通过可调噪声提升变分推断的优化能力,兼顾精度与全局搜索。
Stochastic Variational Inference with Tuneable Stochastic Annealing
- 设定实际与有效批大小,控制梯度噪声方差以平衡收敛与逃逸
- 在三种模型上验证:PMF、LDA、GMM,显著提升优化效果
- 适合需稳定训练且避免局部最优的研究者使用
我们观察到随机变分推断(SVI)本质上是一种退火过程,并提出一种可调节退火程度的改进方法——适用于大中小规模数据集。在SVI中,批大小越大,梯度噪声越接近高斯分布,但方差越小,导致难以逃离不良局部最优解。为此,我们提出一种简单策略:固定实际批大小(可为全数据集),同时设定一个等效较小批大小对应的更高噪声水平,从而在保持数据信息量的同时增强梯度噪声方差。该方法实现目标方差下的最大熵随机梯度近似。我们在共轭指数族模型框架下提供理论支持,并在概率矩阵分解(PMF)、潜在狄利克雷分配(LDA)和高斯混合模型(GMM)上展示其经验性能,证明了该方法在提升优化质量方面的有效性。
原文摘要 · Abstract (English)
We exploit the observation that stochastic variational inference (SVI) is a form of annealing and present a modified SVI approach -- applicable to both large and small datasets -- that allows the amount of annealing done by SVI to be tuned. We are motivated by the fact that, in SVI, the larger the batch size the more approximately Gaussian is the noise of the gradient, but the smaller its variance, which reduces the amount of annealing done to escape bad local optimal solutions. We propose a simple method for achieving both goals of having larger variance noise to escape bad local optimal solutions and more data information to obtain more accurate gradient directions. The idea is to set an actual batch size, which may be the size of the data set, and an effective batch size that matches the increased variance of a smaller batch size. The result is an approximation to the maximum entropy stochastic gradient at a desired variance level. We theoretically motivate our ``SVI+'' approach for conjugate exponential family model framework and illustrate its empirical performance for learning the probabilistic matrix factorization collaborative filter (PMF), the Latent Dirichlet Allocation topic model (LDA), and the Gaussian mixture model (GMM).
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