Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a critical point in nonconvex programming. To address this issue, we introduce a monitor-corrector step and extend APG for general nonconvex and nonsmooth programs. Accordingly, we propose a monotone APG and a non-monotone APG. The latter waives the requirement on monotonic reduction of the objective function and needs less computation in each iteration. To the best of our knowledge, we are the first to provide APG-type algorithms for general nonconvex and nonsmooth problems ensuring that every accumulation point is a critical point, and the convergence rates remain $O(1/k^2)$ when the problems are convex, in which k is the number of iterations. Numerical results testify to the advantage of our algorithms in speed.

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system. In ADVI the user provides a Bayesian model and a dataset, nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.

Super resolving a low-resolution video is usually handled by either single-image super-resolution (SR) or multi-frame SR. Single-Image SR deals with each video frame independently, and ignores intrinsic temporal dependency of video frames which actually plays a very important role in video super-resolution. Multi-Frame SR generally extracts motion information, e.g., optical flow, to model the temporal dependency, which often shows high computational cost. Considering that recurrent neuralnetworks (RNNs) can model long-term contextual information of temporal sequenceswell, we propose a bidirectional recurrent convolutional network for efficient multi-frame SR. Different from vanilla RNNs, 1) the commonly-used recurrent full connections are replaced with weight-sharing convolutional connections and2) conditional convolutional connections from previous input layers to the current hidden layer are added for enhancing visual-temporal dependency modelling. With the powerful temporal dependency modelling, our model can super resolve videos with complex motions and achieve state-of-the-art performance. Dueto the cheap convolution operations, our model has a low computational complexity and runs orders of magnitude faster than other multi-frame methods.

We consider the following detection problem: given a realization of asymmetric matrix $X$ of dimension $n$, distinguish between the hypothesisthat all upper triangular variables are i.i.d. Gaussians variableswith mean 0 and variance $1$ and the hypothesis that there is aplanted principal submatrix $B$ of dimension $L$ for which all upper triangularvariables are i.i.d. Gaussians with mean $1$ and variance $1$, whereasall other upper triangular elements of $X$ not in $B$ are i.i.d.Gaussians variables with mean 0 and variance $1$. We refer to this asthe `Gaussian hidden clique problem'. When $L=( 1 + \epsilon) \sqrt{n}$ ($\epsilon > 0$), it is possible to solve thisdetection problem with probability $1 - o_n(1)$ by computing thespectrum of $X$ and considering the largest eigenvalue of $X$.We prove that when$L < (1-\epsilon)\sqrt{n}$ no algorithm that examines only theeigenvalues of $X$can detect the existence of a hiddenGaussian clique, with error probability vanishing as $n \to \infty$.The result above is an immediate consequence of a more general result on rank-oneperturbations of $k$-dimensional Gaussian tensors.In this context we establish a lower bound on the criticalsignal-to-noise ratio below which a rank-one signal cannot be detected.

This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. We introduce t-level auctions to interpolate between simple auctions, such as welfare maximization with reserve prices, and optimal auctions, thereby balancing the competing demands of expressivity and simplicity. We prove that such auctions have small representation error, in the sense that for every product distribution F over bidders’ valuations, there exists a t-level auction with small t and expected revenue close to optimal. We show that the set of t-level auctions has modest pseudo-dimension (for polynomial t) and therefore leads to small learning error. One consequence of our results is that, in arbitrary single-parameter settings, one can learn a mechanism with expected revenue arbitrarily close to optimal from a polynomial number of samples.

State-of-the-art object detection networks depend on region proposal algorithms to hypothesize object locations. Advances like SPPnet and Fast R-CNN have reduced the running time of these detection networks, exposing region proposal computation as a bottleneck. In this work, we introduce a Region Proposal Network (RPN) that shares full-image convolutional features with the detection network, thus enabling nearly cost-free region proposals. An RPN is a fully-convolutional network that simultaneously predicts object bounds and objectness scores at each position. RPNs are trained end-to-end to generate high-quality region proposals, which are used by Fast R-CNN for detection. With a simple alternating optimization, RPN and Fast R-CNN can be trained to share convolutional features. For the very deep VGG-16 model, our detection system has a frame rate of 5fps (including all steps) on a GPU, while achieving state-of-the-art object detection accuracy on PASCAL VOC 2007 (73.2% mAP) and 2012 (70.4% mAP) using 300 proposals per image. Code is available at https://github.com/ShaoqingRen/faster_rcnn.

Lunch with a Fellow, and the Volunteer high standard, and of special interest AAAI-16 Registration is now available Program, in addition to the Student to the AAAI community.

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering the discriminative ability of DGMs on making accurate predictions. This paper presents max-margin deep generative models (mmDGMs), which explore the strongly discriminative principle of max-margin learning to improve the discriminative power of DGMs, while retaining the generative capability. We develop an efficient doubly stochastic subgradient algorithm for the piecewise linear objective. Empirical results on MNIST and SVHN datasets demonstrate that (1) max-margin learning can significantly improve the prediction performance of DGMs and meanwhile retain the generative ability; and (2) mmDGMs are competitive to the state-of-the-art fully discriminative networks by employing deep convolutional neural networks (CNNs) as both recognition and generative models.

We show that the maximum-likelihood (ML) estimate of models derived from Luce's choice axiom (e.g., the Plackett-Luce model) can be expressed as the stationary distribution of a Markov chain. This conveys insight into several recently proposed spectral inference algorithms. We take advantage of this perspective and formulate a new spectral algorithm that is significantly more accurate than previous ones for the Plackett--Luce model. With a simple adaptation, this algorithm can be used iteratively, producing a sequence of estimates that converges to the ML estimate. The ML version runs faster than competing approaches on a benchmark of five datasets. Our algorithms are easy to implement, making them relevant for practitioners at large.

The alternating direction method of multipliers (ADMM) is an important tool for solving complex optimization problems, but it involves minimization sub-steps that are often difficult to solve efficiently. The Primal-Dual Hybrid Gradient (PDHG) method is a powerful alternative that often has simpler substeps than ADMM, thus producing lower complexity solvers. Despite the flexibility of this method, PDHG is often impractical because it requires the careful choice of multiple stepsize parameters. There is often no intuitive way to choose these parameters to maximize efficiency, or even achieve convergence. We propose self-adaptive stepsize rules that automatically tune PDHG parameters for optimal convergence. We rigorously analyze our methods, and identify convergence rates. Numerical experiments show that adaptive PDHG has strong advantages over non-adaptive methods in terms of both efficiency and simplicity for the user.