Song Liu

Song Liu, Jiahao Yu, Jack Simons et al.

Many machine learning problems can be seen as approximating a \textit{target} distribution using a \textit{particle} distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that minimizes the $f$-divergence between the target and particle distributions. To move particles, we need to calculate the corresponding velocity fields derived from a density ratio function between these two distributions. Previous works estimated such density ratio functions and then differentiated the estimated ratios. These approaches may suffer from overfitting, leading to a less accurate estimate of the velocity fields. Inspired by non-parametric curve fitting, we directly estimate these velocity fields using interpolation techniques. We prove that our estimators are consistent under mild conditions. We validate their effectiveness using novel applications on domain adaptation and missing data imputation.

Song Liu, Yulong Zhang, Mingxuan Yi et al.

Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random variables that are \emph{inferred} from observations. In this paper, we study the problem of estimating the ratio between two posterior probability density functions of a latent variable. Particularly, we assume the posterior ratio function can be well-approximated by a parametric model, which is then estimated using observed information and prior samples. We prove the consistency of our estimator and the asymptotic normality of the estimated parameters as the number of prior samples tending to infinity. Finally, we validate our theories using numerical experiments and demonstrate the usefulness of the proposed method through some real-world applications.

Song Liu, Takafumi Kanamori, Daniel J. Williams

Truncated densities are probability density functions defined on truncated domains. They share the same parametric form with their non-truncated counterparts up to a normalizing constant. Since the computation of their normalizing constants is usually infeasible, Maximum Likelihood Estimation cannot be easily applied to estimate truncated density models. Score Matching (SM) is a powerful tool for fitting parameters using only unnormalized models. However, it cannot be directly applied here as boundary conditions used to derive a tractable SM objective are not satisfied by truncated densities. In this paper, we study parameter estimation for truncated probability densities using SM. The estimator minimizes a weighted Fisher divergence. The weight function is simply the shortest distance from a data point to the boundary of the domain. We show this choice of weight function naturally arises from minimizing the Stein discrepancy as well as upperbounding the finite-sample estimation error. The usefulness of our method is demonstrated by numerical experiments and a study on the Chicago crime data set. We also show that the proposed density estimation can correct the outlier-trimming bias caused by aggressive outlier detection methods.

Yinhe Zheng, Guanyi Chen, Minlie Huang et al.

Endowing a dialogue system with particular personality traits is essential to deliver more human-like conversations. However, due to the challenge of embodying personality via language expression and the lack of large-scale persona-labeled dialogue data, this research problem is still far from well-studied. In this paper, we investigate the problem of incorporating explicit personality traits in dialogue generation to deliver personalized dialogues. To this end, firstly, we construct PersonalDialog, a large-scale multi-turn dialogue dataset containing various traits from a large number of speakers. The dataset consists of 20.83M sessions and 56.25M utterances from 8.47M speakers. Each utterance is associated with a speaker who is marked with traits like Age, Gender, Location, Interest Tags, etc. Several anonymization schemes are designed to protect the privacy of each speaker. This large-scale dataset will facilitate not only the study of personalized dialogue generation, but also other researches on sociolinguistics or social science. Secondly, to study how personality traits can be captured and addressed in dialogue generation, we propose persona-aware dialogue generation models within the sequence to sequence learning framework. Explicit personality traits (structured by key-value pairs) are embedded using a trait fusion module. During the decoding process, two techniques, namely persona-aware attention and persona-aware bias, are devised to capture and address trait-related information. Experiments demonstrate that our model is able to address proper traits in different contexts. Case studies also show interesting results for this challenging research problem.

Yankai Lin, Zhiyuan Liu, Huanbo Luan et al.

Representation learning of knowledge bases (KBs) aims to embed both entities and relations into a low-dimensional space. Most existing methods only consider direct relations in representation learning. We argue that multiple-step relation paths also contain rich inference patterns between entities, and propose a path-based representation learning model. This model considers relation paths as translations between entities for representation learning, and addresses two key challenges: (1) Since not all relation paths are reliable, we design a path-constraint resource allocation algorithm to measure the reliability of relation paths. (2) We represent relation paths via semantic composition of relation embeddings. Experimental results on real-world datasets show that, as compared with baselines, our model achieves significant and consistent improvements on knowledge base completion and relation extraction from text.