arXiv research

IDA adapts to non-iid data in federated learning for medical imaging.

Inversive distance circle packing metric was introduced by P Bowers and K Stephenson \cite{BS} as a generalization of Thurston's circle packing metric \cite{T1}. They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo \cite{Guo} proved the infinitesimal rigidity a…

Proves rigidity of circle packings in the plane, generalizing previous work.

We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.

Paper proves circle packings converge to Riemann mapping for Jordan domains.

Inversive distance circle packing on surfaces was introduced by Bowers-Stephenson as a generalization of Thurston's circle packing and conjectured to be rigid. The infinitesimal and global rigidity of circle packing with nonnegative inversive distance were proved by Guo and Luo respectively. The author proved the globa…

This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the $W_2$ distance has a smoothing effect on the inversion pro…

The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.

This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfaces introduced by P. Bowers and K. Stephenson as a generalization of Andreev-Thurston's circle packing. They conjectured that inversive dist…

A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.

In this paper, we generalize Chow-Luo's combinatorial Ricci flow to inversive distance circle packing setting. Although the solution to the generalized flow may develop singularities in finite time, we can always extend the solution so as it exists for all time and converges exponentially fast. Thus the generalized flo…

The paper proves the existence of a unique circle packing on hyperbolic surfaces.

We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…

The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice and may be inappropriate in some contexts. Our concept sim…

Deep learning models have shown state-of-the-art performance in many inverse reconstruction problems. However, it is not well understood what properties of the latent representation may improve the generalization ability of the network. Furthermore, limited models have been presented for inverse reconstructions over ti…

Given a triangulated surface $M$, we use Ge-Xu's $α$-flow \cite{Ge-Xu1} to deform any initial inversive distance circle packing metric to a metric with constant $α$-curvature. More precisely, we prove that the inversive distance circle packing with constant $α$-curvature is unique if $αχ(M)\leq 0$, which generalize And…

Develops a new method to compute risk-sharing allocations using Laplace transforms.

Data aggregation improves HAC for resource-constrained systems.

Sharp bounds found on expert error in binary advice aggregation.

The aim of the paper is to investigate the relation between inverse limit of branched manifolds and codimension zero laminations. We give necessary and sufficient conditions for such an inverse limit to be a lamination. We also show that codimension zero laminations are inverse limits of branched manifolds. The inverse…

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly matc…

The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.

Robo-advisor uses ML to optimize investment performance.

Probabilistic graphical models are graphical representations of probability distributions. Graphical models have applications in many fields including biology, social sciences, linguistic, neuroscience. In this paper, we propose directed acyclic graphs (DAGs) learning via bootstrap aggregating. The proposed procedure i…

The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.

Paper introduces WWAggr for ensemble CPD, improving accuracy and decision threshold selection.

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time position follows a Gaussian mixture distribution, a fact exploited to softly …

Reconstructing manifolds from partial distance and heat kernel data.

Generative models improve inverse problems by providing tailored priors.

Graph curvature measured by inverse resistance distance.

Unified framework recovers exact input from SOM activation patterns.

Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning algorithm, and develop a distributed scheme learning metrics on moderate-sized subsets…

A new method reduces complexity in estimating dynamic choice models.

New theorem proves rigidity of circle packings in hyperbolic geometry.

Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fixed design and measure the distance between functions by …

Study improves estimation of functions from noisy data using convex penalties.

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the…

AEA dynamically aggregates ensemble targets for actor-critic learning.

New method finds metrics on surfaces with prescribed curvatures using circle packings and surgery.

We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in~\cite{Ma:2012hl} of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary …

Study shows stability of travel time data reconstruction from closed subsets.

In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially conc…

A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated. This approach to evaluate ALD is based on purely non-parametric considerations, i.e., based on the empirical CFs of frequency …

This paper reviews SDR methods for multivariate response regression.

Energy distance measures feature heterogeneity in federated learning.

We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding spaces the direction of data generally contains richer information than magnitude.…

Hierarchical clustering uses OWA operators to generalize linkage methods and avoid dendrogram inversions.

Let $(N,g)$ be a Riemannian manifold with the distance function $d(x,y)$ and an open subset $M\subset N$. For $x\in M$ we denote by $D_x$ the distance difference function $D_x:F\times F\to \mathbb R$, given by $D_x(z_1,z_2)=d(x,z_1)-d(x,z_2)$, $z_1,z_2\in F=N\setminus M$. We consider the inverse problem of determining …