Forward stagewise regression and the monotone lasso

We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the least angle regression algorithm, with a small modification, solves the lasso regression problem. Here we give an analogous result for incremental forward stagewise regression, showing that it solves a version of the lasso problem that enforces monotonicity. One consequence of this is as follows: while lasso makes optimal progress in terms of reducing the residual sum-of-squares per unit increase in $L_1$-norm of the coefficient $\beta$, forward stage-wise is optimal per unit $L_1$ arc-length traveled along the coefficient path. We also study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the lasso and forward stagewise procedures in a simulation study involving a large number of correlated predictors.Comment: Published at http://dx.doi.org/10.1214/07-EJS004 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

A NOVEL SPLIT SELECTION OF A LOGISTIC REGRESSION TREE FOR THE CLASSIFICATION OF DATA WITH HETEROGENEOUS SUBGROUPS

A logistic regression tree (LRT) is a hybrid machine learning method that combines a decision tree model and logistic regression models. An LRT recursively partitions the input data space through splitting and learns multiple logistic regression models optimized for each subpopulation. The split selection is a critical procedure for improving the predictive performance of the LRT. In this paper, we present a novel separability-based split selection method for the construction of an LRT. The separability measure, defined on the feature space of logistic regression models, evaluates the performance of potential child models without fitting, and the optimal split is selected based on the results. Heterogeneous subgroups that have different class-separating patterns can be identified in the split process when they exist in the data. In addition, we compare the performance of our proposed method with the benchmark algorithms through experiments on both synthetic and real-world datasets. The experimental results indicate the effectiveness and generality of our proposed method

Toward Interpretable Deep Reinforcement Learning with Linear Model U-Trees

Deep Reinforcement Learning (DRL) has achieved impressive success in many applications. A key component of many DRL models is a neural network representing a Q function, to estimate the expected cumulative reward following a state-action pair. The Q function neural network contains a lot of implicit knowledge about the RL problems, but often remains unexamined and uninterpreted. To our knowledge, this work develops the first mimic learning framework for Q functions in DRL. We introduce Linear Model U-trees (LMUTs) to approximate neural network predictions. An LMUT is learned using a novel on-line algorithm that is well-suited for an active play setting, where the mimic learner observes an ongoing interaction between the neural net and the environment. Empirical evaluation shows that an LMUT mimics a Q function substantially better than five baseline methods. The transparent tree structure of an LMUT facilitates understanding the network's learned knowledge by analyzing feature influence, extracting rules, and highlighting the super-pixels in image inputs.Comment: This paper is accepted by ECML-PKDD 201

Implicit personalization in driving assistance: State-of-the-art and open issues

In recent decades, driving assistance systems have been evolving towards personalization for adapting to different drivers. With the consideration of driving preferences and driver characteristics, these systems become more acceptable and trustworthy. This article presents a survey on recent advances in implicit personalized driving assistance. We classify the collection of work into three main categories: 1) personalized Safe Driving Systems (SDS), 2) personalized Driver Monitoring Systems (DMS), and 3) personalized In-vehicle Information Systems (IVIS). For each category, we provide a comprehensive review of current applications and related techniques along with the discussion of industry status, benefits of personalization, application prospects, and future focal points. Both relevant driving datasets and open issues about personalized driving assistance are discussed to facilitate future research. By creating an organized categorization of the field, we hope that this survey could not only support future research and the development of new technologies for personalized driving assistance but also facilitate the application of these techniques within the driving automation community</h2

Dynamic Data Mining: Methodology and Algorithms

Supervised data stream mining has become an important and challenging data mining task in modern organizations. The key challenges are threefold: (1) a possibly infinite number of streaming examples and time-critical analysis constraints; (2) concept drift; and (3) skewed data distributions. To address these three challenges, this thesis proposes the novel dynamic data mining (DDM) methodology by effectively applying supervised ensemble models to data stream mining. DDM can be loosely defined as categorization-organization-selection of supervised ensemble models. It is inspired by the idea that although the underlying concepts in a data stream are time-varying, their distinctions can be identified. Therefore, the models trained on the distinct concepts can be dynamically selected in order to classify incoming examples of similar concepts. First, following the general paradigm of DDM, we examine the different concept-drifting stream mining scenarios and propose corresponding effective and efficient data mining algorithms. • To address concept drift caused merely by changes of variable distributions, which we term pseudo concept drift, base models built on categorized streaming data are organized and selected in line with their corresponding variable distribution characteristics. • To address concept drift caused by changes of variable and class joint distributions, which we term true concept drift, an effective data categorization scheme is introduced. A group of working models is dynamically organized and selected for reacting to the drifting concept. Secondly, we introduce an integration stream mining framework, enabling the paradigm advocated by DDM to be widely applicable for other stream mining problems. Therefore, we are able to introduce easily six effective algorithms for mining data streams with skewed class distributions. In addition, we also introduce a new ensemble model approach for batch learning, following the same methodology. Both theoretical and empirical studies demonstrate its effectiveness. Future work would be targeted at improving the effectiveness and efficiency of the proposed algorithms. Meantime, we would explore the possibilities of using the integration framework to solve other open stream mining research problems

The Backbone Method for Ultra-High Dimensional Sparse Machine Learning

We present the backbone method, a generic framework that enables sparse and interpretable supervised machine learning methods to scale to ultra-high dimensional problems. We solve sparse regression problems with $10^7$ features in minutes and $10^8$ features in hours, as well as decision tree problems with $10^5$ features in minutes.The proposed method operates in two phases: we first determine the backbone set, consisting of potentially relevant features, by solving a number of tractable subproblems; then, we solve a reduced problem, considering only the backbone features. For the sparse regression problem, our theoretical analysis shows that, under certain assumptions and with high probability, the backbone set consists of the truly relevant features. Numerical experiments on both synthetic and real-world datasets demonstrate that our method outperforms or competes with state-of-the-art methods in ultra-high dimensional problems, and competes with optimal solutions in problems where exact methods scale, both in terms of recovering the truly relevant features and in its out-of-sample predictive performance.Comment: First submission to Machine Learning: 06/2020. Revised: 10/202