Related papers: From Logistic Regression to the Perceptron Algorit…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
In continual learning, a learner has to keep learning from the data over its whole life time. A key issue is to decide what knowledge to keep and what knowledge to let go. In a neural network, this can be implemented by using a step-size…
Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…
Back-propagation is a popular machine learning algorithm that uses gradient descent in training neural networks for supervised learning, but can be very slow. A number of algorithms have been developed to speed up convergence and improve…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…
Perceptron is a classic online algorithm for learning a classification function. In this paper, we provide a novel extension of the perceptron algorithm to the learning to rank problem in information retrieval. We consider popular listwise…
In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is based on a concept called GSLLN (Generalized Strong Law of…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
The projected gradient descent (PGD) method has shown to be effective in recovering compressed signals described in a data-driven way by a generative model, i.e., a generator which has learned the data distribution. Further reconstruction…
Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Mini-batch stochastic gradient descent (SGD) and variants thereof approximate the objective function's gradient with a small number of training examples, aka the batch size. Small batch sizes require little computation for each model update…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that…
The classical Perceptron algorithm of Rosenblatt can be used to find a linear threshold function to correctly classify $n$ linearly separable data points, assuming the classes are separated by some margin $\gamma > 0$. A foundational result…
This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of…
We consider a model for logistic regression where only a subset of features of size $p$ is used for training a linear classifier over $n$ training samples. The classifier is obtained by running gradient descent (GD) on logistic loss. For…
This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…
Stochastic Gradient Langevin Dynamics (SGLD) ensures strong guarantees with regards to convergence in measure for sampling log-concave posterior distributions by adding noise to stochastic gradient iterates. Given the size of many practical…
Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…