In this paper, we argue for representing networks as a bag of {\it triangular motifs}, particularly for important network problems that current model-based approaches handle poorly due to computational bottlenecks incurred by using edge representations. Such approaches require both 1-edges and 0-edges (missing edges) to be provided as input, and as a consequence, approximate inference algorithms for these models usually require $\Omega(N^2)$ time per iteration, precluding their application to larger real-world networks. In contrast, triangular modeling requires less computation, while providing equivalent or better inference quality. A triangular motif is a vertex triple containing 2 or 3 edges, and the number of such motifs is $\Theta(\sum_{i}D_{i}^{2})$ (where $D_i$ is the degree of vertex $i$), which is much smaller than $N^2$ for low-maximum-degree networks. Using this representation, we develop a novel mixed-membership network model and approximate inference algorithm suitable for large networks with low max-degree. For networks with high maximum degree, the triangular motifs can be naturally subsampled in a {\it node-centric} fashion, allowing for much faster inference at a small cost in accuracy. Empirically, we demonstrate that our approach, when compared to that of an edge-based model, has faster runtime and improved accuracy for mixed-membership community detection. We conclude with a large-scale demonstration on an $N\approx 280,000$-node network, which is infeasible for network models with $\Omega(N^2)$ inference cost.

Two-alternative forced choice (2AFC) and Go/NoGo (GNG) tasks are behavioral choice paradigms commonly used to study sensory and cognitive processing in choice behavior. While GNG is thought to isolate the sensory/decisional component by removing the need for response selection, a consistent bias towards the Go response (higher hits and false alarm rates) in the GNG task suggests possible fundamental differences in the sensory or cognitive processes engaged in the two tasks. Existing mechanistic models of these choice tasks, mostly variants of the drift-diffusion model (DDM; [1,2]) and the related leaky competing accumulator models [3,4] capture various aspects of behavior but do not address the provenance of the Go bias. We postulate that this ``impatience'' to go is a strategic adjustment in response to the implicit asymmetry in the cost structure of GNG: the NoGo response requires waiting until the response deadline, while a Go response immediately terminates the current trial. We show that a Bayes-risk minimizing decision policy that minimizes both error rate and average decision delay naturally exhibits the experimentally observed bias. The optimal decision policy is formally equivalent to a DDM with a time-varying threshold that initially rises after stimulus onset, and collapses again near the response deadline. The initial rise is due to the fading temporal advantage of choosing the Go response over the fixed-delay NoGo response. We show that fitting a simpler, fixed-threshold DDM to the optimal model reproduces the counterintuitive result of a higher threshold in GNG than 2AFC decision-making, previously observed in direct DDM fit to behavioral data [2], although such approximations cannot reproduce the Go bias. Thus, observed discrepancies between GNG and 2AFC decision-making may arise from rational strategic adjustments to the cost structure, and need not imply additional differences in the underlying sensory and cognitive processes.

We propose a novel kernel approach to dimension reduction for supervised learning: feature extraction and variable selection; the former constructs a small number of features from predictors, and the latter finds a subset of predictors. First, a method of linear feature extraction is proposed using the gradient of regression function, based on the recent development of the kernel method. In comparison with other existing methods, the proposed one has wide applicability without strong assumptions on the regressor or type of variables, and uses computationally simple eigendecomposition, thus applicable to large data sets. Second, in combination of a sparse penalty, the method is extended to variable selection, following the approach by Chen et al. (2010). Experimental results show that the proposed methods successfully find effective features and variables without parametric models.

Recently, Liu et al. [6, 7] introduced the notion of a nonparanormal distribution, which generalizes Instead of only analyzing the standard covariance matrix, we show that it is often fruitful to augment the usual covariance matrix with higher-order interaction terms. Other related work on graphical model selection for discrete graphs includes the Classic Chow-Liu algorithm for trees [8]; nodewise logistic regression for discrete models with pairwise interactions [9, 10]; and techniques based on conditional entropy or mutual information [11, 12].

We study consistency properties of surrogate loss functions for general multiclass classification problems, defined by a general loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be classification calibrated with respect to a loss matrix in this setting. We then introduce the notion of \emph{classification calibration dimension} of a multiclass loss matrix, which measures the smallest `size' of a prediction space for which it is possible to design a convex surrogate that is classification calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, as one application, we provide a different route from the recent result of Duchi et al.\ (2010) for analyzing the difficulty of designing `low-dimensional' convex surrogates that are consistent with respect to pairwise subset ranking losses. We anticipate the classification calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.

Robust policy optimization acknowledges that risk-aversion plays a vital role in real-world decision-making. When faced with uncertainty about the effects of actions, the policy that maximizes expected utility over the unknown parameters of the system may also carry with it a risk of intolerably poor performance. One might prefer to accept lower utility in expectation in order to avoid, or reduce the likelihood of, unacceptable levels of utility under harmful parameter realizations. In this paper, we take a Bayesian approach to parameter uncertainty, but unlike other methods avoid making any distributional assumptions about the form of this uncertainty. Instead we focus on identifying optimization objectives for which solutions can be efficiently approximated. We introduce percentile measures: a very general class of objectives for robust policy optimization, which encompasses most existing approaches, including ones known to be intractable. We then introduce a broad subclass of this family for which robust policies can be approximated efficiently. Finally, we frame these objectives in the context of a two-player, zero-sum, extensive-form game and employ a no-regret algorithm to approximate an optimal policy, with computation only polynomial in the number of states and actions of the MDP.

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, an Indian Buffet-like generative process for network growth, and a simple and efficient Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

This paper examines the possibility of a `reject option' in the context of least squares regression. It is shown that using rejection it is theoretically possible to learn `selective' regressors that can $\epsilon$-pointwise track the best regressor in hindsight from the same hypothesis class, while rejecting only a bounded portion of the domain. Moreover, the rejected volume vanishes with the training set size, under certain conditions. We then develop efficient and exact implementation of these selective regressors for the case of linear regression. Empirical evaluation over a suite of real-world datasets corroborates the theoretical analysis and indicates that our selective regressors can provide substantial advantage by reducing estimation error.

The sum-product network (SPN) is a recently-proposed deep model consisting of a network of sum and product nodes, and has been shown to be competitive with state-of-the-art deep models on certain difficult tasks such as image completion. Designing an SPN network architecture that is suitable for the task at hand is an open question. We propose an algorithm for learning the SPN architecture from data. The idea is to cluster variables (as opposed to data instances) in order to identify variable subsets that strongly interact with one another. Nodes in the SPN network are then allocated towards explaining these interactions. Experimental evidence shows that learning the SPN architecture significantly improves its performance compared to using a previously-proposed static architecture.

Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data.