arXiv research

The study shows that several properties are not profinite invariants.

Topic models are popular for modeling discrete data (e.g., texts, images, videos, links), and provide an efficient way to discover hidden structures/semantics in massive data. One of the core problems in this field is the posterior inference for individual data instances. This problem is particularly important in strea…

Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximatio…

We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group $Γ$ has the fixed point property FW for walls (e.g. if it has property (T)), every aperiodic action of $Γ$ by diffeomorphisms that are of class $C^r$ with countably many singularities is con…

We prove the local-in-time well-posedness for the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \fw) \in H^s\times H^s\times H^{s'}$, $2<s'<s$. The classical local well-posedness result for the compressible Euler equations in $3$-D holds f…

Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to $\log(\frac{1}ε)$ for the smooth and strongly convex objective. This complexity result is esp…

Momentum accelerates Frank Wolfe algorithms on certain problems.

We study commensurating actions of groups and the associated properties FW and PW, in connection with wallings, median graphs, CAT(0) cubings and multi-ended Schreier graphs.

Discrete return (DR) Laser Detection and Ranging (Ladar) systems provide a series of echoes that reflect from objects in a scene. These can be first, last or multi-echo returns. In contrast, Full-Waveform (FW)-Ladar systems measure the intensity of light reflected from objects continuously over a period of time. In a c…

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solv…

We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only requires to solve a linear minimization problem over a small \emph{subset} of the or…

We consider the applications of the Frank-Wolfe (FW) algorithm for Apprenticeship Learning (AL). In this setting, we are given a Markov Decision Process (MDP) without an explicit reward function. Instead, we observe an expert that acts according to some policy, and the goal is to find a policy whose feature expectation…

Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the symmetric nonnegative matrix factorization problem under a simplicial constraint, whic…

Two new Frank-Wolfe algorithms improve convergence for constrained optimization.

Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and the incremental nature of the method make FW a very effective choice for many l…

The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known to be slow (sublinear) when the solution lies at the boundary. A simple less-know…

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been successfully applied to train large-scale instances of non-linear Support Vector M…

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling high dimensional constrained problems, as the projection step becomes computationa…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention …

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we cons…

A dissertation on scalable projection-free optimization methods.

Local LMO optimizes constrained problems using local linear minimization.

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the …

Algorithm ensures safe optimization under unknown constraints.

Proposes a new derivative concept for nonlinear DRO problems.

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method …

Frank-Wolfe algorithms have recently regained the attention of the Machine Learning community. Their solid theoretical properties and sparsity guarantees make them a suitable choice for a wide range of problems in this field. In addition, several variants of the basic procedure exist that improve its theoretical proper…

Inference is an integral part of probabilistic topic models, but is often non-trivial to derive an efficient algorithm for a specific model. It is even much more challenging when we want to find a fast inference algorithm which always yields sparse latent representations of documents. In this article, we introduce a si…

Paper develops zeroth and first order stochastic Frank-Wolfe algorithms for constrained optimization.

We say that a group has property $R_{\infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\infty}$. We define a solvable generalization $Γ(S)$ of these groups which we show to have proper…

We use partial actions, as formalized by Exel, to construct various commensurating actions. We use this in the context of groups piecewise preserving a geometric structure, and we interpret the transfixing property of these commensurating actions as the existence of a model for which the group acts preserving the geome…

New algorithm learns human preferences from few comparisons efficiently.

Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boo…

Paper shows $L^\infty$-positivity and stochastic completeness are equivalent.

Accessible groups with infinitely many ends have infinitely many twisted conjugacy classes.

Paper studies R∞-property for braid groups on surfaces, proving it for most cases.

Uniform proof of property R_infinity for specific Artin-Tits groups.

Foundations of derived geometry in smooth settings.

New risk measure extensions preserve key properties.

Study Hamiltonian diffeomorphisms on symplectic manifolds and properties of invariant convex functions.

Proves rigidity of sphere metrics with subsets removed.

The family of translation surfaces $(X_g,ω_g)$ constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus $g$ greater than or equal to $3$. We triangulate these surfaces and deduce general properties they share. The surfaces $(X_g,ω_g)$ converge to a surface $(X_\i…

Infinity-harmonic functions linked to IMCF clusters, revealing new properties in 2D.

A new category generates 1D tangle invariants.

It is proved that the isometry classes of pointed connected complete Riemannian $n$-manifolds form a Polish space, $\mathcal{M}_*^\infty(n)$, with the topology described by the $C^\infty$ convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifo…

Using the symmetry properties of two-dmensional sigma models, we introduce a notion of the Beltrami-Courant differential, so that there is a natural homotopy Gerstenhaber algebra related to it. We conjecture that the generalized Maurer-Cartan equation for the corresponding $L_{\infty}$ subalgebra gives solutions to the…

In this short paper we study $L_f^p$-Liouville property with $0<p<1$ for nonnegative $f$-subharmonic functions on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with $\mathrm{Ric}_f^m$ bounded below for $0<m\leq\infty$. We prove a sharp $L_f^p$-Liouville theorem when $0<m<\infty$. We also prove an $…

In this paper we define the $p$-adic framed braid group ${\mathcal F}_{\infty,n}$, arising as the inverse limit of the modular framed braids and we give topological generators for ${\mathcal F}_{\infty, n}$. We also give geometric interpretations for the $p$-adic framed braids. We then construct a $p$-adic Yokonuma-Hec…