Learning social media data embedding by deep models has attracted extensive research interest as well as boomed a lot of applications, such as link prediction, classification, and cross-modal search. However, for social images which contain both link information and multimodal contents (e.g., text description, and visual content), simply employing the embedding learnt from network structure or data content results in sub-optimal social image representation. In this paper, we propose a novel social image embedding approach called Deep Multimodal Attention Networks (DMAN), which employs a deep model to jointly embed multimodal contents and link information. Specifically, to effectively capture the correlations between multimodal contents, we propose a multimodal attention network to encode the fine-granularity relation between image regions and textual words. To leverage the network structure for embedding learning, a novel Siamese-Triplet neural network is proposed to model the links among images. With the joint deep model, the learnt embedding can capture both the multimodal contents and the nonlinear network information. Extensive experiments are conducted to investigate the effectiveness of our approach in the applications of multi-label classification and cross-modal search. Compared to state-of-the-art image embeddings, our proposed DMAN achieves significant improvement in the tasks of multi-label classification and cross-modal search.

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent findings suggesting kernel methods cannot be extended beyond Hilbert setting. Numerical experiments confirm the effectiveness of the method.

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in practice. A possible remedy is to consider estimators, such as the Concomitant/Scaled Lasso, which jointly optimize over the regression coefficients as well as over the noise level, making the choice of the regularization independent of the noise level. However, when data from different sources are pooled to increase sample size, or when dealing with multimodal datasets, noise levels typically differ and new dedicated estimators are needed. In this work we provide new statistical and computational solutions to deal with such heteroscedastic regression models, with an emphasis on functional brain imaging with combined magneto- and electroencephalographic (M/EEG) signals. Adopting the formulation of Concomitant Lasso-type estimators, we propose a jointly convex formulation to estimate both the regression coefficients and the (square root of the) noise covariance. When our framework is instantiated to de-correlated noise, it leads to an efficient algorithm whose computational cost is not higher than for the Lasso and Concomitant Lasso, while addressing more complex noise structures. Numerical experiments demonstrate that our estimator yields improved prediction and support identification while correctly estimating the noise (square root) covariance. Results on multimodal neuroimaging problems with M/EEG data are also reported.

We consider the problem of quantifying the quality of a model selection problem for a graphical model. We discuss this by formulating the problem as a detection problem. Model selection problems usually minimize a distance between the original distribution and the model distribution. For the special case of Gaussian distributions, the model selection problem simplifies to the covariance selection problem which is widely discussed in literature by Dempster [2] where the likelihood criterion is maximized or equivalently the Kullback-Leibler (KL) divergence is minimized to compute the model covariance matrix. While this solution is optimal for Gaussian distributions in the sense of the KL divergence, it is not optimal when compared with other information divergences and criteria such as Area Under the Curve (AUC). In this paper, we analytically compute upper and lower bounds for the AUC and discuss the quality of model selection problem using the AUC and its bounds as an accuracy measure in detection problem. We define the correlation approximation matrix (CAM) and show that analytical computation of the KL divergence, the AUC and its bounds only depend on the eigenvalues of CAM. We also show the relationship between the AUC, the KL divergence and the ROC curve by optimizing with respect to the ROC curve. In the examples provided, we pick tree structures as the simplest graphical models. We perform simulations on fully-connected graphs and compute the tree structured models by applying the widely used Chow-Liu algorithm [3]. Examples show that the quality of tree approximation models are not good in general based on information divergences, the AUC and its bounds when the number of nodes in the graphical model is large. We show both analytically and by simulations that the 1-AUC for the tree approximation model decays exponentially as the dimension of graphical model increases.

Memristors have recently received significant attention as ubiquitous device-level components for building a novel generation of computing systems. These devices have many promising features, such as non-volatility, low power consumption, high density, and excellent scalability. The ability to control and modify biasing voltages at the two terminals of memristors make them promising candidates to perform matrix-vector multiplications and solve systems of linear equations. In this article, we discuss how networks of memristors arranged in crossbar arrays can be used for efficiently solving optimization and machine learning problems. We introduce a new memristor-based optimization framework that combines the computational merit of memristor crossbars with the advantages of an operator splitting method, alternating direction method of multipliers (ADMM). Here, ADMM helps in splitting a complex optimization problem into subproblems that involve the solution of systems of linear equations. The capability of this framework is shown by applying it to linear programming, quadratic programming, and sparse optimization. In addition to ADMM, implementation of a customized power iteration (PI) method for eigenvalue/eigenvector computation using memristor crossbars is discussed. The memristor-based PI method can further be applied to principal component analysis (PCA). The use of memristor crossbars yields a significant speed-up in computation, and thus, we believe, has the potential to advance optimization and machine learning research in artificial intelligence (AI).

This paper examines and proposes several attribution modeling methods that quantify how revenue should be attributed to online advertising inputs. We adopt and further develop relative importance method, which is based on regression models that have been extensively studied and utilized to investigate the relationship between advertising efforts and market reaction (revenue). Relative importance method aims at decomposing and allocating marginal contributions to the coefficient of determination (R^2) of regression models as attribution values. In particular, we adopt two alternative submethods to perform this decomposition: dominance analysis and relative weight analysis. Moreover, we demonstrate an extension of the decomposition methods from standard linear model to additive model. We claim that our new approaches are more flexible and accurate in modeling the underlying relationship and calculating the attribution values. We use simulation examples to demonstrate the superior performance of our new approaches over traditional methods. We further illustrate the value of our proposed approaches using a real advertising campaign dataset.

Covariate shift classification problems can in principle be tackled by importance-weighting training samples. However, the sampling variance of the risk estimator is often scaled up dramatically by the weights. This means that during cross-validation - when the importance-weighted risk is repeatedly evaluated - suboptimal hyperparameter estimates are produced. We study the sampling variances of the importance-weighted versus the oracle estimator as a function of the relative scale of the training data. We show that introducing a control variate can reduce the variance of the importance-weighted risk estimator, which leads to superior regularization parameter estimates when the training data is much smaller in scale than the test data.

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1) uniformly sampling a polytope and (2) computing its volume, the latter by extending Gaussian cooling to the manifold setting. In both cases, the total number of steps needed is O^{*}(mn^{\frac{2}{3}}), improving the state of the art. A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds.

We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a crucial problem when modeling large, sparse, high-dimensional datasets -- underfitting. We study the extent of underfitting, highlighting that its severity increases with the sparsity of the data. We propose methods to tackle it via iterative optimization inspired by stochastic variational inference \citep{hoffman2013stochastic} and improvements in the sparse data representation used for inference. The proposed techniques drastically improve the ability of these powerful models to fit sparse data, achieving state-of-the-art results on a benchmark text-count dataset and excellent results on the task of top-N recommendation.

This paper considers the problem of inferring image labels for which only a few labelled examples are available at training time. This setup is often referred to as low-shot learning in the literature, where a standard approach is to re-train the last few layers of a convolutional neural network learned on separate classes. We consider a semi-supervised setting in which we exploit a large collection of images to support label propagation. This is made possible by leveraging the recent advances on large-scale similarity graph construction. We show that despite its conceptual simplicity, scaling up label propagation to up hundred millions of images leads to state of the art accuracy in the low-shot learning regime.