The key to overcome class imbalance problems is to capture the distribution of minority class accurately. Generative Adversarial Networks (GANs) have shown some potentials to tackle class imbalance problems due to their capability of reproducing data distributions given ample training data samples. However, the scarce samples of one or more classes still pose a great challenge for GANs to learn accurate distributions for the minority classes. In this work, we propose an Annealing Genetic GAN (AGGAN) method, which aims to reproduce the distributions closest to the ones of the minority classes using only limited data samples. Our AGGAN renovates the training of GANs as an evolutionary process that incorporates the mechanism of simulated annealing. In particular, the generator uses different training strategies to generate multiple offspring and retain the best. Then, we use the Metropolis criterion in the simulated annealing to decide whether we should update the best offspring for the generator. As the Metropolis criterion allows a certain chance to accept the worse solutions, it enables our AGGAN steering away from the local optimum. According to both theoretical analysis and experimental studies on multiple imbalanced image datasets, we prove that the proposed training strategy can enable our AGGAN to reproduce the distributions of minority classes from scarce samples and provide an effective and robust solution for the class imbalance problem.

We present two classes of differentially private optimization algorithms derived from the well-known accelerated first-order methods. The first algorithm is inspired by Polyak's heavy ball method and employs a smoothing approach to decrease the accumulated noise on the gradient steps required for differential privacy. The second class of algorithms are based on Nesterov's accelerated gradient method and its recent multi-stage variant. We propose a noise dividing mechanism for the iterations of Nesterov's method in order to improve the error behavior of the algorithm. The convergence rate analyses are provided for both the heavy ball and the Nesterov's accelerated gradient method with the help of the dynamical system analysis techniques. Finally, we conclude with our numerical experiments showing that the presented algorithms have advantages over the well-known differentially private algorithms.

The E-commerce platform has become the principal battleground where people search, browse and pay for whatever they want. Critical as is to improve the online shopping experience for customers and merchants, how to find a proper approach for user intent prediction are paid great attention in both industry and academia. In this paper, we propose a novel user intent prediction model, TPG-DNN, to complete the challenging task, which is based on adaptive gated recurrent unit (GRU) loss function with multi-task learning. We creatively use the GRU structure and total probability formula as the loss function to model the users' whole online purchase process. Besides, the multi-task weight adjustment mechanism can make the final loss function dynamically adjust the importance between different tasks through data variance. According to the test result of experiments conducted on Taobao daily and promotion data sets, the proposed model performs much better than existing click through rate (CTR) models. At present, the proposed user intent prediction model has been widely used for the coupon allocation, advertisement and recommendation on Taobao platform, which greatly improve the user experience and shopping efficiency, and benefit the gross merchandise volume (GMV) promotion as well.

One fundamental goal of high-dimensional statistics is to detect or recover structure from noisy data. In many cases, the data can be faithfully modeled by a planted structure (such as a low-rank matrix) perturbed by random noise. But even for these simple models, the computational complexity of estimation is sometimes poorly understood. A growing body of work studies low-degree polynomials as a proxy for computational complexity: it has been demonstrated in various settings that low-degree polynomials of the data can match the statistical performance of the best known polynomial-time algorithms for detection. While prior work has studied the power of low-degree polynomials for the task of detecting the presence of hidden structures, it has failed to address the estimation problem in settings where detection is qualitatively easier than estimation. In this work, we extend the method of low-degree polynomials to address problems of estimation and recovery. For a large class of "signal plus noise" problems, we give a user-friendly lower bound for the best possible mean squared error achievable by any degree-D polynomial. To our knowledge, this is the first instance in which the low-degree polynomial method can establish low-degree hardness of recovery problems where the associated detection problem is easy. As applications, we give a tight characterization of the low-degree minimum mean squared error for the planted submatrix and planted dense subgraph problems, resolving (in the low-degree framework) open problems about the computational complexity of recovery in both cases.

Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component analysis (RTPCA) is a very effective tool to extract the low rank and sparse components in tensors. In this paper, a new method to analyze RTPCA is proposed based on the recently developed tensor-tensor product and tensor singular value decomposition (t-SVD). Specifically, it aims to solve a convex optimization problem whose objective function is a weighted combination of the tensor nuclear norm and the l1-norm. In most of literature of RTPCA, the exact recovery is built on the tensor incoherence conditions and the assumption of a uniform model on the sparse support. Unlike this conventional way, in this paper, without any assumption of randomness, the exact recovery can be achieved in a completely deterministic fashion by characterizing the tensor rank-sparsity incoherence, which is an uncertainty principle between the low-rank tensor spaces and the pattern of sparse tensor.

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of problems, e.g., nonnegativity or sparsity-constrained factorization, we take a {\it top-down} approach: we start with general optimization theory (e.g., inexact and accelerated block coordinate descent, stochastic optimization, and Gauss-Newton methods) that covers a wide range of factorization problems with diverse constraints and regularization terms of engineering interest. Then, we go `under the hood' to showcase specific algorithm design under these introduced principles. We pay a particular attention to recent algorithmic developments in structured tensor and matrix factorization (e.g., random sketching and adaptive step size based stochastic optimization and structure-exploiting second-order algorithms), which are the state of the art---yet much less touched upon in the literature compared to {\it block coordinate descent} (BCD)-based methods. We expect that the article to have an educational values in the field of structured factorization and hope to stimulate more research in this important and exciting direction.

In this paper, we develop novel perturbation bounds for the high-order orthogonal iteration (HOOI) [DLDMV00b]. Under mild regularity conditions, we establish blockwise tensor perturbation bounds for HOOI with guarantees for both tensor reconstruction in Hilbert-Schmidt norm $\|\widehat{\bcT} - \bcT \|_{\tHS}$ and mode-$k$ singular subspace estimation in Schatten-$q$ norm $\| \sin \Theta (\widehat{\U}_k, \U_k) \|_q$ for any $q \geq 1$. We show the upper bounds of mode-$k$ singular subspace estimation are unilateral and converge linearly to a quantity characterized by blockwise errors of the perturbation and signal strength. For the tensor reconstruction error bound, we express the bound through a simple quantity $\xi$, which depends only on perturbation and the multilinear rank of the underlying signal. Rate matching deterministic lower bound for tensor reconstruction, which demonstrates the optimality of HOOI, is also provided. Furthermore, we prove that one-step HOOI (i.e., HOOI with only a single iteration) is also optimal in terms of tensor reconstruction and can be used to lower the computational cost. The perturbation results are also extended to the case that only partial modes of $\bcT$ have low-rank structure. We support our theoretical results by extensive numerical studies. Finally, we apply the novel perturbation bounds of HOOI on two applications, tensor denoising and tensor co-clustering, from machine learning and statistics, which demonstrates the superiority of the new perturbation results.

We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging three-dimensional aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional airfoil shape parameterization on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction.

Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law coming to an end and ever increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers like the D-Wave 2000Q can approximately solve NP-hard optimization problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve a problem on adiabatic quantum computers, it must be formulated as a QUBO problem, which is a challenging task in itself. In this paper, we formulate the training problems of three machine learning models---linear regression, support vector machine (SVM) and equal-sized k-means clustering---as QUBO problems so that they can be trained on adiabatic quantum computers efficiently. We also analyze the time and space complexities of our formulations and compare them to the state-of-the-art classical algorithms for training these machine learning models. We show that the time and space complexities of our formulations are better (in the case of SVM and equal-sized k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

Network attacks have been very prevalent as their rate is growing tremendously. Both organization and individuals are now concerned about their confidentiality, integrity and availability of their critical information which are often impacted by network attacks. To that end, several previous machine learning-based intrusion detection methods have been developed to secure network infrastructure from such attacks. In this paper, an effective anomaly detection framework is proposed utilizing Bayesian Optimization technique to tune the parameters of Support Vector Machine with Gaussian Kernel (SVM-RBF), Random Forest (RF), and k-Nearest Neighbor (k-NN) algorithms. The performance of the considered algorithms is evaluated using the ISCX 2012 dataset. Experimental results show the effectiveness of the proposed framework in term of accuracy rate, precision, low-false alarm rate, and recall.