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Stochastic gradient methods are among the most widely used algorithms for large-scale optimization and machine learning. A key technique for improving the statistical efficiency and stability of these methods is the use of averaging schemes…
Streaming principal component analysis (PCA) is an integral tool in large-scale machine learning for rapidly estimating low-dimensional subspaces from very high-dimensional data arriving at a high rate. However, modern datasets increasingly…
Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along.…
The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially for huge data sets and online learning. While this recursive algorithm is popular for computation and memory efficiency, quantifying…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…
Online Passive-Aggressive (PA) learning is a class of online margin-based algorithms suitable for a wide range of real-time prediction tasks, including classification and regression. PA algorithms are formulated in terms of deterministic…
Since its inception in 1982, Oja's algorithm has become an established method for streaming principle component analysis (PCA). We study the problem of streaming PCA, where the data-points are sampled from an irreducible, aperiodic, and…
Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…
Online prediction for streaming time series data has practical use for many real-world applications where downstream decisions depend on accurate forecasts for the future. Deployment in dynamic environments requires models to adapt quickly…
A stochastic queueing network model with parameter-dependent service times and routing mechanism, and its related performance measures are considered. An estimate of performance measure gradient is proposed, and rather general sufficient…
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…
In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…
ListNet is a well-known listwise learning to rank model and has gained much attention in recent years. A particular problem of ListNet, however, is the high computation complexity in model training, mainly due to the large number of object…
Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…
We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise…
Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another.…
For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…