While graphs with continuous node attributes arise in many applications, state-of-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity; for instance, the popular shortest path kernel scales as $\mathcal{O}(n^4)$, where $n$ is the number of nodes. In this paper, we present a class of path kernels with computational complexity $\mathcal{O}(n^2 (m + \delta^2))$, where $\delta$ is the graph diameter and $m$ the number of edges. Due to the sparsity and small diameter of real-world graphs, these kernels scale comfortably to large graphs. In our experiments, the presented kernels outperform state-of-the-art kernels in terms of speed and accuracy on classification benchmark datasets.

For data assumed to come from a finite mixture with an unknown number of components, ithas become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. Thetypical approach is to use the posterior distribution on the number of clusters -- that is, the posterior on the number of components represented in the observed data. However, it turns out that this posterior is not consistent -- it does not concentrate at the true number of components. In this note, we give an elementary proofof this inconsistency in what is perhaps the simplest possible setting: a DPM with normal components of unit variance, applied to data from a "mixture" with one standard normal component. Further, we show that this example exhibits severe inconsistency: instead of going to 1, the posterior probability that there is one cluster converges (in probability) to 0.

Time series often have a temporal hierarchy, with information that is spread out over multiple time scales. Common recurrent neural networks, however, do not explicitly accommodate such a hierarchy, and most research on them has been focusing on training algorithms rather than on their basic architecture. In this pa- per we study the effect of a hierarchy of recurrent neural networks on processing time series. Here, each layer is a recurrent network which receives the hidden state of the previous layer as input. This architecture allows us to perform hi- erarchical processing on difficult temporal tasks, and more naturally capture the structure of time series. We show that they reach state-of-the-art performance for recurrent networks in character-level language modelling when trained with sim- ple stochastic gradient descent. We also offer an analysis of the different emergent time scales.

Stochastic gradient optimization is a class of widely used algorithms for training machine learning models. To optimize an objective, it uses the noisy gradient computed from the random data samples instead of the true gradient computed from the entire dataset. However, when the variance of the noisy gradient is large, the algorithm might spend much time bouncing around, leading to slower convergence and worse performance. In this paper, we develop a general approach of using control variate for variance reduction in stochastic gradient. Data statistics such as low-order moments (pre-computed or estimated online) is used to form the control variate. We demonstrate how to construct the control variate for two practical problems using stochastic gradient optimization. One is convex---the MAP estimation for logistic regression, and the other is non-convex---stochastic variational inference for latent Dirichlet allocation. On both problems, our approach shows faster convergence and better performance than the classical approach.

The sparse additive model for text modeling involves the sum-of-exp computing, with consuming costs for large scales. Moreover, the assumption of equal background across all classes/topics may be too strong. This paper extends to propose sparse additive model with low rank background (SAM-LRB), and simple yet efficient estimation. Particularly, by employing a double majorization bound, we approximate the log-likelihood into a quadratic lower-bound with the sum-of-exp terms absent. The constraints of low rank and sparsity are then simply embodied by nuclear norm and $\ell_1$-norm regularizers. Interestingly, we find that the optimization task in this manner can be transformed into the same form as that in Robust PCA. Consequently, parameters of supervised SAM-LRB can be efficiently learned using an existing algorithm for Robust PCA based on accelerated proximal gradient. Besides the supervised case, we extend SAM-LRB to also favor unsupervised and multifaceted scenarios. Experiments on real world data demonstrate the effectiveness and efficiency of SAM-LRB, showing state-of-the-art performances.

Causal inference uses observational data to infer the causal structure of the data generating system. We study a class of restricted Structural Equation Models for time series that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. This work contains two main contributions: (1) Theoretical: By restricting the model class (e.g. to additive noise) we provide more general identifiability results than existing ones. The results cover lagged and instantaneous effects that can be nonlinear and unfaithful, and non-instantaneous feedbacks between the time series. (2) Practical: If there are no feedback loops between time series, we propose an algorithm based on non-linear independence tests of time series. When the data are causally insufficient, or the data generating process does not satisfy the model assumptions, this algorithm may still give partial results, but mostly avoids incorrect answers. The Structural Equation Model point of view allows us to extend both the theoretical and the algorithmic part to situations in which the time series have been measured with different time delays (as may happen for fMRI data, for example). TiMINo outperforms existing methods on artificial and real data. Code is provided.

The increased availability of data in recent years led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible to use the extra examples to speed up the computation time required to perform the learning task? We give the first positive answer to this question for a {\em natural supervised learning problem} --- we consider agnostic PAC learning of halfspaces over $3$-sparse vectors in $\{-1,1,0\}^n$. This class is inefficiently learnable using $O\left(n/\epsilon^2\right)$ examples. Our main contribution is a novel, non-cryptographic, methodology for establishing computational-statistical gaps, which allows us to show that, under a widely believed assumption that refuting random $\mathrm{3CNF}$ formulas is hard, efficiently learning this class using $O\left(n/\epsilon^2\right)$ examples is impossible. We further show that under stronger hardness assumptions, even $O\left(n^{1.499}/\epsilon^2\right)$ examples do not suffice. On the other hand, we show a new algorithm that learns this class efficiently using $\tilde{\Omega}\left(n^2/\epsilon^2\right)$ examples. This formally establishes the tradeoff between sample and computational complexity for a natural supervised learning problem.

This paper considers the problem of transferring experimental findings learned from multiple heterogeneous domains to a target domain, in which only limited experiments can be performed. We reduce questions of transportability from multiple domainsand with limited scope to symbolic derivations in the causal calculus, thus extending the original setting of transportability introduced in [1], which assumes only one domain with full experimental information available. We further provide different graphical and algorithmic conditions for computing the transport formula in this setting, that is, a way of fusing the observational and experimental informationscattered throughout different domains to synthesize a consistent estimate of the desired effects in the target domain. We also consider the issue of minimizing the variance of the produced estimand in order to increase power.

Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in sparsity-related techniques. We cast the problem, resembling group or collaborative sparsity formulations, as a non-smooth convex optimization problem that can be efficiently solved using augmented Lagrangian techniques. The method can deal with weighted or unweighted graphs, as well as multimodal data, where different graphs represent different types of data. The proposed approach is also naturally integrated with collaborative graph inference techniques, solving general network inference problems where the observed variables, possibly coming from different modalities, are not in correspondence. The algorithm is tested and compared with state-of-the-art graph matching techniques in both synthetic and real graphs. We also present results on multimodal graphs and applications to collaborative inference of brain connectivity from alignment-free functional magnetic resonance imaging (fMRI) data.

Visual clutter, the perception of an image as being crowded and disordered, affects aspects of our lives ranging from object detection to aesthetics, yet relatively little effort has been made to model this important and ubiquitous percept. Our approach models clutter as the number of proto-objects segmented from an image, with proto-objects defined as groupings of superpixels that are similar in intensity, color, and gradient orientation features. We introduce a novel parametric method of merging superpixels by modeling mixture of Weibull distributions on similarity distance statistics, then taking the normalized number of proto-objects following partitioning as our estimate of clutter perception. We validated this model using a new $\text{90}-$image dataset of realistic scenes rank ordered by human raters for clutter, and showed that our method not only predicted clutter extremely well (Spearman's $\rho = 0.81$, $p < 0.05$), but also outperformed all existing clutter perception models and even a behavioral object segmentation ground truth. We conclude that the number of proto-objects in an image affects clutter perception more than the number of objects or features.