Continual learning is increasingly sought after in real world machine
learning applications, as it enables learning in a more human-like manner.
Conventional machine learning approaches fail to achieve this, as incrementally
updating the model with non-identically distributed data leads to catastrophic
forgetting, where existing representations are overwritten. Although
traditional continual learning methods have mostly focused on batch learning,
which involves learning from large collections of labeled data sequentially,
this approach is not well-suited for real-world applications where we would
like new data to be integrated directly. This necessitates a paradigm shift
towards streaming learning. In this paper, we propose a streaming version of
regularized discriminant analysis as a solution to this challenge. We combine
our algorithm with a convolutional neural network and demonstrate that it
outperforms both batch learning and existing streaming learning algorithms on
the ImageNet ILSVRC-2012 dataset.

我们提出了流媒体版本的正则判别分析算法，与卷积神经网络结合，证明在 ImageNet ILSVRC-2012 数据集上表现优于批量学习和现有的流媒体学习算法。

深度流式正则判别分析的持续学习

Continual Learning with Deep Streaming Regularized Discriminant Analysis

We provide a unified analysis of the predictive risk of ridge regression and
regularized discriminant analysis in a dense random effects model. We work in a
high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma
\in (0, \, \infty)$, and allow for arbitrary covariance among the features. For
both methods, we provide an explicit and efficiently computable expression for
the limiting predictive risk, which depends only on the spectrum of the
feature-covariance matrix, the signal strength, and the aspect ratio $\gamma$.
Especially in the case of regularized discriminant analysis, we find that
predictive accuracy has a nuanced dependence on the eigenvalue distribution of
the covariance matrix, suggesting that analyses based on the operator norm of
the covariance matrix may not be sharp. Our results also uncover several
qualitative insights about both methods: for example, with ridge regression,
there is an exact inverse relation between the limiting predictive risk and the
limiting estimation risk given a fixed signal strength. Our analysis builds on
recent advances in random matrix theory.

本文在高维渐近极端条件下，对岭回归和正则化判别分析在密集随机效应模型中的预测风险进行了统一分析，并提供了两种方法的极限预测风险的明确和高效可计算的表达式。同时，揭示了岭回归和正则化判别分析各自的一些定性见解，本分析基于最近在随机矩阵理论领域的一些新进展。