90 research outputs found
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
-norm of the coefficient , forward stage-wise is optimal per unit
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
An update on statistical boosting in biomedicine
Statistical boosting algorithms have triggered a lot of research during the
last decade. They combine a powerful machine-learning approach with classical
statistical modelling, offering various practical advantages like automated
variable selection and implicit regularization of effect estimates. They are
extremely flexible, as the underlying base-learners (regression functions
defining the type of effect for the explanatory variables) can be combined with
any kind of loss function (target function to be optimized, defining the type
of regression setting). In this review article, we highlight the most recent
methodological developments on statistical boosting regarding variable
selection, functional regression and advanced time-to-event modelling.
Additionally, we provide a short overview on relevant applications of
statistical boosting in biomedicine
Exploiting Universum data in AdaBoost using gradient descent
Recently, Universum data that does not belong to any class of the training data, has been applied for training better classifiers. In this paper, we address a novel boosting algorithm called UAdaBoost that can improve the classification performance of AdaBoost with Universum data. UAdaBoost chooses a function by minimizing the loss for labeled data and Universum data. The cost function is minimized by a greedy, stagewise, functional gradient procedure. Each training stage of UAdaBoost is fast and efficient. The standard AdaBoost weights labeled samples during training iterations while UAdaBoost gives an explicit weighting scheme for Universum samples as well. In addition, this paper describes the practical conditions for the effectiveness of Universum learning. These conditions are based on the analysis of the distribution of ensemble predictions over training samples. Experiments on handwritten digits classification and gender classification problems are presented. As exhibited by our experimental results, the proposed method can obtain superior performances over the standard AdaBoost by selecting proper Universum data. © 2014 Elsevier B.V
Advanced Statistical Methods for Atomic-Level Quantification of Multi-Component Alloys
This thesis comprises a collection of papers whose common theme is data analysis of high entropy alloys. The experimental technique used to view these alloys at the nano-scale produces a dataset that, while comprised of approximately 10^7 atoms, is corrupted by observational noise and sparsity. Our goal is to developstatistical methods to quantify the atomic structure of these materials. Understanding the atomic structure of these materials involves three parts: 1. Determining the crystal structure of the material 2. Finding the optimal transformation onto a reference structure 3. Finding the optimal matching between structures and the lattice constantFrom identifying these elements, we may map a noisy and sparse representation of an HEA onto its reference structure and determine the probabilities of different elemental types that are immediately adjacent, i.e., first neighbors, or are one-level removed and are second neighbors. Having these elemental descriptors of a material, researchers may then develop interaction potentials for molecular dynamics simulations, and make accurate predictions about these novel metallic alloys
Optimization by gradient boosting
Gradient boosting is a state-of-the-art prediction technique that
sequentially produces a model in the form of linear combinations of simple
predictors---typically decision trees---by solving an infinite-dimensional
convex optimization problem. We provide in the present paper a thorough
analysis of two widespread versions of gradient boosting, and introduce a
general framework for studying these algorithms from the point of view of
functional optimization. We prove their convergence as the number of iterations
tends to infinity and highlight the importance of having a strongly convex risk
functional to minimize. We also present a reasonable statistical context
ensuring consistency properties of the boosting predictors as the sample size
grows. In our approach, the optimization procedures are run forever (that is,
without resorting to an early stopping strategy), and statistical
regularization is basically achieved via an appropriate penalization of
the loss and strong convexity arguments
Overview of AdaBoost : Reconciling its views to better understand its dynamics
Boosting methods have been introduced in the late 1980's. They were born
following the theoritical aspect of PAC learning. The main idea of boosting
methods is to combine weak learners to obtain a strong learner. The weak
learners are obtained iteratively by an heuristic which tries to correct the
mistakes of the previous weak learner. In 1995, Freund and Schapire [18]
introduced AdaBoost, a boosting algorithm that is still widely used today.
Since then, many views of the algorithm have been proposed to properly tame its
dynamics. In this paper, we will try to cover all the views that one can have
on AdaBoost. We will start with the original view of Freund and Schapire before
covering the different views and unify them with the same formalism. We hope
this paper will help the non-expert reader to better understand the dynamics of
AdaBoost and how the different views are equivalent and related to each other
Ensemble deep learning: A review
Ensemble learning combines several individual models to obtain better
generalization performance. Currently, deep learning models with multilayer
processing architecture is showing better performance as compared to the
shallow or traditional classification models. Deep ensemble learning models
combine the advantages of both the deep learning models as well as the ensemble
learning such that the final model has better generalization performance. This
paper reviews the state-of-art deep ensemble models and hence serves as an
extensive summary for the researchers. The ensemble models are broadly
categorised into ensemble models like bagging, boosting and stacking, negative
correlation based deep ensemble models, explicit/implicit ensembles,
homogeneous /heterogeneous ensemble, decision fusion strategies, unsupervised,
semi-supervised, reinforcement learning and online/incremental, multilabel
based deep ensemble models. Application of deep ensemble models in different
domains is also briefly discussed. Finally, we conclude this paper with some
future recommendations and research directions
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