The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

Category-level object detection has a crucial need for informative object representations. This demand has led to feature descriptors of ever increasing dimensionality like co-occurrence statistics and self-similarity. In this paper we propose a new object representation based on curvature self-similarity that goes beyond the currently popular approximation of objects using straight lines. However, like all descriptors using second order statistics, ours also exhibits a high dimensionality. Although improving discriminability, the high dimensionality becomes a critical issue due to lack of generalization ability and curse of dimensionality. Given only a limited amount of training data, even sophisticated learning algorithms such as the popular kernel methods are not able to suppress noisy or superfluous dimensions of such high-dimensional data. Consequently, there is a natural need for feature selection when using present-day informative features and, particularly, curvature self-similarity. We therefore suggest an embedded feature selection method for SVMs that reduces complexity and improves generalization capability of object models. By successfully integrating the proposed curvature self-similarity representation together with the embedded feature selection in a widely used state-of-the-art object detection framework we show the general pertinence of the approach.

We formulate clustering aggregation as a special instance of Maximum-Weight Independent Set (MWIS) problem. For a given dataset, an attributed graph is constructed from the union of the input clusterings generated by different underlying clustering algorithms with different parameters. The vertices, which represent the distinct clusters, are weighted by an internal index measuring both cohesion and separation. The edges connect the vertices whose corresponding clusters overlap. Intuitively, an optimal aggregated clustering can be obtained by selecting an optimal subset of non-overlapping clusters partitioning the dataset together. We formalize this intuition as the MWIS problem on the attributed graph, i.e., finding the heaviest subset of mutually non-adjacent vertices. This MWIS problem exhibits a special structure. Since the clusters of each input clustering form a partition of the dataset, the vertices corresponding to each clustering form a maximal independent set (MIS) in the attributed graph. We propose a variant of simulated annealing method that takes advantage of this special structure. Our algorithm starts from each MIS, which is close to a distinct local optimum of the MWIS problem, and utilizes a local search heuristic to explore its neighborhood in order to find the MWIS. Extensive experiments on many challenging datasets show that: 1. our approach to clustering aggregation automatically decides the optimal number of clusters; 2. it does not require any parameter tuning for the underlying clustering algorithms; 3. it can combine the advantages of different underlying clustering algorithms to achieve superior performance; 4. it is robust against moderate or even bad input clusterings.

We propose a high dimensional semiparametric scale-invariant principle component analysis,named TCA, by utilize the natural connection between the elliptical distribution family and the principal component analysis. Elliptical distribution familyincludes many well-known multivariate distributions like multivariate Gaussian, t and logistic and it is extended to the meta-elliptical by Fang et.al (2002) using the copula techniques. In this paper we extend the meta-elliptical distribution family to a even larger family, called transelliptical. We prove that TCA can obtain a near-optimal s logd/n estimation consistency rate in recovering the leading eigenvector of the latent generalized correlation matrix under the transelliptical distribution family, even if the distributions are very heavy-tailed, have infinite second moments, do not have densities and possess arbitrarily continuous marginaldistributions. A feature selection result with explicit rate is also provided. TCA is further implemented in both numerical simulations and largescale stockdata to illustrate its empirical usefulness. Both theories and experiments confirmthat TCA can achieve model flexibility, estimation accuracy and robustness at almost no cost.

Our personal social networks are big and cluttered, and currently there is no good way to organize them. Social networking sites allow users to manually categorize their friends into social circles (e.g. 'circles' on Google, and'lists' on Facebook and Twitter), however they are laborious to construct and must be updated whenever auser's network grows. We define a novel machine learning task of identifying users'social circles. We pose the problem as a node clustering problem on a user's ego-network, a network of connections between her friends. We develop a model for detecting circles that combines network structure as well as user profile information.For each circle we learn its members and the circle-specific user profile similarity metric. Modeling node membership to multiple circles allows us to detect overlapping as well as hierarchically nested circles. Experiments show that our model accurately identifies circles on a diverse set of data from Facebook, Google, and Twitter for all of which we obtain hand-labeled ground-truth.

The representer theorem is a property that lies at the foundation of regularization theory and kernel methods. A class of regularization functionals is said to admit a linear representer theorem if every member of the class admits minimizers that lie in the finite dimensional subspace spanned by the representers of the data. A recent characterization states that certain classes of regularization functionals with differentiable regularization term admit a linear representer theorem for any choice of the data if and only if the regularization term is a radial nondecreasing function. In this paper, we extend such result by weakening the assumptions on the regularization term. In particular, the main result of this paper implies that, for a sufficiently large family of regularization functionals, radial nondecreasing functions are the only lower semicontinuous regularization terms that guarantee existence of a representer theorem for any choice of the data.

We study surrogate losses for learning to rank, in a framework where the rankings are induced by scores and the task is to learn the scoring function. We focus on the calibration of surrogate losses with respect to a ranking evaluation metric, where the calibration is equivalent to the guarantee that near-optimal values of the surrogate riskimply near-optimal values of the risk defined by the evaluation metric. We prove that if a surrogate loss is a convex function of the scores, then it is not calibrated with respect to two evaluation metrics widely used for search engine evaluation, namely the Average Precision and the Expected Reciprocal Rank. We also show that such convex surrogate losses cannot be calibrated with respect to the Pairwise Disagreement, an evaluation metric used when learning from pairwise preferences.Our results cast lights on the intrinsic difficulty of some ranking problems, as well as on the limitations of learning-to-rank algorithms based on the minimization of a convex surrogate risk.

In this paper we study sparsity-inducing nonconvex penalty functions using Lévy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly,we propose a novel approach for the construction of sparsityinducing nonconvexpenalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively. Additionally, we explore the concave conjugate of nonconvex penalties. We find that the LOG and EXP penalties are the concave conjugates of negative Kullback-Leiber (KL) distance functions.Furthermore, the relationship between these two penalties is due to asymmetricity of the KL distance.

Finding contours in natural images is a fundamental problem that serves as the basis of many tasks such as image segmentation and object recognition. At the core of contour detection technologies are a set of hand-designed gradient features, used by most existing approaches including the state-of-the-art Global Pb (gPb) operator. In this work, we show that contour detection accuracy can be significantly improved by computing Sparse Code Gradients (SCG), which measure contrast using patch representations automatically learned through sparse coding. We use K-SVD and Orthogonal Matching Pursuit for efficient dictionary learning and encoding, and use multi-scale pooling and power transforms to code oriented local neighborhoods before computing gradients and applying linear SVM. By extracting rich representations from pixels and avoiding collapsing them prematurely, Sparse Code Gradients effectively learn how to measure local contrasts and find contours. We improve the F-measure metric on the BSDS500 benchmark to 0.74 (up from 0.71 of gPb contours). Moreover, our learning approach can easily adapt to novel sensor data such as Kinect-style RGB-D cameras: Sparse Code Gradients on depth images and surface normals lead to promising contour detection using depth and depth+color, as verified on the NYU Depth Dataset. Our work combines the concept of oriented gradients with sparse representation and opens up future possibilities for learning contour detection and segmentation.

Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of derivatives of the Bethe free energy, provide bounds on the derivatives and bracket the locations of stationary points, introducing a new technique called Bethe bound propagation. Several results apply to pairwise models whether associative or not. Applying these to discretized pseudo-marginals in the associative case we present a polynomial time approximation scheme for global optimization provided the maximum degree is $O(\log n)$, and discuss several extensions.