social environment of multiple agents and multiple groups. The Multiagent Group Perception and Interaction (MGpi) network is a deep neural network that predi…

New method identifies causal relationships without strong assumptions.

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…

The observer moduli space of Riemannian metrics is the quotient of the space $\mathcal{R}(M)$ of all Riemannian metrics on a manifold $M$ by the group of diffeomorphisms $\mathrm{Diff}_{x_0}(M)$ which fix both a basepoint $x_0$ and the tangent space at $x_0$. The group $\mathrm{Diff}_{x_0}(M)$ acts freely on $\mathcal{…

New challenges in causal inference with big data.

Autoencoder learns group representations from actions, improving future prediction accuracy.

Derives geometrically a description of a 3-manifold's second homotopy group.

PD_3-groups split as HNN extensions, revealing homology class properties.

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…

Criterion for periodic orbits convergence proved.

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…

New hyperbolic groups exhibit unusual finiteness properties.

The paper explores metrics on tree moduli spaces and a new topological group.

Given a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmuller space of the surface, and will study the isometric action of the mapping class group on it. The main observation is that the geometric characteristics of the setting bear strong similarities to the ones in semi-simple Lie …

Study group actions in metric spaces, proving convergence of lens spaces.