This paper describes the autofeat Python library, which provides a scikit-learn style linear regression model with automatic feature engineering and selection capabilities. Complex non-linear machine learning models such as neural networks are in practice often difficult to train and even harder to explain to non-statisticians, who require transparent analysis results as a basis for important business decisions. While linear models are efficient and intuitive, they generally provide lower prediction accuracies. Our library provides a multi-step feature engineering and selection process, where first a large pool of non-linear features is generated, from which then a small and robust set of meaningful features is selected, which improve the prediction accuracy of a linear model while retaining its interpretability.

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.

Birg{\'e} and Massart proposed in 2001 the slope heuristics as a way to choose optimally from data an unknown multiplicative constant in front of a penalty. It is built upon the notion of minimal penalty, and it has been generalized since to some 'minimal-penalty algorithms'. This paper reviews the theoretical results obtained for such algorithms, with a self-contained proof in the simplest framework, precise proof ideas for further generalizations, and a few new results. Explicit connections are made with residual-variance estimators-with an original contribution on this topic, showing that for this task the slope heuristics performs almost as well as a residual-based estimator with the best model choice-and some classical algorithms such as L-curve or elbow heuristics, Mallows' C p , and Akaike's FPE. Practical issues are also addressed, including two new practical definitions of minimal-penalty algorithms that are compared on synthetic data to previously-proposed definitions. Finally, several conjectures and open problems are suggested as future research directions.

An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised representation learning have been demonstrated to give the state-of-the-art performance in downstream tasks such as vertex classification and edge prediction. These techniques rely on random walks performed on the graph in order to capture its structural properties. These structural properties are then encoded in the vector representation space. However, most contemporary representation learning methods only apply to static graphs while real-world graphs are often dynamic and change over time. Static representation learning methods are not able to update the vector representations when the graph changes; therefore, they must re-generate the vector representations on an updated static snapshot of the graph regardless of the extent of the change in the graph. In this work, we propose computationally efficient algorithms for vertex representation learning that extend random walk based methods to dynamic graphs. The computation complexity of our algorithms depends upon the extent and rate of changes (the number of edges changed per update) and on the density of the graph. We empirically evaluate our algorithms on real world datasets for downstream machine learning tasks of multi-class and multi-label vertex classification. The results show that our algorithms can achieve competitive results to the state-of-the-art methods while being computationally efficient.

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n} \sum_{i=1}^n f_i(w)$ has been proven to be at least $\Omega(\sqrt{n}/\epsilon)$ where $\epsilon$ denotes the attained accuracy $\mathbb{E}[ \|\nabla F(\tilde{w})\|^2] \leq \epsilon$ for the outputted approximation $\tilde{w}$ (Fang et al.,2018). This paper is the first to show that this lower bound is tight for the class of variance reduction methods which only assume the Lipschitz continuous gradient assumption. We prove this complexity result for a slightly modified version of the SARAH algorithm in (Nguyen et al.,2017a;b) - showing that SARAH is optimal and dominates all existing results. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance.

In an earlier post, I discussed a model agnostic feature selection technique called forward feature selection which basically extracted the most important features required for the optimal value of chosen KPI. It had one caveat though -- large time complexity. In order to circumvent that issue feature importance can directly be obtained from the model being trained. In this post, I will consider 2 classification and 1 regression algorithms to explain model-based feature importance in detail. An inherently binary classification algorithm, it tries to find the best hyperplane in k-dimensional space that separates the 2 classes, minimizing logistic loss.

Algorithms are the smart and powerful soldier of a complex machine learning model. In other words, machine learning algorithms are the core foundation when we play with data or when it's come to training the model. In this article, you and I are going on a tour called "7 major machine learning algorithms and their application " The purpose of this tour is to either brush up the mind or to gain an essential understanding of machine learning algorithm. We will find the major answer in this tour like for what purpose machine learning algorithms works, where to use them, when to use them and how to use them. Before getting deeper let's have a brief introduction. Machine learning algorithms are mainly classified into 3 broad categories i.e supervised learning, unsupervised learning, and reinforcement learning. In supervised learning machine learning algorithms, the machine is taught by example. Here the operator provides the machine learning algorithm with the dataset. This dataset includes desired inputs and outputs variables. By the use of these set of variables, we generate a function that map inputs to desired outputs.

Gradient-based optimization of absolute errors is tricky, since the gradient is "never" zero. In theory, adaptive methods should be able to damp oscillations so that it converges to the minimum. However, I found none of the'standard' methods were able to do this "out of the box". Learning rate decay could alleviate the problem, but needs manual tuning which I would rather avoid. Does anyone know of a method that can do this?

Abstract--As cellular networks become denser, a scalable and dynamic tuning of wireless base station parameters can only be achieved through automated optimization. Although the contextual banditframework arises as a natural candidate for such a task, its extension to a parallel setting is not straightforward: one needs to carefully adapt existing methods to fully leverage the multi-agent structure of this problem. We propose two approaches: one derived from a deterministic UCB-like method and the other relying on Thompson sampling. Thanks to its bayesian nature, the latter is intuited to better preserve the exploration-exploitation balance in the bandit batch. This is verified on toy experiments, where Thompson sampling shows robustness to the variability of the contexts. Finally, we apply both methods on a real base station network dataset and evidence that Thompson sampling outperforms both manual tuning and contextual UCB. I. INTRODUCTION The land area covered by a cellular wireless network, such as a mobile phone network, is divided into small areas called cells, each cell being covered by the antenna of a fixed base station (see Figure 1).

Positioning data offer a remarkable source of information to analyze crowds urban dynamics. However, discovering urban activity patterns from the emergent behavior of crowds involves complex system modeling. An alternative approach is to adopt computational techniques belonging to the emergent paradigm, which enables self-organization of data and allows adaptive analysis. Specifically, our approach is based on stigmergy. By using stigmergy each sample position is associated with a digital pheromone deposit, which progressively evaporates and aggregates with other deposits according to their spatiotemporal proximity. Based on this principle, we exploit positioning data to identify high density areas (hotspots) and characterize their activity over time. This characterization allows the comparison of dynamics occurring in different days, providing a similarity measure exploitable by clustering techniques. Thus, we cluster days according to their activity behavior, discovering unexpected urban activity patterns. As a case study, we analyze taxi traces in New York City during 2015.