Stochastic version of alternating direction method of multiplier (ADMM) and its variants (linearized ADMM, gradient-based ADMM) plays a key role for modern large scale machine learning problems. One example is the regularized empirical risk minimization problem. In this work, we put different variants of stochastic ADMM into a unified form, which includes standard, linearized and gradient-based ADMM with relaxation, and study their dynamics via a continuous-time model approach. We adapt the mathematical framework of stochastic modified equation (SME), and show that the dynamics of stochastic ADMM is approximated by a class of stochastic differential equations with small noise parameters in the sense of weak approximation. The continuous-time analysis would uncover important analytical insights into the behaviors of the discrete-time algorithm, which are non-trivial to gain otherwise. For example, we could characterize the fluctuation of the solution paths precisely, and decide optimal stopping time to minimize the variance of solution paths.

Adversarial Machine Learning (AML) is emerging as a major field aimed at the protection of automated ML systems against security threats. The majority of work in this area has built upon a game-theoretic framework by modelling a conflict between an attacker and a defender. After reviewing game-theoretic approaches to AML, we discuss the benefits that a Bayesian Adversarial Risk Analysis perspective brings when defending ML based systems. A research agenda is included.

SGD performs frequent updates with a high variance, causing the objective function to fluctuate heavily. SGD's fluctuation enables it to jump from a local minima to a potentially better local minima, but complicates convergence to an exact minimum. Momentum is a parameter of SGD that can be added to assist SGD in ravines -- areas where the surface curves more steeply in one dimension than in another, common around optima. Momentum helps accelerate SGD in the correct direction, therefore dampening the redundant oscillations as seen in image 2. Nesterov momentum is an improvement over standard momentum -- a ball that blindly follows the slope is unsatisfactory. Ideally, the ball would know where it is going so it can slow down before the hill slopes up again.

In this 2-hour long project-based course, you will learn how to implement Logistic Regression using Python and Numpy. Logistic Regression is an important fundamental concept if you want break into Machine Learning and Deep Learning. Even though popular machine learning frameworks have implementations of logistic regression available, it's still a great idea to learn to implement it on your own to understand the mechanics of optimization algorithm, and the training and validation process. Since this is a practical, project-based course, you will need to have a theoretical understanding of logistic regression, and gradient descent. We will focus on the practical aspect of implementing logistic regression with gradient descent, but not on the theoretical aspect.

Multi-dimensional Time Series Analysis and OLAP methods are important, when working with Time Series Data. Often multi-dimensional Time Series Analysis as term is referred to is a complete set of methods in applying machine learning in forms of forecasts or searching for anomalies and patterns. In this article we focus on good old deterministic multi-dimensional Time Series Analysis foundations to prepare, investigate and aggregate the Time Series Data in a deterministic way. Knowing these multi-dimensional Time Series Analysis foundations is essential, because at least 80% of Data Science work is Big Data and Big Data Landscape preparation. Common multi-dimensional analysis operations get applied in Business Intelligence and Data Warehousing where they are often called Online AnaLytical Processing (OLAP) operations [1]. In this article, we discuss and describe what the most important multi-dimensional Time Series Analysis and OLAP methods are and show examples of how the different operations are applied on a Time Series Data sets. In the beginning, we talk about OLAP in Data Warehouse landscapes and Time Series Data processing in Big Data landscapes. Subsequently, we give some insights into why and to whom multi-dimensional time series analysis with OLAP matters within an enterprise.

Distributed training is useful to train complicated models to shorten the training time. As each of the workers only sees a small fraction of data, workers need to synchronize on the parameter updates. One of the central questions in distributed training is how to parsimoniously synchronize parameters while preserving model quality. To address this problem, we propose the \textbf{ShadowSync} framework, in which we isolate synchronization from training and run it in the background. In contrast to common strategies including synchronous stochastic gradient descent (SGD), asynchronous SGD, and model averaging on independently trained sub-models, where synchronization happens in the foreground, ShadowSync synchronization is neither part of the backward pass, nor happens every $k$ iterations. Our framework is generic to host various types of synchronization algorithms, and we propose 3 approaches under this theme. The superiority of ShadowSync is confirmed by experiments on training deep neural networks for click-through-rate prediction. Our methods all succeed in making the training throughput linearly scale with the number of trainers. Comparing to their foreground counterparts, our methods exhibit neutral to better model quality and better scalability when we keep the number of parameter servers the same. In our training system which expresses both replication and Hogwild parallelism, ShadowSync also accomplishes the highest example level parallelism number comparing to the prior arts.

We study the performance of decentralized stochastic gradient descent (DSGD) in a wireless network, where the nodes collaboratively optimize an objective function using their local datasets. Unlike the conventional setting, where the nodes communicate over error-free orthogonal communication links, we assume that transmissions are prone to additive noise and interference.We first consider a point-to-point (P2P) transmission strategy, termed the OAC-P2P scheme, in which the node pairs are scheduled in an orthogonal fashion to minimize interference. Since in the DSGD framework, each node requires a linear combination of the neighboring models at the consensus step, we then propose the OAC-MAC scheme, which utilizes the signal superposition property of the wireless medium to achieve over-the-air computation (OAC). For both schemes, we cast the scheduling problem as a graph coloring problem. We numerically evaluate the performance of these two schemes for the MNIST image classification task under various network conditions. We show that the OAC-MAC scheme attains better convergence performance with a fewer communication rounds.

A mobility map, which provides maximum achievable speed on a given terrain, is essential for path planning of autonomous ground vehicles in off-road settings. While physics-based simulations play a central role in creating next-generation, high-fidelity mobility maps, they are cumbersome and expensive. For instance, a typical simulation can take weeks to run on a supercomputer and each map requires thousands of such simulations. Recent work at the U.S. Army CCDC Ground Vehicle Systems Center has shown that trained machine learning classifiers can greatly improve the efficiency of this process. However, deciding which simulations to run in order to train the classifier efficiently is still an open problem. According to PAC learning theory, data that can be separated by a classifier is expected to require $\mathcal{O}(1/\epsilon)$ randomly selected points (simulations) to train the classifier with error less than $\epsilon$. In this paper, building on existing algorithms, we introduce an active learning paradigm that substantially reduces the number of simulations needed to train a machine learning classifier without sacrificing accuracy. Experimental results suggest that our sampling algorithm can train a neural network, with higher accuracy, using less than half the number of simulations when compared to random sampling.

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors.

One of the challenging aspects of applying machine learning is the need to identify the algorithms that will perform best for a given dataset. This process can be difficult, time consuming and often requires a great deal of domain knowledge. We present Sommelier, an expert system for recommending the machine learning algorithms that should be applied on a previously unseen dataset. Sommelier is based on word embedding representations of the domain knowledge extracted from a large corpus of academic publications. When presented with a new dataset and its problem description, Sommelier leverages a recommendation model trained on the word embedding representation to provide a ranked list of the most relevant algorithms to be used on the dataset. We demonstrate Sommelier's effectiveness by conducting an extensive evaluation on 121 publicly available datasets and 53 classification algorithms. The top algorithms recommended for each dataset by Sommelier were able to achieve on average 97.7% of the optimal accuracy of all surveyed algorithms.