arXiv research

Optimal microlending group size is 5 people.

Proposes a differentiable hypergeometric distribution for learning group importance.

New theorem bounds group quotient size to subgroups index.

Paper classifies totally symmetric sets in groups and bounds their sizes.

Multi-group learners suffer a penalty in transductive learning.

We prove that the rank (that is, the minimal size of a generating set) of lattices in a general connected Lie group is bounded by the co-volume of the projection of the lattice to the semi-simple part of the group. This was proved by Gelander for semi-simple Lie groups and by Mostow for solvable Lie groups. Here we con…

The paper analyzes how contagion affects the survival probability of investment groups in microfinance.

For $n$ at least 7 and $n$ equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on $n$ strands. These generating sets are of the smallest possible cardinality. For $n$ equal to 4 or 6, we give generating sets of size three. We also prove that the commutator subgroup of the braid …

The paper characterizes simply connected quandles using cocycles with prime values.

We present a novel approach which is able to explore the configuration of grouped convolutions within neural networks. Group-size Series (GroSS) decomposition is a mathematical formulation of tensor factorisation into a series of approximations of increasing rank terms. GroSS allows for dynamic and differentiable selec…

1-D CNNs classify pupil size variations in scotopic conditions.

Develops a new model to predict training dynamics of large language models.

Throwing away data can improve worst-group error in imbalanced datasets.

Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed individually because of their small sample size. Bayesian nonparametric modellin…

We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the braid group.

Estimates sample size for subgroup analysis in randomized experiments.

In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary.

Reduced sample complexity for group-invariant distributions.

Using the classification of transitive groups we classify indecomposable quandles of size <36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all indecomposable quandles of size <36 not of type D is computed.

Sharp bounds found on nonabelian quotients of surface braid groups.

Maximizes filling systems on surfaces with given boundary components.

Unified framework for fair decision-making across diverse groups.

Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup of the mapping class group has a finite generating set whose size grows cubically with respect to the genus of the surface. Our main tool is a new space called the handle graph on which the Torelli group acts cocompactly.

Study shows pooling scores for conformal prediction distorts group coverage.

The study examines how equivariance in networks affects generalization error using PAC-Bayesian bounds.

Loss minimization leads to multicalibration for neural networks.

A new bootstrapping method reduces key sizes and runtime in FHE.

E2GC optimizes energy efficiency in DNNs by balancing computational and data movement costs.

New algorithm groups variables by ancestral relationships to improve causal graph estimation accuracy.

New bounds on sample size for identifying mixture models with grouped samples.

MRI image quality affects statistical and predictive analysis of brain morphology.

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion…

Group Shapley evaluates feature groups in business data, improving explainability in AI.

Reflective of income and wealth distributions, philanthropic gifting appears to follow an approximate power-law size distribution as measured by the size of gifts received by individual institutions. We explore the ecology of gifting by analysing data sets of individual gifts for a diverse group of institutions dedicat…

Study identifies negative data externalities affecting model performance on specific groups.

The paper explores properties of continuous actions on manifolds, proving bounds on subgroup size and fixed points.

New mathematical framework proves the effectiveness of reducing neural network sizes.

Connectivity studies using resting-state functional magnetic resonance imaging are increasingly pooling data acquired at multiple sites. While this may allow investigators to speed up recruitment or increase sample size, multisite studies also potentially introduce systematic biases in connectivity measures across site…

Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional filters over joint steerable bases across the space and the group …

Automorphisms of free groups yield invariant posets of lamination orbits.

In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure efficiency in terms of the size of the quotients required to distinguish a distinc…

The paper improves A/B testing for non-Gaussian data, ensuring reliable results with large sample sizes.

In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past the common approach has been to use various "group sparsity-inducing" norms such as the Group LASSO norm for this purpose. By using the theory of convex relaxations, we show that it is also po…

We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected tr…

Facing a heavy task, any single person can only make a limited contribution and team cooperation is needed. As one enjoys the benefit of the public goods, the potential benefits of the project are not always maximized and may be partly wasted. By incorporating individual ability and project benefit into the original pu…

In this paper we consider the problem of grouped variable selection in high-dimensional regression using $\ell_1-\ell_q$ regularization ($1\leq q \leq \infty$), which can be viewed as a natural generalization of the $\ell_1-\ell_2$ regularization (the group Lasso). The key condition is that the dimensionality $p_n$ can…

In this paper we purpose a blockwise descent algorithm for group-penalized multiresponse regression. Using a quasi-newton framework we extend this to group-penalized multinomial regression. We give a publicly available implementation for these in R, and compare the speed of this algorithm to a competing algorithm --- w…

A new method improves AI fairness assessment by estimating performance across intersectional subgroups.