Guangjian Tian

Yuanming Zhang, Pinghui Wang, Yiyan Qi et al.

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a non-negative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and weighted cardinality estimation require to generate $k$ independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large $k$ (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, FastGM, which reduces the time complexity from $O(kn^+)$ to $O(k \ln k + n^+)$, where $n^+$ is the number of positive elements in the vector of interest. FastGM stops the procedure of Gumbel random variables computing for many elements, especially for those with small weights. We perform experiments on a variety of real-world datasets and the experimental results demonstrate that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy or incurring additional expenses.

Longyuan Li, Jihai Zhang, Junchi Yan et al.

Time-series is ubiquitous across applications, such as transportation, finance and healthcare. Time-series is often influenced by external factors, especially in the form of asynchronous events, making forecasting difficult. However, existing models are mainly designated for either synchronous time-series or asynchronous event sequence, and can hardly provide a synthetic way to capture the relation between them. We propose Variational Synergetic Multi-Horizon Network (VSMHN), a novel deep conditional generative model. To learn complex correlations across heterogeneous sequences, a tailored encoder is devised to combine the advances in deep point processes models and variational recurrent neural networks. In addition, an aligned time coding and an auxiliary transition scheme are carefully devised for batched training on unaligned sequences. Our model can be trained effectively using stochastic variational inference and generates probabilistic predictions with Monte-Carlo simulation. Furthermore, our model produces accurate, sharp and more realistic probabilistic forecasts. We also show that modeling asynchronous event sequences is crucial for multi-horizon time-series forecasting.

Yiyan Qi, Pinghui Wang, Yuanming Zhang et al.

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a nonnegative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ (or a Gumbel-Max variable $i$) in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and graph embedding require to generate $k$ independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large $k$ (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, \emph{FastGM}, that reduces the time complexity from $O(kn^+)$ to $O(k \ln k + n^+)$, where $n^+$ is the number of positive elements in the vector of interest. Instead of computing $k$ independent Gumbel random variables directly, we find that there exists a technique to generate these variables in descending order. Using this technique, our method FastGM computes variables $g_i+\ln v_i$ for all positive elements $i$ in descending order. As a result, FastGM significantly reduces the computation time because we can stop the procedure of Gumbel random variables computing for many elements especially for those with small weights. Experiments on a variety of real-world datasets show that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy and incurring additional expenses.