Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building…
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “Greedy Coordinate Descent”
Improved greedy 2-coordinate updates for optimization problems with constraints.
problem Minimizing smooth functions subject to constraints.
method Exploiting a connection to steepest descent in the 1-norm, we give faster convergence rates and efficient computation.
result Greedy selection converges faster than random selection and can be computed in time.
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension , and requiring upto times fewer iterations. In this pap…
New algorithm improves privacy in high-dimensional machine learning models.
problem Privacy issues in learning large machine learning models.
method Differentially private greedy coordinate descent (DP-GCD) algorithm.
result Achieves logarithmic dependence on dimension for quasi-sparse solutions.
We present a generic framework for parallel coordinate descent (CD) algorithms that includes, as special cases, the original sequential algorithms Cyclic CD and Stochastic CD, as well as the recent parallel Shotgun algorithm. We introduce two novel parallel algorithms that are also special cases---Thread-Greedy CD and …
We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small sub-problems. The challenge in variable decomposition algorithms is the identificati…
In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it communication efficient. It is based on coordinate descent and uses locally greedy u…
We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual algorithms and their capability in solving other problems in large-scale, such …
Three privacy-preserving methods for median regression are proposed.
problem Protecting individual privacy in median regression analysis.
method Three privacy-preserving methods: finite smoothing, iterative, and greedy coordinate descent.
result Numerical results show varying performance across different sample sizes.
The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied in this paper utilize dictionaries instead of a canonical basis used in the coord…
Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In spite of the usefulness of GBM in practice, our current theoretical un…
Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Conditioncs.LG
In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Łojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older…
Accelerates coordinate descent methods for machine learning problems.
problem Slowness of coordinate descent methods in machine learning.
method Extrapolation-based accelerated coordinate descent.
result Significant speed-up in practice compared to existing methods.
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in …
Develops DP-SCD for stochastic coordinate descent, making it differentially private.
problem Privacy leak in auxiliary information during stochastic coordinate descent training.
method Develops DP-SCD, leveraging independent noise addition and decoupling/parallelizing coordinate updates.
result Demonstrates competitive performance against DP-SGD with less tuning.
Coordinate descent methods usually minimize a cost function by updating a random decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest decrease in the cost function. However, finding this coordinate would require checking all of them, which…
Cyclic coordinate descent identifies models in finite time and converges linearly.
problem Model identification in composite nonsmooth optimization problems.
method Cyclic coordinate descent for a wide class of functions.
result Explicit local linear convergence rates for coordinate descent.
New algorithm for reinforcement learning reduces complexity and guarantees convergence.
problem Reinforcement learning problems with convex occupancy measures.
method MD-CURL, inspired by mirror descent, uses non-standard regularization.
result Achieves convergence guarantees and simple closed-form solution.
This monograph presents a class of algorithms called coordinate descent algorithms for mathematicians, statisticians, and engineers outside the field of optimization. This particular class of algorithms has recently gained popularity due to their effectiveness in solving large-scale optimization problems in machine lea…
Differentially private random block coordinate descent improves utility in machine learning.
problem Lack of privacy in classical CD methods when handling sensitive information.
method Proposes a differentially private random block coordinate descent method using sketch matrices and importance sampling.
result Demonstrates improved convergence rates and utility guarantees compared to non-private methods.
Accelerated Randomized Coordinate Descent Algorithms for Stochastic Optimization and Online Learningcs.LG
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…
Enhances PMD with lookahead to improve RL performance.
problem Improving RL performance with greedy policies over 1-step.
method Integrates multi-step greedy policies into PMD with lookahead.
result Shows faster convergence rate for -PMD.
Greedy selection finds smaller, more accurate subnetworks.
problem Finding smaller, accurate subnetworks in large neural networks.
method Greedy forward selection starting from an empty network.
result Theoretical guarantee of finding subnetworks with lower loss.
We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration, homotopy, and coordinate descent with non-uniform sampling. As a result, our method…
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection be…
New algorithm optimizes Bayesian network learning from Gaussian data.
problem Learning Bayesian networks from Gaussian observational data.
method Proposes a coordinate descent algorithm for -penalized maximum likelihood estimation.
result The algorithm converges to a coordinate-wise minimum and achieves optimal objective value as sample size increases.
