RAPHS are generic mathematical structures consisting of sets of vertices and edges, which are used for modeling pairwise relations (edges) between a number of objects (vertices). In practice, this representation is often extended to weighted graphs, for which a set of scalar values (weights) are assigned to edges and potentially to vertices. Thus, weighted graphs offer general and flexible representations for modeling affinity relations between the objects of interest. Many practical problems can be represented using weighted graphs. For example, a broad class of combinatorial problems such as weighted matching, shortest-path and network-flow [2] are defined using weighted graphs. In signal/data-oriented problems, weighted graphs provide concise (sparse) representations for robust modeling of signals/data [3]. Such graphbased models are also useful for analyzing and visualizing the relations between their samples/features. Moreover, weighted graphs naturally emerge in networked data applications, such as learning, signal processing and analysis on computer, social, sensor, energy, transportation and biological networks [4], where the signals/data are inherently related to a graph associated with the underlying network.

A core challenge in the analysis of experimental data is that the impact of some intervention is often not entirely captured by a single, well-defined outcome. Instead there may be a large number of outcome variables that are potentially affected and of interest. In this paper, we propose a data-driven approach rooted in machine learning to the problem of testing effects on such groups of outcome variables. It is based on two simple observations. First, the 'false-positive' problem that a group of outcomes is similar to the concern of 'over-fitting,' which has been the focus of a large literature in statistics and computer science. We can thus leverage sample-splitting methods from the machine-learning playbook that are designed to control over-fitting to ensure that statistical models express generalizable insights about treatment effects. The second simple observation is that the question whether treatment affects a group of variables is equivalent to the question whether treatment is predictable from these variables better than some trivial benchmark (provided treatment is assigned randomly). This formulation allows us to leverage data-driven predictors from the machine-learning literature to flexibly mine for effects, rather than rely on more rigid approaches like multiple-testing corrections and pre-analysis plans. We formulate a specific methodology and present three kinds of results: first, our test is exactly sized for the null hypothesis of no effect; second, a specific version is asymptotically equivalent to a benchmark joint Wald test in a linear regression; and third, this methodology can guide inference on where an intervention has effects. Finally, we argue that our approach can naturally deal with typical features of real-world experiments, and be adapted to baseline balance checks.

We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method operates at a particular point in covariate space by considering a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dimensionality, we use an adaptive weighting function derived from a forest designed to express heterogeneity in the specified quantity of interest. We propose a flexible, computationally efficient algorithm for growing generalized random forests, develop a large sample theory for our method showing that our estimates are consistent and asymptotically Gaussian, and provide an estimator for their asymptotic variance that enables valid confidence intervals. We use our approach to develop new methods for three statistical tasks: non-parametric quantile regression, conditional average partial effect estimation, and heterogeneous treatment effect estimation via instrumental variables. A software implementation, grf for R and C++, is available from CRAN.

Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally important in precision medicine, but genomic information on which the predictions are based is also particularly sensitive, as it directly identifies the patients and hence cannot easily be anonymised. Differential privacy has emerged as a potentially promising solution: privacy is considered sufficient if presence of individual patients cannot be distinguished. However, differentially private learning with current methods does not improve predictions with feasible data sizes and dimensionalities. Here we show that useful predictors can be learned under powerful differential privacy guarantees, and even from moderately-sized data sets, by demonstrating significant improvements with a new robust private regression method in the accuracy of private drug sensitivity prediction. The method combines two key properties not present even in recent proposals, which can be generalised to other predictors: we prove it is asymptotically consistently and efficiently private, and demonstrate that it performs well on finite data. Good finite data performance is achieved by limiting the sharing of private information by decreasing the dimensionality and by projecting outliers to fit tighter bounds, therefore needing to add less noise for equal privacy. As already the simple-to-implement method shows promise on the challenging genomic data, we anticipate rapid progress towards practical applications in many fields, such as mobile sensing and social media, in addition to the badly needed precision medicine solutions.

When it comes to effectiveness of machine learning, more data almost always yields better results--and the healthcare sector is sitting on a data goldmine. McKinsey estimates that big data and machine learning in pharma and medicine could generate a value of up to $100B annually, based on better decision-making, optimized innovation, improved efficiency of research/clinical trials, and new tool creation for physicians, consumers, insurers, and regulators. Where does all this data come from? If we could look at labeled data streams, we might see research and development (R&D); physicians and clinics; patients; caregivers; etc. The array of (at present) disparate origins is part of the issue in synchronizing this information and using it to improve healthcare infrastructure and treatments.

In the first and second parts of this series, I introduced the Outbrain Click Prediction machine learning competition and my initial tasks to tackle the challenge. I presented the main techniques used for exploratory data analysis, feature engineering, cross-validation strategy and modeling of baseline predictors using basic statistics and machine learning. In this last post of the series, I describe how I used more powerful machine learning algorithms for the click prediction problem as well as the ensembling techniques that took me up to the 19th position on the leaderboard (top 2%). One of the popular approaches for CTR Prediction is Logistic Regression with a Follow-the-Regularized-Leader (FTRL) optimizer, which have been used in production by Google to predict billions of events per day, using a correspondingly large feature space. It is a linear model with a lazy representation of the coefficients (weights) and, in conjunction with L1 regularization, it leads to very sparse coefficient vectors. This sparsity property shrinks memory usage, making it scalable for feature vectors with billions of dimensions, because each instance will typically have only a few hundreds of nonzero values.

This book is a discussion about machine learning. It is the best book for those with little or no knowledge about machine learning. The book begins by helping you understand what machine learning is. You will also learn the areas in which machine learning is applicable. In machine learning, training is very essential, as it is what helps the machine learning algorithms to learn and show an improvement next time from their experience.

In the first part in a series on Tidy Time Series Analysis, we'll use tidyquant to investigate CRAN downloads. Most people think of tidyquant as purely a financial package and rightfully so. However, because of its integration with xts, zoo and TTR, it's naturally suited for "tidy" time series analysis. In this post, we'll discuss the the "period apply" functions from the xts package, which make it easy to apply functions to time intervals in a "tidy" way using tq_transmute()! We'll primarily be using two libraries today.

Feature selection is an important problem in statistical machine learning, and is a common method for dimensionality reduction that encourages model interpretability. With large data sets becoming ever more prevalent, feature selection has seen widespread usage across a variety of real-world tasks in recent years, including text classification, gene selection from microarray data, and face recognition [3, 13, 17]. In this work, we consider the supervised variant of feature selection, which entails finding a subset of the input features that explains the output well. This practice can reduce the computational expense of downstream learning by removing features that are redundant or noisy, while simultaneously providing insight into the data through the features that remain. Feature selection algorithms can generally be divided into three main categories: filter methods, wrapper methods, and embedded methods [13].

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns $\alpha$-approximate solutions for distributions over objectives, we compute a distribution over solutions that is $\alpha$-approximate in the worst case. We show that de-randomizing this solution is NP-hard in general, but can be done for a broad class of statistical learning tasks. We apply our results to robust neural network training and submodular optimization. We evaluate our approach experimentally on corrupted character classification, and robust influence maximization in networks.