We present 3DP3, a framework for inverse graphics that uses inference in a structured generative model of objects, scenes, and images.

Eliminating the covariate shift cross domains is one of the common methods to deal with the issue of domain shift in visual unsupervised domain adaptation. However, current alignment methods, especially the prototype based or sample-level based methods neglect the structural properties of the underlying distribution and even break the condition of covariate shift. To relieve the limitations and conflicts, we introduce a novel concept named (virtual) mirror, which represents the equivalent sample in another domain. The equivalent sample pairs, named mirror pairs reflect the natural correspondence of the empirical distributions. Then a mirror loss, which aligns the mirror pairs cross domains, is constructed to enhance the alignment of the domains. The proposed method does not distort the internal structure of the underlying distribution. We also provide theoretical proof that the mirror samples and mirror loss have better asymptotic properties in reducing the domain shift. By applying the virtual mirror and mirror loss to the generic unsupervised domain adaptation model, we achieved consistently superior performance on several mainstream benchmarks.

Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by Dasgupta [12], and present two polynomial-time approximation algorithms: Our first result is an O(1)-approximation algorithm for graphs of high conductance. Our simple construction bypasses complicated recursive routines of finding sparse cuts known in the literature (e.g., [6, 11]). Our second and main result is an O(1)approximation algorithm for a wide family of graphs that exhibit a well-defined structure of clusters. This result generalises the previous state-of-the-art [10], which holds only for graphs generated from stochastic models. The significance of our work is demonstrated by the empirical analysis on both synthetic and real-world data sets, on which our presented algorithm outperforms the previously proposed algorithm for graphs with a well-defined cluster structure [10].

Feature Selection and Functional Data Analysis are two dynamic areas of research, with important applications in the analysis of large and complex data sets. Straddling these two areas, we propose a new highly efficient algorithm to perform Group Elastic Net with application to function-on-scalar feature selection, where a functional response is modeled against a very large number of potential scalar predictors. First, we introduce a new algorithm to solve Group Elastic Net in ultrahigh dimensional settings, which exploits the sparsity structure of the Augmented Lagrangian to greatly reduce computational burden. Next, taking advantage of the properties of Functional Principal Components, we extend our algorithm to the function-on-scalar regression framework. We use simulations to demonstrate the CPU time gains afforded by our approach compared to its best existing competitors, and present an application to data from a Genome Wide Association Study on childhood obesity.

Modeling directed graphs with differentiable representations is a fundamental requirement for performing machine learning on graph-structured data.