Hierarchical clustering is typically performed using algorithmic-based optimization searching over the discrete space of trees. While these optimization methods are often effective, their discreteness restricts them from many of the benefits of their continuous counterparts, such as scalable stochastic optimization and the joint optimization of multiple objectives or components of a model (e.g. end-to-end training). In this paper, we present an approach for hierarchical clustering that searches over continuous representations of trees in hyperbolic space by running gradient descent. We compactly represent uncertainty over tree structures with vectors in the Poincare ball. We show how the vectors can be optimized using an objective related to recently proposed cost functions for hierarchical clustering (Dasgupta, 2016; Wang and Wang, 2018). Using our method with a mini-batch stochastic gradient descent inference procedure, we are able to outperform prior work on clustering millions of ImageNet images by 15 points of dendrogram purity. Further, our continuous tree representation can be jointly optimized in multi-task learning applications offering a 9 point improvement over baseline methods.

Long Short-Term Memory (LSTM) is one of the most powerful sequence models for user browsing history \citetan2016improved,korpusik2016recurrent or natural language text \citemikolov2010recurrent.Despite the strong performance, it has not gained popularity for user-facing applications, mainly owing to a large number of parameters and lack of interpretability. Recently \citetzaheer2017latent introduced latent LSTM Allocation (LLA) to address these problems by incorporating topic models with LSTM, where the topic model maps observed words in each sequence to topics that evolve using an LSTM model. In our experiments, we found the resulting model, although powerful and interpretable, to show shortcomings when applied to sequence data that exhibit multi-modes of behaviors with abrupt dynamic changes. To address this problem we introduce thLLA: a threading LLA model. thLLA has the ability to break each sequence into a set of segments and then model the dynamic in each segment using an LSTM mixture. In that way, thLLA can model abrupt changes in sequence dynamics and provides a better fit for sequence data while still being interpretable and requiring fewer parameters. In addition, thLLA uncovers hidden themes in the data via its dynamic mixture components. However, such generalization and interpretability come at a cost of complex dependence structure, for which inference would be extremely non-trivial. To remedy this, we present an efficient sampler based on particle MCMC method for inference that can draw from the joint posterior directly. Experimental results confirm the superiority of thLLA and the stability of the new inference algorithm on a variety of domains.

Topic models are often applied in industrial settings to discover user profiles from activity logs where documents correspond to users and words to complex objects such as web sites and installed apps. Standard topic models ignore the content-based similarity structure between these objects largely because of the inability of the Dirichlet prior to capture such side information of word-word correlation. Several approaches were proposed to replace the Dirichlet prior with more expressive alternatives. However, this added expressivity comes with a heavy premium: inference becomes intractable and sparsity is lost which renders these alternatives not suitable for industrial scale applications. In this paper we take a radically different approach to incorporating word-word correlation in topic models by applying this side information at the posterior level rather than at the prior level. We show that this choice preserves sparsity and results in a graph-based sampler for LDA whose computational complexity is asymptotically on bar with the state of the art Alias base sampler for LDA \cite{aliasLDA}. We illustrate the efficacy of our approach over real industrial datasets that span up to billion of users, tens of millions of words and thousands of topics. To the best of our knowledge, our approach provides the first practical and scalable solution to this important problem.