In discrete undirected graphical models, the conditional independence of node labels Y is specified by the graph structure. We study the case where there is another input random vector X (e.g. observed features) such that the distribution P (Y | X) is determined by functions of X that characterize the (higher-order) interactions among the Y ’s. The main contribution of this paper is to learn the graph structure and the functions conditioned on X at the same time. We prove that discrete undirected graphical models with feature X are equivalent to mul- tivariate discrete models. The reparameterization of the potential functions in graphical models by conditional log odds ratios of the latter offers advantages in representation of the conditional independence structure. The functional spaces can be flexibly determined by kernels. Additionally, we impose a Structure Lasso (SLasso) penalty on groups of functions to learn the graph structure. These groups with overlaps are designed to enforce hierarchical function selection. In this way, we are able to shrink higher order interactions to obtain a sparse graph structure.

Inexpensive RGB-D cameras that give an RGB image together with depth data have become widely available. In this paper, we use this data to build 3D point clouds of full indoor scenes such as an office and address the task of semantic labeling of these 3D point clouds. We propose a graphical model that captures various features and contextual relations, including the local visual appearance and shape cues, object co-occurence relationships and geometric relationships. With a large number of object classes and relations, the model’s parsimony becomes important and we address that by using multiple types of edge potentials. The model admits efficient approximate inference, and we train it using a maximum-margin learning approach. In our experiments over a total of 52 3D scenes of homes and offices (composed from about 550 views, having 2495 segments labeled with 27 object classes), we get a performance of 84.06% in labeling 17 object classes for offices, and 73.38% in labeling 17 object classes for home scenes. Finally, we applied these algorithms successfully on a mobile robot for the task of finding objects in large cluttered rooms.

Determining interactions between entities and the overall organization and clustering of nodes in networks is a major challenge when analyzing biological and social network data. Here we extend the Indian Buffet Process (IBP), a nonparametric Bayesian model, to integrate noisy interaction scores with properties of individual entities for inferring interaction networks and clustering nodes within these networks. We present an application of this method to study how microRNAs regulate mRNAs in cells. Analysis of synthetic and real data indicates that the method improves upon prior methods, correctly recovers interactions and clusters, and provides accurate biological predictions.

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.

Variational Bayesian matrix factorization (VBMF) efficiently approximates the posterior distribution of factorized matrices by assuming matrix-wise independence of the two factors. A recent study on fully-observed VBMF showed that, under a stronger assumption that the two factorized matrices are column-wise independent, the global optimal solution can be analytically computed. However, it was not clear how restrictive the column-wise independence assumption is. In this paper, we prove that the global solution under matrix-wise independence is actually column-wise independent, implying that the column-wise independence assumption is harmless. A practical consequence of our theoretical finding is that the global solution under matrix-wise independence (which is a standard setup) can be obtained analytically in a computationally very efficient way without any iterative algorithms. We experimentally illustrate advantages of using our analytic solution in probabilistic principal component analysis.

Categorizing digital images using keywords, however, is the quintessential example of a Challenging classification problem.

Sparse coding, a method of explaining sensory data with as few dictionary bases as possible, has attracted much attention in computer vision. For visual object category recognition, L1 regularized sparse coding is combined with spatial pyramid representation to obtain state-of-the-art performance. However, because of its iterative optimization, applying sparse coding onto every local feature descriptor extracted from an image database can become a major bottleneck. To overcome this computational challenge, this paper presents "Generalized Lasso based Approximation of Sparse coding" (GLAS). By representing the distribution of sparse coefficients with slice transform, we fit a piece-wise linear mapping function with generalized lasso. We also propose an efficient post-refinement procedure to perform mutual inhibition between bases which is essential for an overcomplete setting. The experiments show that GLAS obtains comparable performance to L1 regularized sparse coding, yet achieves significant speed up demonstrating its effectiveness for large-scale visual recognition problems.

Cancer has complex patterns of progression that include converging as well as diverging progressional pathways. Vogelstein's path model of colon cancer was a pioneering contribution to cancer research. Since then, several attempts have been made at obtaining mathematical models of cancer progression, devising learning algorithms, and applying these to cross-sectional data. Beerenwinkel {\em et al.} provided, what they coined, EM-like algorithms for Oncogenetic Trees (OTs) and mixtures of such. Given the small size of current and future data sets, it is important to minimize the number of parameters of a model. For this reason, we too focus on tree-based models and introduce Hidden-variable Oncogenetic Trees (HOTs). In contrast to OTs, HOTs allow for errors in the data and thereby provide more realistic modeling. We also design global structural EM algorithms for learning HOTs and mixtures of HOTs (HOT-mixtures). The algorithms are global in the sense that, during the M-step, they find a structure that yields a global maximum of the expected complete log-likelihood rather than merely one that improves it. The algorithm for single HOTs performs very well on reasonable-sized data sets, while that for HOT-mixtures requires data sets of sizes obtainable only with tomorrow's more cost-efficient technologies.

In this paper, we consider the 'Precis' problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and pre-filtering. We formulate a general theory which encompasses not just traditional techniques devised for vector spaces, but also non-Euclidean manifolds, thereby enabling these techniques to shapes, human activities, textures and many other image and video based datasets. We propose intrinsic manifold measures for measuring the quality of a selection of points with respect to their representative power, and their diversity. We then propose efficient algorithms to optimize the cost function using a novel annealing-based iterative alternation algorithm. The proposed formulation is applicable to manifolds of known geometry as well as to manifolds whose geometry needs to be estimated from samples. Experimental results show the strength and generality of the proposed approach.

We describe a simple algorithm that runs in time poly(n,1/gamma,1/eps) and learns an unknown n-dimensional gamma-margin halfspace to accuracy 1-eps in the presence of malicious noise, when the noise rate is allowed to be as high as Theta(eps gamma sqrt(log(1/gamma))). Previous efficient algorithms could only learn to accuracy eps in the presence of malicious noise of rate at most Theta(eps gamma). Our algorithm does not work by optimizing a convex loss function. We show that no algorithm for learning gamma-margin halfspaces that minimizes a convex proxy for misclassification error can tolerate malicious noise at a rate greater than Theta(eps gamma); this may partially explain why previous algorithms could not achieve the higher noise tolerance of our new algorithm.