In many learning tasks with structural properties, structured sparse modeling usually leads to better interpretability and higher generalization performance. While great efforts have focused on the convex regularization, recent studies show that nonconvex regularizers can outperform their convex counterparts in many situations. However, the resulting nonconvex optimization problems are still challenging, especially for the structured sparsity-inducing regularizers. In this paper, we propose a splitting method for solving nonconvex structured sparsity optimization problems. The proposed method alternates between a gradient step and an easily solvable proximal step, and thus enjoys low per-iteration computational complexity. We prove that the whole sequence generated by the proposed method converges to a critical point with at least sublinear convergence rate, relying on the Kurdyka-Łojasiewicz inequality. Experiments on both simulated and real-world data sets demonstrate the efficiency and efficacy of the proposed method.

We consider the problem of subspace clustering using the SSC (Sparse Subspace Clustering) approach, which has several desirable theoretical properties and has been shown to be effective in various computer vision applications.We develop a large scale distributed framework for the computation of SSC via an alternating direction method of multiplier (ADMM) algorithm. The proposed framework solves SSC in column blocks and only involves parallel multivariate Lasso regression subproblems and sample-wise operations. This appealing property allows us to allocate multiple cores/machines for the processing of individual column blocks.We evaluate our algorithm on a shared-memory architecture. Experimental results on real-world datasets confirm that the proposed block-wise ADMM framework is substantially more efficient than its matrix counterpart used by SSC,without sacrificing accuracy. Moreover, our approach is directly applicable to decentralized neighborhood selection for Gaussian graphical models structure estimation.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) are a family of diffusion-based sampling methods for large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient thermostats (mSGNHT) augment each parameter of interest, with a momentum and a thermostat variable to maintain stationary distributions as target posterior distributions. As the number of variables in a continuous-time diffusion increases, its numerical approximation error becomes a practical bottleneck, so better use of a numerical integrator is desirable. To this end, we propose use of an efficient symmetric splitting integrator in mSGNHT, instead of the traditional Euler integrator. We demonstrate that the proposed scheme is more accurate, robust, and converges faster. These properties are demonstrated to be desirable in Bayesian deep learning. Extensive experiments on two canonical models and their deep extensions demonstrate that the proposed scheme improves general Bayesian posterior sampling, particularly for deep models.

In the past decade, social and information networks have become prevalent, and research on the network data has attracted much attention. Besides the link structure, network data are often equipped with the content information (i.e, node attributes) that is usually noisy and characterized by high dimensionality. As the curse of dimensionality could hamper the performance of many machine learning tasks on networks (e.g., community detection and link prediction), feature selection can be a useful technique for alleviating such issue. In this paper, we investigate the problem of unsupervised feature selection on networks. Most existing feature selection methods fail to incorporate the linkage information, and the state-of-the-art approaches usually rely on pseudo labels generated from clustering. Such cluster labels may be far from accurate and can mislead the feature selection process. To address these issues, we propose a generative point of view for unsupervised features selection on networks that can seamlessly exploit the linkage and content information in a more effective manner. We assume that the link structures and node content are generated from a succinct set of high-quality features, and we find these features through maximizing the likelihood of the generation process. Experimental results on three real-world datasets show that our approach can select more discriminative features than state-of-the-art methods.

Instead of using a uniform metric, instance specific distance learning methods assign multiple metrics for different localities, which take data heterogeneity into consideration. Therefore, they may improve the performance of distance based classifiers, e.g., kNN. Existing methods obtain multiple metrics of test data by either transductively assigning metrics for unlabeled instances or designing distance functions manually, which are with limited generalization ability. In this paper, we propose isMets (Instance Specific METric Subspace) framework which can automatically span the whole metric space in a generative manner and is able to inductively learn a specific metric subspace for each instance via inferring the expectation over the metric bases in a Bayesian manner. The whole framework can be solved with Variational Bayes (VB). Experiment on synthetic data shows that the learned results are with good interpretability. Moreover, comprehensive results on real world datasets validate the effectiveness and robustness of isMets.

The Model AI Assignments session seeks to gather and disseminate the best assignment designs of the Artificial Intelligence (AI) Education community. Recognizing that assignments form the core of student learning experience, we here present abstracts of six AI assignments from the 2016 session that are easily adoptable, playfully engaging, and flexible for a variety of instructor needs.

Automatic image annotation is an important problem in several machine learning applications such as image search. Since there exists a semantic gap between low-level image features and high-level semantics, the description ability of image representation can largely affect annotation results. In fact, image representation learning and image tagging are two closely related tasks. A proper image representation can achieve better image annotation results, and image tags can be treated as guidance to learn more effective image representation. In this paper, we present an optimal predictive subspace learning method which jointly conducts multi-view representation learning and image tagging. The two tasks can promote each other and the annotation performance can be further improved. To make the subspace to be more compact and discriminative, both visual structure and semantic information are exploited during learning. Moreover, we introduce powerful predictors (SVM) for image tagging to achieve better annotation performance. Experiments on standard image annotation datasets demonstrate the advantages of our method over the existing image annotation methods.

You can test the accuracy of the results using an evaluation function.

Please kindly note that some mathematical expressions might not be properly rendered in the Github online IPython viewer.

Once one has computed all derivatives of the cost with respect to weights and biases / errors, what, exactly, does one do? How does one update the weights/biases? I can think of a simple way of doing it for a net with no hidden layer, but I have no idea how one would do it on one with more layers, since changing any weight or bias will change the value of the error of neurons in earlier and later layers - hence my question.