论文标题
全跨度对数线性模型和快速学习算法
Full-Span Log-Linear Model and Fast Learning Algorithm
论文作者
论文摘要
本文中引入的全跨度日志线性（FSLL）模型被认为是$ n $ ther订单玻尔兹曼机器，其中$ n $是目标系统中所有变量的数量。令$ x =（x_0，...，x_ {n-1}）$为有限的离散随机变量，可以采用$ | x | = | x_0 | ... | ... | x_ {n-1} | $不同的值。 FSLL模型具有$ | x | -1 $参数，可以代表$ x $的任意正分布。 FSLL模型是“最高级”的玻尔兹曼机器；尽管如此，我们可以计算模型分布的双重参数，该分布在指数族中扮演着重要角色，在$ o（| x | \ log | x |）$ time中。此外，使用FSLL模型的双重参数的属性，我们可以构建有效的学习算法。 FSLL模型仅限于最高$ | x | \ act2^{25} $的小概率模型;但是，在此问题域中，FSLL模型灵活地拟合了训练数据基础的各种真实分布，而无需进行任何超参数调整。实验表明，FSLL成功地学习了六个培训数据集，因此使用笔记本电脑PC在一分钟内$ | x | = 2^{20} $。
The full-span log-linear(FSLL) model introduced in this paper is considered an $n$-th order Boltzmann machine, where $n$ is the number of all variables in the target system. Let $X=(X_0,...,X_{n-1})$ be finite discrete random variables that can take $|X|=|X_0|...|X_{n-1}|$ different values. The FSLL model has $|X|-1$ parameters and can represent arbitrary positive distributions of $X$. The FSLL model is a "highest-order" Boltzmann machine; nevertheless, we can compute the dual parameters of the model distribution, which plays important roles in exponential families, in $O(|X|\log|X|)$ time. Furthermore, using properties of the dual parameters of the FSLL model, we can construct an efficient learning algorithm. The FSLL model is limited to small probabilistic models up to $|X|\approx2^{25}$; however, in this problem domain, the FSLL model flexibly fits various true distributions underlying the training data without any hyperparameter tuning. The experiments presented that the FSLL successfully learned six training datasets such that $|X|=2^{20}$ within one minute with a laptop PC.
