Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture Model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, called PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.

Two major challenges in distributed learning and estimation are 1) preserving the privacy of the local samples; and 2) communicating them efficiently to a central server, while achieving high accuracy for the end-to-end task. While there has been significant interest in addressing each of these challenges separately in the recent literature, treatments that simultaneously address both challenges are still largely missing. In this paper, we develop novel encoding and decoding mechanisms that simultaneously achieve optimal privacy and communication efficiency in various canonical settings. In particular, we consider the problems of mean estimation and frequency estimation under $\varepsilon$-local differential privacy and $b$-bit communication constraints. For mean estimation, we propose a scheme based on Kashin's representation and random sampling, with order-optimal estimation error under both constraints. For frequency estimation, we present a mechanism that leverages the recursive structure of Walsh-Hadamard matrices and achieves order-optimal estimation error for all privacy levels and communication budgets. As a by-product, we also construct a distribution estimation mechanism that is rate-optimal for all privacy regimes and communication constraints, extending recent work that is limited to $b=1$ and $\varepsilon=O(1)$. Our results demonstrate that intelligent encoding under joint privacy and communication constraints can yield a performance that matches the optimal accuracy achievable under either constraint alone.

Most of the two-dimensional (2D) hydraulic/hydrodynamic models are still computationally too demanding for real-time applications. In this paper, an innovative modelling approach based on a deep convolutional neural network (CNN) method is presented for rapid prediction of fluvial flood inundation. The CNN model is trained using outputs from a 2D hydraulic model (i.e. LISFLOOD-FP) to predict water depths. The pre-trained model is then applied to simulate the January 2005 and December 2015 floods in Carlisle, UK. The CNN predictions are compared favourably with the outputs produced by LISFLOOD-FP. The performance of the CNN model is further confirmed by benchmarking against a support vector regression (SVR) method. The results show that the CNN model outperforms SVR by a large margin. The CNN model is highly accurate in capturing flooded cells as indicated by several quantitative assessment matrices. The estimated error for reproducing maximum flood depth is 0 ~ 0.2 meters for the 2005 event and 0 ~ 0.5 meters for the 2015 event at over 99% of the cells covering the computational domain. The proposed CNN method offers great potential for real-time flood modelling/forecasting considering its simplicity, superior performance and computational efficiency.

Adversarial machine learning has attracted a great amount of attention in recent years. In a poisoning attack, the adversary can inject a small number of specially crafted samples into the training data which make the decision boundary severely deviate and cause unexpected misclassification. Due to the great importance and popular use of support vector machines (SVM), we consider defending SVM against poisoning attacks in this paper. We study two commonly used strategies for defending: designing robust SVM algorithms and data sanitization. Though several robust SVM algorithms have been proposed before, most of them either are in lack of adversarial-resilience, or rely on strong assumptions about the data distribution or the attacker's behavior. Moreover, the research on their complexities is still quite limited. We are the first, to the best of our knowledge, to prove that even the simplest hard-margin one-class SVM with outliers problem is NP-complete, and has no fully PTAS unless P$=$NP (that means it is hard to achieve an even approximate algorithm). For the data sanitization defense, we link it to the intrinsic dimensionality of data; in particular, we provide a sampling theorem in doubling metrics for explaining the effectiveness of DBSCAN (as a density-based outlier removal method) for defending against poisoning attacks. In our empirical experiments, we compare several defenses including the DBSCAN and robust SVM methods, and investigate the influences from the intrinsic dimensionality and data density to their performances.

Clustering Algorithms are essential aspects of Data Science and every data scientist must be aware of its concepts. Before discussing the top 5 clustering algorithms, we shall briefly see what clustering is and how it helps in Data Science. Clustering is a Machine Learning technique involving the grouping of data points. It is an unsupervised learning method and a famous technique for statistical data analysis. For a given set of data points, you can use clustering algorithms to classify these into specific groups.

An exciting, quite new branch of econometrics studies how machine learning techniques can be adapted to consistently estimate causal effects. For example, the widely cited article by Belloni, Chernozhukov and Hansen (2014) introduces a post double selection method where one first runs two lasso regressions to select suitable control variables for a final OLS regression. When I first heard about the method, it had the alluring promise to provide an objective way to select control variables that may reduce the scope of p-hacking. But assumptions may be violated and there may be plausible settings where the method fails. Unfortunately, I lack the deep econometric background to have a good intuitive assessment of the assumptions. But luckily even without a deep grasp of asymptotic theory, one can always combine some intuition with Monte-Carlo simulation to assess an econometric method.

Clustering is part of an unsupervised algorithm in machine learning. Unlike supervised algorithms like linear regression, logistic regression, etc, clustering works with unlabeled data or data without target variables. The task of clustering is to group similar data points. Clustering comes under the data mining topic and there is a lot of research going on in this field and there exist many clustering algorithms. The following are the main types of clustering algorithms.

Support Vector Machine (SVM) is an approach for classification which uses the concept of separating hyperplane. It was developed in the 1990s. It is a generalization of an intuitive and simple classifier called maximal margin classifier. In order to study Support Vector Machine (SVM), we first need to understand what is maximal margin classifier and support vector classifier. In maximal margin classifier, we use a hyperplane to separate the classes.

Sentiment analysis is a technique that detects the underlying sentiment in a piece of text. It is the process of classifying text as either positive, negative, or neutral. Machine learning techniques are used to evaluate a piece of text and determine the sentiment behind it. Sentiment analysis is essential for businesses to gauge customer response. Picture this: Your company has just released a new product that is being advertised on a number of different channels.

Strategic recommendations (SR) refer to the problem where an intelligent agent observes the sequential behaviors and activities of users and decides when and how to interact with them to optimize some long-term objectives, both for the user and the business. These systems are in their infancy in the industry and in need of practical solutions to some fundamental research challenges. At Adobe research, we have been implementing such systems for various use-cases, including points of interest recommendations, tutorial recommendations, next step guidance in multi-media editing software, and ad recommendation for optimizing lifetime value. There are many research challenges when building these systems, such as modeling the sequential behavior of users, deciding when to intervene and offer recommendations without annoying the user, evaluating policies offline with high confidence, safe deployment, non-stationarity, building systems from passive data that do not contain past recommendations, resource constraint optimization in multi-user systems, scaling to large and dynamic actions spaces, and handling and incorporating human cognitive biases. In this paper we cover various use-cases and research challenges we solved to make these systems practical.