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.
Global-QSGD accelerates distributed training by up to 3.51%.
The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.
BCD algorithm finds global minima in neural networks.
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algor…
Global convergence of multilayer neural networks proven for any depth.
Efficiently certifies global robustness of large neural networks with probabilistic guarantees.
Improved guarantees for nonconvex matrix factorization with rank overparameterization.
Sharp global guarantees for noisy overparameterized low-rank recovery.
New algorithm ensures global convergence in deep neural networks beyond NTK regime.
Gradient descent proves global convergence for 4-layer matrix factorization.
New quasi-Newton method guarantees global superlinear convergence.
New framework for DNN training guarantees convergence to global minimum.
In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank- update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence g…
Adaptive method improves prediction intervals with global coverage guarantees and local error distribution.
In this paper, we consider the problem of unsupervised video object segmentation via background subtraction. Specifically, we pose the nonsemantic extraction of a video's moving objects as a nonconvex optimization problem via a sum of sparse and low-rank matrices. The resulting formulation, a nonnegative variant of rob…
StochasticRank optimizes ranking metrics efficiently and guarantees global convergence.
SyncRank recovers global ranking from noisy comparisons with theoretical guarantees.
We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial ti…
Global convergence for robust regression problems via IRLS with enhancements.
The Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its observation process is often addressed via the Baum-Welch algorithm, which is known t…
The optimization problem behind neural networks is highly non-convex. Training with stochastic gradient descent and variants requires careful parameter tuning and provides no guarantee to achieve the global optimum. In contrast we show under quite weak assumptions on the data that a particular class of feedforward neur…
GBML with deep nets converges globally and generalizes well.
A new algorithm solves semidefinite programs using Langevin diffusion.
AGGLIO optimizes non-convex functions with local convexity guarantees.
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local optimization heuristics without global optimality guarantees or with guarantees valid only…
New method calibrates eSSVI volatility surfaces without arbitrage.
Extracting actionable intelligence from distributed, heterogeneous, correlated and high-dimensional data sources requires run-time processing and learning both locally and globally. In the last decade, a large number of meta-learning techniques have been proposed in which local learners make online predictions based on…
Constructs tail-specific prediction intervals for financial applications
Paper provides a performance guarantee for spectral clustering.
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear whether the fixed point identified by the variational inference algorithm is a local…
This paper introduces a scalable benchmark for evaluating local posterior sampling in neural networks.
Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze the class of homotopy or continuation methods for global optimi…
Many generative models have to combat . The conventional wisdom to this end is by reducing through training a statistical distance (such as -divergence) between the generated distribution and provided data distribution. But this is more of a heuristic than a guarantee. The statistical distanc…
CRPO solves challenging SRL problems with convergence guarantee.
EM algorithm converges to global max in latent Gaussian tree models.
Optimizes MMD learning for generative models with theoretical guarantees.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
New IRL algorithm identifies optimal reward and policy from expert demonstrations.
This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are lack of global convergence guarantee. Though the general FSPCA problem is NP-ha…
We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive because it escapes strict saddle points and it provides stronger convergence gu…
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to…
Proposes a wave-constrained matrix factorization for signal learning.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
The paper analyzes PPM for nonconvex-nonconcave problems, identifying three regions with varying convergence guarantees.
Meta algorithm solves multivariate optimization using univariate optimizers.
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel…
Wide neural networks converge linearly to zero loss with feature learning.
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization variables appear only locally at a single node in the network. We term the resulting a…