This paper analyzes and guarantees convergence of prior-guided ZO algorithms.
problem Understanding convergence properties of prior-guided zeroth-order optimization algorithms.
method Analysis of convergence under a greedy descent framework with various gradient estimators, and development of ARS algorithm.
result Convergence guarantee for prior-guided random gradient-free (PRGF) algorithms and accelerated random search (ARS) algorithm.
We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces. The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed e…
New DP-CD method outperforms DP-SGD in solving composite DP-ERM problems.
problem Privacy-preserving machine learning with differential privacy.
method Differentially Private proximal Coordinate Descent (DP-CD) for composite Empirical Risk Minimization (ERM).
result DP-CD outperforms DP-SGD due to larger step sizes and better gradient exploitation.
Isometry pursuitstat.ML
Isometry pursuit identifies orthonormal submatrices from wide matrices.
problem Identifying isometric embeddings from wide matrices.
method A convex algorithm combining normalization and multitask basis pursuit.
result The method identifies isometric embeddings from interpretable dictionaries.
Gradient flow with infinitesimal initialization converges to Greedy Low-Rank Learning for matrix factorization.
problem Understanding implicit regularization in gradient descent for matrix factorization.
method Theoretical and empirical analysis of gradient flow with infinitesimal initialization and Greedy Low-Rank Learning.
result Gradient flow with infinitesimal initialization is mathematically equivalent to Greedy Low-Rank Learning for depth-2 matrix factorization under reasonable assumptions.
New method speeds up optimization over probability measures.
problem High computational overhead in optimizing probability measures.
method Randomized coordinate descent on Wasserstein space.
result Significant speedups over full-gradient methods.
In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small prediction error. We develop an efficient algorithm based on the greedy coordinate d…
We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates each regression coefficient and its corresponding subgradient simultaneousl…
Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we imp…
Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated patterns can be positioned anywhere in signals or images, optimization techniques face…
We demonstrate that distributed block coordinate descent can quickly solve kernel regression and classification problems with millions of data points. Armed with this capability, we conduct a thorough comparison between the full kernel, the Nyström method, and random features on three large classification tasks from va…
Paper introduces robust learning methods using coordinate gradient descent.
problem Supervised learning with corrupted features and labels.
method Coordinate gradient descent combined with robust estimators of partial derivatives.
result Robust learning methods with nearly identical numerical complexity to non-robust ones.
We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is the first time such a method is proposed. In the special case when the number of…
A new method uses Coordinate Descent to optimize ResNet networks for private inference.
problem Reducing ReLU count in ResNet networks for private inference.
method Directly optimizing in the discrete domain using Coordinate Descent.
result Our method yields a sparse solution and is state-of-the-art.
This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates t…
CD converges linearly for MCP/SCAD penalized least squares.
problem Recovering sparse signals from data.
method Coordinate descent for MCP/SCAD penalized least squares.
result CD converges linearly to solutions of MCP/SCAD penalized least squares.
Due to diverse nature of data acquisition and modern applications, many contemporary problems involve high dimensional datum $\x \in \R^\d$ whose entries often lie in a union of subspaces and the goal is to find out which entries of $\x$ match with a particular subspace $\sU$, classically called \emph {matched subspace…
We propose and analyze a new parallel coordinate descent method---`NSync---in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities t…
Paper proposes an -policy gradient for online pricing, reducing regret to .
problem Online pricing learning task
method Combines model-based and model-free reinforcement learning, using -greedy with gradient descent.
result Achieves expected regret of order .
In this paper, we study the randomized distributed coordinate descent algorithm with quantized updates. In the literature, the iteration complexity of the randomized distributed coordinate descent algorithm has been characterized under the assumption that machines can exchange updates with an infinite precision. We con…
Coordinate descent (CD) algorithms have become the method of choice for solving a number of optimization problems in machine learning. They are particularly popular for training linear models, including linear support vector machine classification, LASSO regression, and logistic regression. We consider general CD with …
This paper investigates the grant-free random access with massive IoT devices. By embedding the data symbols in the signature sequences, joint device activity detection and data decoding can be achieved, which, however, significantly increases the computational complexity. Coordinate descent algorithms that enjoy a low…