We present an efficient coreset construction algorithm for large-scale Support Vector Machine (SVM) training in Big Data and streaming applications. A coreset is a small, representative subset of the original data points such that a models trained on the coreset are provably competitive with those trained on the original data set. Since the size of the coreset is generally much smaller than the original set, our preprocess-then-train scheme has potential to lead to significant speedups when training SVM models. We prove lower and upper bounds on the size of the coreset required to obtain small data summaries for the SVM problem. As a corollary, we show that our algorithm can be used to extend the applicability of any off-the-shelf SVM solver to streaming, distributed, and dynamic data settings. We evaluate the performance of our algorithm on real-world and synthetic data sets. Our experimental results reaffirm the favorable theoretical properties of our algorithm and demonstrate its practical effectiveness in accelerating SVM training.

Comparing the underlying distributions of two given datasets has been an important task in machine learning community and has a wide range of applications. For example, change detection algorithms Kawahara and Sugiyama ((2012)) compare datasets collected at different time points and report how the underlying distribution has shifted over time; Transfer learning algorithms Quionero-Candela et al. ((2009)) utilize the estimated differences between two datasets to efficiently share information between different tasks. Generative Adversarial Net (GAN) Goodfellow et al. ((2014)) learns an implicit generative model whose output minimizes the differences between an artificial dataset and a real dataset. Various computational methods have been proposed for comparing underlying distributions given two sets of observations. For example, Maximum Mean Discrepancy (MMD) Gretton et al. ((2012)) computes the distance between the kernel mean embeddings of two datasets in Reproducing Kernel Hilbert Space (RKHS).

Cloud Infrastructure as a Service (IaaS) is vulnerable to malware due to its exposure to external adversaries, making it a lucrative attack vector for malicious actors. A datacenter infected with malware can cause data loss and/or major disruptions to service for its users. This paper analyzes and compares various Convolutional Neural Networks (CNNs) for online detection of malware in cloud IaaS. The detection is performed based on behavioural data using process level performance metrics including cpu usage, memory usage, disk usage etc. We have used the state of the art DenseNets and ResNets in effectively detecting malware in online cloud system. CNN are designed to extract features from data gathered from a live malware running on a real cloud environment. Experiments are performed on OpenStack (a cloud IaaS software) testbed designed to replicate a typical 3-tier web architecture. Comparative analysis is performed for different metrics for different CNN models used in this research.

Important insights towards the explainability of neural networks and their properties reside in the formation of their decision boundaries. In this work, we borrow tools from the field of adversarial robustness and propose a new framework that permits to relate the features of the dataset with the distance of data samples to the decision boundary along specific directions. We demonstrate that the inductive bias of deep learning has the tendency to generate classification functions that are invariant along non-discriminative directions of the dataset. More surprisingly, we further show that training on small perturbations of the data samples are sufficient to completely change the decision boundary. This is actually the characteristic exploited by the so-called adversarial training to produce robust classifiers. Our general framework can be used to reveal the effect of specific dataset features on the macroscopic properties of deep models and to develop a better understanding of the successes and limitations of deep learning.

In supervised learning using kernel methods, we encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space(RKHS). Often times large-scale finite-sum problems can be solved using efficient variants of Newton's method where the Hessian is approximated via sub-samples. In RKHS, however, the dependence of the penalty function to kernel makes standard sub-sampling approaches inapplicable, since the gram matrix is not readily available in a low-rank form. In this paper, we observe that for this class of problems, one can naturally use kernel approximation to speed up the Newton's method. Focusing on randomized features for kernel approximation, we provide a novel second-order algorithm that enjoys local superlinear convergence and global convergence in the high probability sense. The key to our analysis is showing that the approximated Hessian via random features preserves the spectrum of the original Hessian. We provide numerical experiments verifying the efficiency of our approach, compared to variants of sub-sampling methods.

Recent years have seen much research on fairness in machine learning. Here, mean difference (MD) or demographic parity is one of the most popular measures of fairness. However, MD quantifies not only discrimination but also explanatory bias which is the difference of outcomes justified by explanatory features. In this paper, we devise novel models, called FairCEEs, which remove discrimination while keeping explanatory bias. The models are based on estimators of causal effect utilizing propensity score analysis. We prove that FairCEEs with the squared loss theoretically outperform a naive MD constraint model. We provide an efficient algorithm for solving FairCEEs in regression and binary classification tasks. In our experiment on synthetic and real-world data in these two tasks, FairCEEs outperformed an existing model that considers explanatory bias in specific cases.

In this paper, we introduce two novel metric learning algorithms, χ2-LMNN and GB-LMNN, which are explicitly designed to be non-linear and easy-to-use. The two approaches achieve this goal in fundamentally different ways: χ2-LMNN inherits the computational benefits of a linear mapping from linear metric learning, but uses a non-linear χ2-distance to explicitly capture similarities within histogram data sets; GB-LMNN applies gradient-boosting to learn non-linear mappings directly in function space and takes advantage of this approach's robustness, speed, parallelizability and insensitivity towards the single additional hyper-parameter. On various benchmark data sets, we demonstrate these methods not only match the current state-of-the-art in terms of kNN classification error, but in the case of χ2-LMNN, obtain best results in 19 out of 20 learning settings. Papers published at the Neural Information Processing Systems Conference.

We consider regularized risk minimization in a large dictionary of Reproducing kernel Hilbert Spaces (RKHSs) over which the target function has a sparse representation. This setting, commonly referred to as Sparse Multiple Kernel Learning (MKL), may be viewed as the non-parametric extension of group sparsity in linear models. While the two dominant algorithmic strands of sparse learning, namely convex relaxations using l1 norm (e.g., Lasso) and greedy methods (e.g., OMP), have both been rigorously extended for group sparsity, the sparse MKL literature has so farmainly adopted the former withmild empirical success. In this paper, we close this gap by proposing a Group-OMP based framework for sparse multiple kernel learning. Unlike l1-MKL, our approach decouples the sparsity regularizer (via a direct l0 constraint) from the smoothness regularizer (via RKHS norms) which leads to better empirical performance as well as a simpler optimization procedure that only requires a black-box single-kernel solver.

Markov Random Fields (MRFs) have proven very powerful both as density estimators and feature extractors for classification. However, their use is often limited by an inability to estimate the partition function $Z$. In this paper, we exploit the gradient descent training procedure of restricted Boltzmann machines (a type of MRF) to {\bf track} the log partition function during learning. Our method relies on two distinct sources of information: (1) estimating the change $\Delta Z$ incurred by each gradient update, (2) estimating the difference in $Z$ over a small set of tempered distributions using bridge sampling. The two sources of information are then combined using an inference procedure similar to Kalman filtering.

The development of statistical models for continuous-time longitudinal network data is of increasing interest in machine learning and social science. Leveraging ideas from survival and event history analysis, we introduce a continuous-time regression modeling framework for network event data that can incorporate both time-dependent network statistics and time-varying regression coefficients. We also develop an efficient inference scheme that allows our approach to scale to large networks. On synthetic and real-world data, empirical results demonstrate that the proposed inference approach can accurately estimate the coefficients of the regression model, which is useful for interpreting the evolution of the network; furthermore, the learned model has systematically better predictive performance compared to standard baseline methods. Papers published at the Neural Information Processing Systems Conference.