We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized M-estimators in the high-dimensional setting, including the popular Least Trimmed Squares estimator, as well as analogous estimators for generalized linear models and graphical models, using possibly non-convex loss functions. We present a general analysis of their statistical convergence rates and consistency, and then take a closer look at the trimmed versions of the Lasso and Graphical Lasso estimators as special cases. On the optimization side, we show how to extend algorithms for M-estimators to fit trimmed variants and provide guarantees on their numerical convergence. The generality and competitive performance of high-dimensional trimmed estimators are illustrated numerically on both simulated and real-world genomics data.

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference in the absence of a likelihood function. The popular synthetic likelihood approach infers the parameters by modelling summary statistics of the data by a Gaussian probability distribution. In another popular approach called approximate Bayesian computation, the inference is performed by identifying parameter values for which the summary statistics of the simulated data are close to those of the observed data. Synthetic likelihood is easier to use as no measure of "closeness" is required but the Gaussianity assumption is often limiting. Moreover, both approaches require judiciously chosen summary statistics. We here present an alternative inference approach that is as easy to use as synthetic likelihood but not as restricted in its assumptions, and that, in a natural way, enables automatic selection of relevant summary statistic from a large set of candidates. The basic idea is to frame the problem of estimating the posterior as a problem of estimating the ratio between the data generating distribution and the marginal distribution. This problem can be solved by logistic regression, and including regularising penalty terms enables automatic selection of the summary statistics relevant to the inference task. We illustrate the general theory on toy problems and use it to perform inference for stochastic nonlinear dynamical systems.

Abstract--Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classifier requires a kernel function, and the Gaussian kernel is a common choice for the kernel function. The Gaussian kernel has a bandwidth parameter, whose value is important for good results. A small bandwidth leads to overfitting, and the resulting SVDD classifier overestimates the number of anomalies. A large bandwidth leads to underfitting, and the classifier fails to detect many anomalies. In this paper we present a new automatic, unsupervised method for selecting the Gaussian kernel bandwidth. The selected value can be computed quickly, and it is competitive with existing bandwidth selection methods. Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and anomaly detection.

Active Search has become an increasingly useful tool in information retrieval problems where the goal is to discover as many target elements as possible using only limited label queries. With the advent of big data, there is a growing emphasis on the scalability of such techniques to handle very large and very complex datasets. In this paper, we consider the problem of Active Search where we are given a similarity function between data points. We look at an algorithm introduced by Wang et al. [2013] for Active Search over graphs and propose crucial modifications which allow it to scale significantly. Their approach selects points by minimizing an energy function over the graph induced by the similarity function on the data. Our modifications require the similarity function to be a dot-product between feature vectors of data points, equivalent to having a linear kernel for the adjacency matrix. With this, we are able to scale tremendously: for $n$ data points, the original algorithm runs in $O(n^2)$ time per iteration while ours runs in only $O(nr + r^2)$ given $r$-dimensional features. We also describe a simple alternate approach using a weighted-neighbor predictor which also scales well. In our experiments, we show that our method is competitive with existing semi-supervised approaches. We also briefly discuss conditions under which our algorithm performs well.

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demonstrated to efficiently solve eigenvalue problems for graph Laplacians that appear in spectral clustering. For static graph partitioning, 10-20 iterations of LOBPCG without preconditioning result in ~10x error reduction, enough to achieve 100% correctness for all Challenge datasets with known truth partitions, e.g., for graphs with 5K/.1M (50K/1M) Vertices/Edges in 2 (7) seconds, compared to over 5,000 (30,000) seconds needed by the baseline Python code. Our Python code 100% correctly determines 98 (160) clusters from the Challenge static graphs with 0.5M (2M) vertices in 270 (1,700) seconds using 10GB (50GB) of memory. Our single-precision MATLAB code calculates the same clusters at half time and memory. For streaming graph partitioning, LOBPCG is initiated with approximate eigenvectors of the graph Laplacian already computed for the previous graph, in many cases reducing 2-3 times the number of required LOBPCG iterations, compared to the static case. Our spectral clustering is generic, i.e. assuming nothing specific of the block model or streaming, used to generate the graphs for the Challenge, in contrast to the base code. Nevertheless, in 10-stage streaming comparison with the base code for the 5K graph, the quality of our clusters is similar or better starting at stage 4 (7) for emerging edging (snowballing) streaming, while the computations are over 100-1000 faster.

This course not only covers machine learning techniques, it also covers in depth the rationale of investing strategy development. This course is the first of the Machine Learning for Finance and Algorithmic Trading & Investing Series. If you are looking for a course on applying machine learning to investing, the Machine Learning for Finance and Algorithmic Trading & Investing Series is for you. With over 30 machine learning techniques test cases, which included popular techniques such as Lasso regression, Ridge regression, SVM, XGBoost, random forest, Hidden Markov Model, common clustering techniques and many more, to get you started with applying Machine Learning to investing quickly.

Today, businesses need to be able to predict demand and trends to stay in line with any sudden market changes and economy swings. This is exactly where forecasting tools, powered by Data Science, come into play, enabling organizations to successfully deal with strategic and capacity planning. Smart forecasting techniques can be used to reduce any possible risks and assist in making well-informed decisions. One of our customers, an enterprise from the Middle East, needed to predict their market demand for the upcoming twelve weeks. They required a market forecast to help them set their short-term objectives, such as production strategy, as well as assist in capacity planning and price control.

Boosted decision trees are responsible for more than half of the winning solutions in machine learning challenges hosted at Kaggle, according to KDnuggets. In addition to superior performance, these algorithms have practical appeal as they require minimal tuning. In this post, we evaluate two popular tree boosting software packages: XGBoost and LightGBM, including their GPU implementations. All our code is open-source and can be found in this repo. We will explain the algorithms behind these libraries and evaluate them across different datasets.

It explores main concepts from basic to expert level which can help you achieve better grades, develop your academic career, apply your knowledge at work or make business forecasting related decisions. Learning regression machine learning is indispensable for data mining applications in areas such as consumer analytics, finance, banking, health care, science, e-commerce and social media. It is also essential for academic careers in data mining, applied statistical learning or artificial intelligence. And it is necessary for any business forecasting related decision. But as learning curve can become steep as complexity grows, this course helps by leading you through step by step real world practical examples for greater effectiveness.

There are many problems associated with analyzing data sets that contain missing data. However, there are various techniques to'fill in,' or impute, missing data values with reasonable estimates based on the characteristics of the data itself and on the patterns of'missingness.' Generally, techniques appropriate for imputing missing values in multivariate normal data and not as useful when applied to non-multivariate-normal data. This Visualization and Imputation of Missing Data course focuses on understanding patterns of'missingness' in a data sample, especially non-multivariate-normal data sets, and teaches one to use various appropriate imputation techniques to "fill in" the missing data. Using the VIM and VIMGUI packages in R, the course also teaches how to create dozens of different and unique visualizations to better understand existing patterns of both the missing and imputed data in your samples.