A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New theoretical framework improves error rates for sparse learning with convex regularization.
RTC-GTNLN model recovers traffic data from missing values and noise.
Deep neural networks (DNNs) are known vulnerable to adversarial attacks. That is, adversarial examples, obtained by adding delicately crafted distortions onto original legal inputs, can mislead a DNN to classify them as any target labels. In a successful adversarial attack, the targeted mis-classification should be ach…
We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via L1-L1 and L1-L2 minimization. We then provide lower bounds on the number of measuremen…
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either study the group sparsity in the parametric setting (e.g., group lasso), or addre…
In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds of the complex dimension bigger than or equal to 2.
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…
We consider the problem of learning a high-dimensional multi-task regression model, under sparsity constraints induced by presence of grouping structures on the input covariates and on the output predictors. This problem is primarily motivated by expression quantitative trait locus (eQTL) mapping, of which the goal is …
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regulariz…
We present a generalization of the Cauchy/Lorentzian, Geman-McClure, Welsch/Leclerc, generalized Charbonnier, Charbonnier/pseudo-Huber/L1-L2, and L2 loss functions. By introducing robustness as a continuous parameter, our loss function allows algorithms built around robust loss minimization to be generalized, which imp…
This paper analyzes Stochastic Depth regularization in ResNets.
A new method for sparse regression models using graph structure.
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discov…
In this paper, we focus on online representation learning in non-stationary environments which may require continuous adaptation of model architecture. We propose a novel online dictionary-learning (sparse-coding) framework which incorporates the addition and deletion of hidden units (dictionary elements), and is inspi…
ICCNLS models complex relationships as convex and concave components.
The performance of the state-of-the-art image segmentation methods heavily relies on the high-quality annotations, which are not easily affordable, particularly for medical data. To alleviate this limitation, in this study, we propose a weakly supervised image segmentation method based on a deep geodesic prior. We hypo…
Throughout the past five years, the susceptibility of neural networks to minimal adversarial perturbations has moved from a peculiar phenomenon to a core issue in Deep Learning. Despite much attention, however, progress towards more robust models is significantly impaired by the difficulty of evaluating the robustness …
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…
Study improves generalization bounds for linear regression across tasks.
Statistical characteristics of deep network representations, such as sparsity and correlation, are known to be relevant to the performance and interpretability of deep learning. When a statistical characteristic is desired, often an adequate regularizer can be designed and applied during the training phase. Typically, …
We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regressio…
Multi-label text classification is a popular machine learning task where each document is assigned with multiple relevant labels. This task is challenging due to high dimensional features and correlated labels. Multi-label text classifiers need to be carefully regularized to prevent the severe over-fitting in the high …
New link groups are derived from torus necklaces, connecting braid groups to reflection groups.
Computes cohomology groups for NEC groups, focusing on Fuchsian groups.
The study proves super-rigidity of Gromov's random monster group for various types of groups.
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi--direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi--direct product of free groups. From these results we obtain a normal form of words…
Virtual twin groups map to symmetric groups, revealing automorphism structure.
Characterizes group connections on group bundles.
Study on totally symmetric sets with group applications.
Affine cactus groups are CAT(0) and hyperbolic.
The study restricts groups in graph of groups structures.
New Garside structures found for torus knot groups and related braid groups.
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
New Garside structures derived from groups, leading to new group properties.
We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F, V, Vbr and Fbr arise from this procedure using, respectively, the systems of trivial groups, symmetric groups, braid groups and pur…
The group of 2-by-2 matrices with integer entries and determinant can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional torus. Thus this group is the beginning of three natural sequences of groups, name…
The study restricts normal subgroups of Kähler groups, proving specific cases and general restrictions.
New reflection groups derived from torus knots with finite meridians.
Graphically discrete groups have strong rigidity properties.
Paper proves vanishing homology groups for certain hyperbolic groups.
Study fundamental groups of geometric transformation groups using loop spaces.
The paper describes geometrically how certain groups act on surfaces.
Simple construction of Lie 2-groups from loop group extensions.
Study knot invariants using automorphism groups of free nilpotent groups.
We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…
We exhibit a family of infinite, finitely-presented, nilpotent-by-abelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic…
The study shows that certain groups can be uniquely identified by their finite abelian summands.
Survey on Coxeter groups for Lie group examples.