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We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…

Optimization and Control · Mathematics 2025-12-09 Tao Jiang , Lin Xiao

The mismatch between the numerical and actual nonlinear models is a challenge to nonlinear acoustic echo cancellation (NAEC) when the nonlinear adaptive filter is utilized. To alleviate this problem, we combine a basis-generic expansion of…

Signal Processing · Electrical Eng. & Systems 2021-04-07 Guoliang Cheng , Lele Liao , Hongsheng Chen , Jing Lu

Adam is widely recognized as one of the most effective optimizers for training deep neural networks (DNNs). Despite its remarkable empirical success, its theoretical convergence analysis remains unsatisfactory. Existing works predominantly…

Machine Learning · Computer Science 2025-07-10 Hanyang Peng , Shuang Qin , Yue Yu , Fangqing Jiang , Hui Wang , Zhouchen Lin

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been…

Machine Learning · Computer Science 2024-10-29 Kushal Chakrabarti , Nikhil Chopra

Deep learning methods - usually consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays omnipresent in data-driven learning problems as well as in scientific…

Optimization and Control · Mathematics 2025-01-13 Steffen Dereich , Arnulf Jentzen , Adrian Riekert

Adaptive Moment Estimation (Adam) is a cornerstone optimization algorithm in deep learning, widely recognized for its flexibility with adaptive learning rates and efficiency in handling large-scale data. However, despite its practical…

Machine Learning · Computer Science 2025-05-21 Ruinan Jin , Xiao Li , Yaoliang Yu , Baoxiang Wang

Given a time series of multicomponent measurements x(t), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s(t), comprised of statistically independent combinations of the measured components.…

Artificial Intelligence · Computer Science 2015-05-13 David N. Levin

Source separation is one of the signal processing's main emerging domain. Many techniques such as maximum likelihood (ML), Infomax, cumulant matching, estimating function, etc. have been used to address this difficult problem.…

Mathematical Physics · Physics 2009-10-31 Ali Mohammad-Djafari

Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural networks in artificial intelligence (AI)…

Optimization and Control · Mathematics 2025-11-11 Steffen Dereich , Thang Do , Arnulf Jentzen , Philippe von Wurstemberger

In this paper, a Blind Source Separation (BSS) algorithm for multichannel audio contents is proposed. Unlike common BSS algorithms targeting stereo audio contents or microphone array signals, our technique is targeted at multichannel audio…

Sound · Computer Science 2015-12-29 Taejin Park , Taejin Lee

The adaptive moment estimation (Adam) optimizer proposed by Kingma & Ba (2014) is presumably the most popular stochastic gradient descent (SGD) optimization method for the training of deep neural networks (DNNs) in artificial intelligence…

Machine Learning · Computer Science 2026-03-20 Steffen Dereich , Thang Do , Arnulf Jentzen

This paper proposes a novel algorithm for signal classification problems. We consider a non-stationary random signal, where samples can be classified into several different classes, and samples in each class are identically independently…

Information Theory · Computer Science 2009-03-02 Xudong Ma

Blind source separation is a research hotspot in the field of signal processing because it aims to separate unknown source signals from observed mixtures through an unknown transmission channel. A low computational complexity instantaneous…

Signal Processing · Electrical Eng. & Systems 2019-03-08 Pengfei Xu , Yinjie Jia , Zhijian Wang

Blind source separation, i.e. extraction of independent sources from a mixture, is an important problem for both artificial and natural signal processing. Here, we address a special case of this problem when sources (but not the mixing…

Neurons and Cognition · Quantitative Biology 2017-10-20 Cengiz Pehlevan , Sreyas Mohan , Dmitri B. Chklovskii

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many…

In this article, we develop an algorithm for probabilistic and constrained projection pursuit. Our algorithm called ADIS (automated decomposition into sources) accepts arbitrary non-linear contrast functions and constraints from the user…

Computation · Statistics 2009-03-02 Gautam Pendse , David Borsook , Lino Becerra

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

Machine Learning · Computer Science 2026-05-29 Sakshi Kumari , Shyam Kumar M , Sushmitha P

Optimal selection of optimization algorithms is crucial for training deep learning models. The Adam optimizer has gained significant attention due to its efficiency and wide applicability. However, to enhance the adaptability of optimizers…

Machine Learning · Computer Science 2024-09-09 Chengxi Pan , Junshang Chen , Jingrui Ye

With the increasing practicality of deep learning applications, practitioners are inevitably faced with datasets corrupted by noise from various sources such as measurement errors, mislabeling, and estimated surrogate inputs/outputs that…

Machine Learning · Computer Science 2023-08-30 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Takamitsu Matsubara

In this paper, we test the performance of some modern stochastic optimization methods and practices in application to digital pre-distortion problem, that is a valuable part of processing signal on base stations providing wireless…

Optimization and Control · Mathematics 2022-01-31 A. V. Alpatov , E. A. Peters , D. A. Pasechnyuk , A. M. Raigorodskii