Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor.

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.

Editing faces in videos is a popular yet challenging aspect of computer vision and graphics, which encompasses several applications including facial attractiveness enhancement, makeup transfer, face replacement, and expression manipulation. Simply applying image-based warping algorithms to video-based face editing produces temporal incoherence in the synthesized videos because it is impossible to consistently localize facial features in two frames representing two different faces in two different videos (or even two consecutive frames representing the same face in one video). Therefore, high performance face editing usually requires significant manual manipulation. In this paper we propose a novel temporal-spatial-smooth warping (TSSW) algorithm to effectively exploit the temporal information in two consecutive frames, as well as the spatial smoothness within each frame. TSSW precisely estimates two control lattices in the horizontal and vertical directions respectively from the corresponding control lattices in the previous frame, by minimizing a novel energy function that unifies a data-driven term, a smoothness term, and feature point constraints. Corresponding warping surfaces then precisely map source frames to the target frames. Experimental testing on facial attractiveness enhancement, makeup transfer, face replacement, and expression manipulation demonstrates that the proposed approaches can effectively preserve spatial smoothness and temporal coherence in editing facial geometry, skin detail, identity, and expression, which outperform the existing face editing methods. In particular, TSSW is robust to subtly inaccurate localization of feature points and is a vast improvement over image-based warping methods.

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.

Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry from propositional logic. It is shown how the notions of `possibility' and `property' may be suffciently represented in propositional logic such that 1) the principle of indifference drops out and becomes essentially combinatoric in nature and 2) one may appropriately represent assumptions where one assumes there is a space of possibilities but does not assume the size of the space.

Active learning strategies respond to the costly labelling task in a supervised classification by selecting the most useful unlabelled examples in training a predictive model. Many conventional active learning algorithms focus on refining the decision boundary, rather than exploring new regions that can be more informative. In this setting, we propose a sequential algorithm named EG Active that can improve any Active learning algorithm by an optimal random exploration. Experimental results show a statistically significant and appreciable improvement in the performance of our new approach over the existing active feedback methods.

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze in detail both the loop series and the Pfaffian series for models with binary variables and pairwise interactions, and show that the first term of the Pfaffian series can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.

In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While linear non-Gaussian variants have been well-studied, inference in nonparametric structural equation models is still underdeveloped. We introduce a sparse Gaussian process parameterization that defines a non-linear structure connecting latent variables, unlike common formulations of Gaussian process latent variable models. The sparse parameterization is given a full Bayesian treatment without compromising Markov chain Monte Carlo efficiency. We compare the stability of the sampling procedure and the predictive ability of the model against the current practice.

We consider the problem of estimating the conditional probability of a label in time O(log n), where n is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly 106 labels.

It is often the case that, within an online recommender system, multiple users share a common account. Can such shared accounts be identified solely on the basis of the userprovided ratings? Once a shared account is identified, can the different users sharing it be identified as well? Whenever such user identification is feasible, it opens the way to possible improvements in personalized recommendations, but also raises privacy concerns. We develop a model for composite accounts based on unions of linear subspaces, and use subspace clustering for carrying out the identification task. We show that a significant fraction of such accounts is identifiable in a reliable manner, and illustrate potential uses for personalized recommendation.