Recent studies have revealed the vulnerability of deep neural networks - A small adversarial perturbation that is imperceptible to human can easily make a well-trained deep neural network mis-classify. This makes it unsafe to apply neural networks in security-critical applications. In this paper, we propose a new defensive algorithm called Random Self-Ensemble (RSE) by combining two important concepts: ${\bf randomness}$ and ${\bf ensemble}$. To protect a targeted model, RSE adds random noise layers to the neural network to prevent from state-of-the-art gradient-based attacks, and ensembles the prediction over random noises to stabilize the performance. We show that our algorithm is equivalent to ensemble an infinite number of noisy models $f_\epsilon$ without any additional memory overhead, and the proposed training procedure based on noisy stochastic gradient descent can ensure the ensemble model has good predictive capability. Our algorithm significantly outperforms previous defense techniques on real datasets. For instance, on CIFAR-10 with VGG network (which has $92\%$ accuracy without any attack), under the state-of-the-art C&W attack within a certain distortion tolerance, the accuracy of unprotected model drops to less than $10\%$, the best previous defense technique has $48\%$ accuracy, while our method still has $86\%$ prediction accuracy under the same level of attack. Finally, our method is simple and easy to integrate into any neural network.

Missing data is an expected issue when large amounts of data is collected, and several imputation techniques have been proposed to tackle this problem. Beneath classical approaches such as MICE, the application of Machine Learning techniques is tempting. Here, the recently proposed missForest imputation method has shown high imputation accuracy under the Missing (Completely) at Random scheme with various missing rates. In its core, it is based on a random forest for classification and regression, respectively. In this paper we study whether this approach can even be enhanced by other methods such as the stochastic gradient tree boosting method, the C5.0 algorithm or modified random forest procedures. In particular, other resampling strategies within the random forest protocol are suggested. In an extensive simulation study, we analyze their performances for continuous, categorical as well as mixed-type data. Therein, MissBooPF, a combination of the stochastic gradient tree boosting method together with the parametrically bootstrapped random forest method, appeared to be promising. Finally, an empirical analysis focusing on credit information and Facebook data is conducted.

In this paper, we propose a method for training neural networks when we have a large set of data with weak labels and a small amount of data with true labels. In our proposed model, we train two neural networks: a target network, the learner and a confidence network, the meta-learner. The target network is optimized to perform a given task and is trained using a large set of unlabeled data that are weakly annotated. We propose to control the magnitude of the gradient updates to the target network using the scores provided by the second confidence network, which is trained on a small amount of supervised data. Thus we avoid that the weight updates computed from noisy labels harm the quality of the target network model.

The problem descriptions are taken straightaway from the assignments. In this assignment a linear classifier will be implemented and it will be trained using stochastic gradient descent with numpy. To make things more intuitive, let's solve a 2D classification problem with synthetic data. As we can notice the data above isn't linearly separable. Hence we should add features(or use non-linear model). Note that decision line between two classes have form of circle, since that we can add quadratic features to make the problem linearly separable.

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the unique advantages of SVGD to the Riemannian world. To appropriately transfer to Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD, which are required by the intrinsically different characteristics of general Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show the advantages over SVGD of exploring distribution geometry and the advantages of particle-efficiency, iteration-effectiveness and approximation flexibility over other inference methods on Riemann manifolds.

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to approximate a target distribution. However, the samples are typically highly correlated due to the sequential generation process, an undesired property in SG-MCMC. In contrary, Stein variational gradient descent (SVGD) directly optimizes a set of particles, and it is able to approximate a target distribution with much fewer samples. In this paper, we propose a novel method to directly optimize particles (or samples) in SG-MCMC from scratch. Specifically, we propose efficient methods to solve the corresponding Fokker-Planck equation on the space of probability distributions, whose solution (i.e., a distribution) is approximated by particles. Through our framework, we are able to show connections of SG-MCMC to SVGD, as well as the seemly unrelated generative-adversarial-net framework. Under certain relaxations, particle optimization in SG-MCMC can be interpreted as an extension of standard SVGD with momentum.

Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant of AGD, and shows that it escapes saddle points and finds a second-order stationary point in $\tilde{O}(1/\epsilon^{7/4})$ iterations, faster than the $\tilde{O}(1/\epsilon^{2})$ iterations required by GD. To the best of our knowledge, this is the first Hessian-free algorithm to find a second-order stationary point faster than GD, and also the first single-loop algorithm with a faster rate than GD even in the setting of finding a first-order stationary point. Our analysis is based on two key ideas: (1) the use of a simple Hamiltonian function, inspired by a continuous-time perspective, which AGD monotonically decreases per step even for nonconvex functions, and (2) a novel framework called improve or localize, which is useful for tracking the long-term behavior of gradient-based optimization algorithms. We believe that these techniques may deepen our understanding of both acceleration algorithms and nonconvex optimization.

Despite their popularity, the practical performance of asynchronous stochastic gradient descent methods (ASGD) for solving large scale machine learning problems are not as good as theoretical results indicate. We adopt and analyze a synchronous K-step averaging stochastic gradient descent algorithm which we call K-AVG. We establish the convergence results of K-AVG for nonconvex objectives and explain why the K-step delay is necessary and leads to better performance than traditional parallel stochastic gradient descent which is a special case of K-AVG with $K=1$. We also show that K-AVG scales better than ASGD. Another advantage of K-AVG over ASGD is that it allows larger stepsizes. On a cluster of $128$ GPUs, K-AVG is faster than ASGD implementations and achieves better accuracies and faster convergence for \cifar dataset.

Motivation: How do we integratively analyze large-scale multi-platform genomic data that are high dimensional and sparse? Furthermore, how can we incorporate prior knowledge, such as the association between genes, in the analysis systematically? Method: To solve this problem, we propose a Scalable Network Constrained Tucker decomposition method we call SNeCT. SNeCT adopts parallel stochastic gradient descent approach on the proposed parallelizable network constrained optimization function. SNeCT decomposition is applied to tensor constructed from large scale multi-platform multi-cohort cancer data, PanCan12, constrained on a network built from PathwayCommons database. Results: The decomposed factor matrices are applied to stratify cancers, to search for top-k similar patients, and to illustrate how the matrices can be used for personalized interpretation. In the stratification test, combined twelve-cohort data is clustered to form thirteen subclasses. The thirteen subclasses have a high correlation to tissue of origin in addition to other interesting observations, such as clear separation of OV cancers to two groups, and high clinical correlation within subclusters formed in cohorts BRCA and UCEC. In the top-k search, a new patient's genomic profile is generated and searched against existing patients based on the factor matrices. The similarity of the top-k patient to the query is high for 23 clinical features, including estrogen/progesterone receptor statuses of BRCA patients with average precision value ranges from 0.72 to 0.86 and from 0.68 to 0.86, respectively. We also provide an illustration of how the factor matrices can be used for interpretable personalized analysis of each patient.

In recent years, significant progress has been made in solving challenging problems across various domains using deep reinforcement learning (RL). Reproducing existing work and accurately judging the improvements offered by novel methods is vital to sustaining this progress. Unfortunately, reproducing results for state-of-the-art deep RL methods is seldom straightforward. In particular, non-determinism in standard benchmark environments, combined with variance intrinsic to the methods, can make reported results tough to interpret. Without significance metrics and tighter standardization of experimental reporting, it is difficult to determine whether improvements over the prior state-of-the-art are meaningful. In this paper, we investigate challenges posed by reproducibility, proper experimental techniques, and reporting procedures. We illustrate the variability in reported metrics and results when comparing against common baselines and suggest guidelines to make future results in deep RL more reproducible. We aim to spur discussion about how to ensure continued progress in the field by minimizing wasted effort stemming from results that are non-reproducible and easily misinterpreted.