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.
Improves CRRR for better mobility analysis with DCTM.
Proves conditions for Fourier transforms in rank 1 symmetric spaces.
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational da…
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
Low-rank matrix recovery has found many applications in science and engineering such as machine learning, signal processing, collaborative filtering, system identification, and Euclidean embedding. But the low-rank matrix recovery problem is an NP hard problem and thus challenging. A commonly used heuristic approach is…
ScaledGD accelerates ill-conditioned low-rank estimation.
Derives smooth homogeneous structures for low-rank tensors.
The paper examines how gradient descent stabilizes low-rank matrix factorization in noisy conditions.
We address some theoretical guarantees for Schatten- quasi-norm minimization () in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition…
Paper classifies structures on 5D manifolds with specific rank and conditions.
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
RSIC identifies multiple ranks of interest in NMF by analyzing residual sensitivity.
Improved convergence for overparameterized low-rank matrix sensing.
Develops new oracle inequalities for Gaussian ranking estimators.
New ranking models for time series data using GARCH-type approach.
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite matrix without any assumptions on the rank-matching, the condition number or eigensp…
We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion}, \textit{phase retrieval}, and more. The computational limitation of applying SGD to so…
Efficiently reduces tensor ranks using mean-field approximation.
New algorithm improves deep learning models' robustness without sacrificing accuracy.
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ens…
Proposes a model for identifying edges in low-rank dynamical networks.
The authors found necessary and sufficient conditions for Samuelson's web to be of maximum rank.
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is NP-HARD, and for most practical problems there are no efficient algorithms that…
Paper proposes fast, robust methods for low-rank matrix recovery.
Proposes a new method for rank-consistent ordinal regression without weight-sharing constraints.
Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank- projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These condit…
We simplify SSL by approximating redundant structural components with low-rank factorization.
The paper proposes using low rank assumption to improve causal structure learning in DAGs.
Optimizes tensor rank selection for neural network compression.
This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements …
We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete, irreducible, simply connected Riemannian manifold M of rank at least 2 (the high…
We solve linear equations with tensors of any rank.
This paper improves entropy bounds for ranking time-series complexity.
Paper develops inference methods for low-rank tensors without debiasing.
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the online and batch settings. First, we propose a perceptron-like algorithm for learnin…
Let G be a rank two finite group, and let $\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\cH$, whose fixed sets are homotopy spheres. Ou…
Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete matrix is finitely rank- completable if there are at …
Study consumption-investment problem in markets with rank-based returns.
Paper develops methods for non-quadratic loss low-rank matrix recovery.
Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly …
We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the go…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable. We answer the question fro…
In the present paper we define Samuelson's webs and their rank. The main result of the paper is the proof that the rank of the Samuelson webs does not exceed 6, as well as finding the conditions under which this rank is maximal for the general Samuelson webs as well as for their singular cases.
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
New examples of deformed Hermitian-Yang-Mills connections found.
We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA), when the population covariance matrix has an additional latent graphical constraint, namely, a latent star topology. In particular, we have shown that CMTFA can have either a …
New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.